diff options
Diffstat (limited to 'thirdparty')
| -rw-r--r-- | thirdparty/README.md | 9 | ||||
| -rw-r--r-- | thirdparty/misc/patches/polypartition-godot-types.patch | 819 | ||||
| -rw-r--r-- | thirdparty/misc/polypartition.cpp | 1849 | ||||
| -rw-r--r-- | thirdparty/misc/polypartition.h | 378 | ||||
| -rw-r--r-- | thirdparty/misc/triangulator.cpp | 1550 | ||||
| -rw-r--r-- | thirdparty/misc/triangulator.h | 306 |
6 files changed, 3051 insertions, 1860 deletions
diff --git a/thirdparty/README.md b/thirdparty/README.md index 6df303015b..3803e87fea 100644 --- a/thirdparty/README.md +++ b/thirdparty/README.md @@ -424,6 +424,11 @@ Collection of single-file libraries used in Godot components. * Upstream: http://www.pcg-random.org * Version: minimal C implementation, http://www.pcg-random.org/download.html * License: Apache 2.0 +- `polypartition.{cpp,h}` + * Upstream: https://github.com/ivanfratric/polypartition (`src/polypartition.{cpp,h}`) + * Version: git (7bdffb428b2b19ad1c43aa44c714dcc104177e84, 2021) + * Modifications: Change from STL to Godot types (see provided patch). + * License: MIT - `r128.h` * Upstream: https://github.com/fahickman/r128 * Version: 1.4.4 (cf2e88fc3e7d7dfe99189686f914874cd0bda15e, 2020) @@ -441,10 +446,6 @@ Collection of single-file libraries used in Godot components. * Upstream: https://github.com/nothings/stb * Version: 1.20 (314d0a6f9af5af27e585336eecea333e95c5a2d8, 2020) * License: Public Domain or Unlicense or MIT -- `triangulator.{cpp,h}` - * Upstream: https://github.com/ivanfratric/polypartition (`src/polypartition.cpp`) - * Version: TBD, class was renamed - * License: MIT - `yuv2rgb.h` * Upstream: http://wss.co.uk/pinknoise/yuv2rgb/ (to check) * Version: ? diff --git a/thirdparty/misc/patches/polypartition-godot-types.patch b/thirdparty/misc/patches/polypartition-godot-types.patch new file mode 100644 index 0000000000..59fdb2707c --- /dev/null +++ b/thirdparty/misc/patches/polypartition-godot-types.patch @@ -0,0 +1,819 @@ +diff --git a/thirdparty/misc/polypartition.cpp b/thirdparty/misc/polypartition.cpp +index 3a8a6efa8319..4f1b6dcb21d8 100644 +--- a/thirdparty/misc/polypartition.cpp ++++ b/thirdparty/misc/polypartition.cpp +@@ -23,10 +23,7 @@ + + #include "polypartition.h" + +-#include <math.h> +-#include <string.h> + #include <algorithm> +-#include <vector> + + TPPLPoly::TPPLPoly() { + hole = false; +@@ -186,7 +183,7 @@ int TPPLPartition::Intersects(TPPLPoint &p11, TPPLPoint &p12, TPPLPoint &p21, TP + // Removes holes from inpolys by merging them with non-holes. + int TPPLPartition::RemoveHoles(TPPLPolyList *inpolys, TPPLPolyList *outpolys) { + TPPLPolyList polys; +- TPPLPolyList::iterator holeiter, polyiter, iter, iter2; ++ TPPLPolyList::Element *holeiter, *polyiter, *iter, *iter2; + long i, i2, holepointindex, polypointindex; + TPPLPoint holepoint, polypoint, bestpolypoint; + TPPLPoint linep1, linep2; +@@ -198,15 +195,15 @@ int TPPLPartition::RemoveHoles(TPPLPolyList *inpolys, TPPLPolyList *outpolys) { + + // Check for the trivial case of no holes. + hasholes = false; +- for (iter = inpolys->begin(); iter != inpolys->end(); iter++) { +- if (iter->IsHole()) { ++ for (iter = inpolys->front(); iter; iter = iter->next()) { ++ if (iter->get().IsHole()) { + hasholes = true; + break; + } + } + if (!hasholes) { +- for (iter = inpolys->begin(); iter != inpolys->end(); iter++) { +- outpolys->push_back(*iter); ++ for (iter = inpolys->front(); iter; iter = iter->next()) { ++ outpolys->push_back(iter->get()); + } + return 1; + } +@@ -216,8 +213,8 @@ int TPPLPartition::RemoveHoles(TPPLPolyList *inpolys, TPPLPolyList *outpolys) { + while (1) { + // Find the hole point with the largest x. + hasholes = false; +- for (iter = polys.begin(); iter != polys.end(); iter++) { +- if (!iter->IsHole()) { ++ for (iter = polys.front(); iter; iter = iter->next()) { ++ if (!iter->get().IsHole()) { + continue; + } + +@@ -227,8 +224,8 @@ int TPPLPartition::RemoveHoles(TPPLPolyList *inpolys, TPPLPolyList *outpolys) { + holepointindex = 0; + } + +- for (i = 0; i < iter->GetNumPoints(); i++) { +- if (iter->GetPoint(i).x > holeiter->GetPoint(holepointindex).x) { ++ for (i = 0; i < iter->get().GetNumPoints(); i++) { ++ if (iter->get().GetPoint(i).x > holeiter->get().GetPoint(holepointindex).x) { + holeiter = iter; + holepointindex = i; + } +@@ -237,24 +234,24 @@ int TPPLPartition::RemoveHoles(TPPLPolyList *inpolys, TPPLPolyList *outpolys) { + if (!hasholes) { + break; + } +- holepoint = holeiter->GetPoint(holepointindex); ++ holepoint = holeiter->get().GetPoint(holepointindex); + + pointfound = false; +- for (iter = polys.begin(); iter != polys.end(); iter++) { +- if (iter->IsHole()) { ++ for (iter = polys.front(); iter; iter = iter->next()) { ++ if (iter->get().IsHole()) { + continue; + } +- for (i = 0; i < iter->GetNumPoints(); i++) { +- if (iter->GetPoint(i).x <= holepoint.x) { ++ for (i = 0; i < iter->get().GetNumPoints(); i++) { ++ if (iter->get().GetPoint(i).x <= holepoint.x) { + continue; + } +- if (!InCone(iter->GetPoint((i + iter->GetNumPoints() - 1) % (iter->GetNumPoints())), +- iter->GetPoint(i), +- iter->GetPoint((i + 1) % (iter->GetNumPoints())), ++ if (!InCone(iter->get().GetPoint((i + iter->get().GetNumPoints() - 1) % (iter->get().GetNumPoints())), ++ iter->get().GetPoint(i), ++ iter->get().GetPoint((i + 1) % (iter->get().GetNumPoints())), + holepoint)) { + continue; + } +- polypoint = iter->GetPoint(i); ++ polypoint = iter->get().GetPoint(i); + if (pointfound) { + v1 = Normalize(polypoint - holepoint); + v2 = Normalize(bestpolypoint - holepoint); +@@ -263,13 +260,13 @@ int TPPLPartition::RemoveHoles(TPPLPolyList *inpolys, TPPLPolyList *outpolys) { + } + } + pointvisible = true; +- for (iter2 = polys.begin(); iter2 != polys.end(); iter2++) { +- if (iter2->IsHole()) { ++ for (iter2 = polys.front(); iter2; iter2->next()) { ++ if (iter2->get().IsHole()) { + continue; + } +- for (i2 = 0; i2 < iter2->GetNumPoints(); i2++) { +- linep1 = iter2->GetPoint(i2); +- linep2 = iter2->GetPoint((i2 + 1) % (iter2->GetNumPoints())); ++ for (i2 = 0; i2 < iter2->get().GetNumPoints(); i2++) { ++ linep1 = iter2->get().GetPoint(i2); ++ linep2 = iter2->get().GetPoint((i2 + 1) % (iter2->get().GetNumPoints())); + if (Intersects(holepoint, polypoint, linep1, linep2)) { + pointvisible = false; + break; +@@ -292,18 +289,18 @@ int TPPLPartition::RemoveHoles(TPPLPolyList *inpolys, TPPLPolyList *outpolys) { + return 0; + } + +- newpoly.Init(holeiter->GetNumPoints() + polyiter->GetNumPoints() + 2); ++ newpoly.Init(holeiter->get().GetNumPoints() + polyiter->get().GetNumPoints() + 2); + i2 = 0; + for (i = 0; i <= polypointindex; i++) { +- newpoly[i2] = polyiter->GetPoint(i); ++ newpoly[i2] = polyiter->get().GetPoint(i); + i2++; + } +- for (i = 0; i <= holeiter->GetNumPoints(); i++) { +- newpoly[i2] = holeiter->GetPoint((i + holepointindex) % holeiter->GetNumPoints()); ++ for (i = 0; i <= holeiter->get().GetNumPoints(); i++) { ++ newpoly[i2] = holeiter->get().GetPoint((i + holepointindex) % holeiter->get().GetNumPoints()); + i2++; + } +- for (i = polypointindex; i < polyiter->GetNumPoints(); i++) { +- newpoly[i2] = polyiter->GetPoint(i); ++ for (i = polypointindex; i < polyiter->get().GetNumPoints(); i++) { ++ newpoly[i2] = polyiter->get().GetPoint(i); + i2++; + } + +@@ -312,8 +309,8 @@ int TPPLPartition::RemoveHoles(TPPLPolyList *inpolys, TPPLPolyList *outpolys) { + polys.push_back(newpoly); + } + +- for (iter = polys.begin(); iter != polys.end(); iter++) { +- outpolys->push_back(*iter); ++ for (iter = polys.front(); iter; iter = iter->next()) { ++ outpolys->push_back(iter->get()); + } + + return 1; +@@ -524,13 +521,13 @@ int TPPLPartition::Triangulate_EC(TPPLPoly *poly, TPPLPolyList *triangles) { + + int TPPLPartition::Triangulate_EC(TPPLPolyList *inpolys, TPPLPolyList *triangles) { + TPPLPolyList outpolys; +- TPPLPolyList::iterator iter; ++ TPPLPolyList::Element *iter; + + if (!RemoveHoles(inpolys, &outpolys)) { + return 0; + } +- for (iter = outpolys.begin(); iter != outpolys.end(); iter++) { +- if (!Triangulate_EC(&(*iter), triangles)) { ++ for (iter = outpolys.front(); iter; iter = iter->next()) { ++ if (!Triangulate_EC(&(iter->get()), triangles)) { + return 0; + } + } +@@ -543,7 +540,7 @@ int TPPLPartition::ConvexPartition_HM(TPPLPoly *poly, TPPLPolyList *parts) { + } + + TPPLPolyList triangles; +- TPPLPolyList::iterator iter1, iter2; ++ TPPLPolyList::Element *iter1, *iter2; + TPPLPoly *poly1 = NULL, *poly2 = NULL; + TPPLPoly newpoly; + TPPLPoint d1, d2, p1, p2, p3; +@@ -578,19 +575,19 @@ int TPPLPartition::ConvexPartition_HM(TPPLPoly *poly, TPPLPolyList *parts) { + return 0; + } + +- for (iter1 = triangles.begin(); iter1 != triangles.end(); iter1++) { +- poly1 = &(*iter1); ++ for (iter1 = triangles.front(); iter1; iter1 = iter1->next()) { ++ poly1 = &(iter1->get()); + for (i11 = 0; i11 < poly1->GetNumPoints(); i11++) { + d1 = poly1->GetPoint(i11); + i12 = (i11 + 1) % (poly1->GetNumPoints()); + d2 = poly1->GetPoint(i12); + + isdiagonal = false; +- for (iter2 = iter1; iter2 != triangles.end(); iter2++) { ++ for (iter2 = iter1; iter2; iter2 = iter2->next()) { + if (iter1 == iter2) { + continue; + } +- poly2 = &(*iter2); ++ poly2 = &(iter2->get()); + + for (i21 = 0; i21 < poly2->GetNumPoints(); i21++) { + if ((d2.x != poly2->GetPoint(i21).x) || (d2.y != poly2->GetPoint(i21).y)) { +@@ -660,16 +657,16 @@ int TPPLPartition::ConvexPartition_HM(TPPLPoly *poly, TPPLPolyList *parts) { + } + + triangles.erase(iter2); +- *iter1 = newpoly; +- poly1 = &(*iter1); ++ iter1->get() = newpoly; ++ poly1 = &(iter1->get()); + i11 = -1; + + continue; + } + } + +- for (iter1 = triangles.begin(); iter1 != triangles.end(); iter1++) { +- parts->push_back(*iter1); ++ for (iter1 = triangles.front(); iter1; iter1 = iter1->next()) { ++ parts->push_back(iter1->get()); + } + + return 1; +@@ -677,13 +674,13 @@ int TPPLPartition::ConvexPartition_HM(TPPLPoly *poly, TPPLPolyList *parts) { + + int TPPLPartition::ConvexPartition_HM(TPPLPolyList *inpolys, TPPLPolyList *parts) { + TPPLPolyList outpolys; +- TPPLPolyList::iterator iter; ++ TPPLPolyList::Element *iter; + + if (!RemoveHoles(inpolys, &outpolys)) { + return 0; + } +- for (iter = outpolys.begin(); iter != outpolys.end(); iter++) { +- if (!ConvexPartition_HM(&(*iter), parts)) { ++ for (iter = outpolys.front(); iter; iter = iter->next()) { ++ if (!ConvexPartition_HM(&(iter->get()), parts)) { + return 0; + } + } +@@ -824,8 +821,8 @@ int TPPLPartition::Triangulate_OPT(TPPLPoly *poly, TPPLPolyList *triangles) { + newdiagonal.index1 = 0; + newdiagonal.index2 = n - 1; + diagonals.push_back(newdiagonal); +- while (!diagonals.empty()) { +- diagonal = *(diagonals.begin()); ++ while (!diagonals.is_empty()) { ++ diagonal = diagonals.front()->get(); + diagonals.pop_front(); + bestvertex = dpstates[diagonal.index2][diagonal.index1].bestvertex; + if (bestvertex == -1) { +@@ -873,10 +870,10 @@ void TPPLPartition::UpdateState(long a, long b, long w, long i, long j, DPState2 + pairs->push_front(newdiagonal); + dpstates[a][b].weight = w; + } else { +- if ((!pairs->empty()) && (i <= pairs->begin()->index1)) { ++ if ((!pairs->is_empty()) && (i <= pairs->front()->get().index1)) { + return; + } +- while ((!pairs->empty()) && (pairs->begin()->index2 >= j)) { ++ while ((!pairs->is_empty()) && (pairs->front()->get().index2 >= j)) { + pairs->pop_front(); + } + pairs->push_front(newdiagonal); +@@ -885,7 +882,7 @@ void TPPLPartition::UpdateState(long a, long b, long w, long i, long j, DPState2 + + void TPPLPartition::TypeA(long i, long j, long k, PartitionVertex *vertices, DPState2 **dpstates) { + DiagonalList *pairs = NULL; +- DiagonalList::iterator iter, lastiter; ++ DiagonalList::Element *iter, *lastiter; + long top; + long w; + +@@ -902,23 +899,23 @@ void TPPLPartition::TypeA(long i, long j, long k, PartitionVertex *vertices, DPS + } + if (j - i > 1) { + pairs = &(dpstates[i][j].pairs); +- iter = pairs->end(); +- lastiter = pairs->end(); +- while (iter != pairs->begin()) { ++ iter = pairs->back(); ++ lastiter = pairs->back(); ++ while (iter != pairs->front()) { + iter--; +- if (!IsReflex(vertices[iter->index2].p, vertices[j].p, vertices[k].p)) { ++ if (!IsReflex(vertices[iter->get().index2].p, vertices[j].p, vertices[k].p)) { + lastiter = iter; + } else { + break; + } + } +- if (lastiter == pairs->end()) { ++ if (lastiter == pairs->back()) { + w++; + } else { +- if (IsReflex(vertices[k].p, vertices[i].p, vertices[lastiter->index1].p)) { ++ if (IsReflex(vertices[k].p, vertices[i].p, vertices[lastiter->get().index1].p)) { + w++; + } else { +- top = lastiter->index1; ++ top = lastiter->get().index1; + } + } + } +@@ -927,7 +924,7 @@ void TPPLPartition::TypeA(long i, long j, long k, PartitionVertex *vertices, DPS + + void TPPLPartition::TypeB(long i, long j, long k, PartitionVertex *vertices, DPState2 **dpstates) { + DiagonalList *pairs = NULL; +- DiagonalList::iterator iter, lastiter; ++ DiagonalList::Element *iter, *lastiter; + long top; + long w; + +@@ -946,21 +943,21 @@ void TPPLPartition::TypeB(long i, long j, long k, PartitionVertex *vertices, DPS + if (k - j > 1) { + pairs = &(dpstates[j][k].pairs); + +- iter = pairs->begin(); +- if ((!pairs->empty()) && (!IsReflex(vertices[i].p, vertices[j].p, vertices[iter->index1].p))) { ++ iter = pairs->front(); ++ if ((!pairs->is_empty()) && (!IsReflex(vertices[i].p, vertices[j].p, vertices[iter->get().index1].p))) { + lastiter = iter; +- while (iter != pairs->end()) { +- if (!IsReflex(vertices[i].p, vertices[j].p, vertices[iter->index1].p)) { ++ while (iter) { ++ if (!IsReflex(vertices[i].p, vertices[j].p, vertices[iter->get().index1].p)) { + lastiter = iter; +- iter++; ++ iter = iter->next(); + } else { + break; + } + } +- if (IsReflex(vertices[lastiter->index2].p, vertices[k].p, vertices[i].p)) { ++ if (IsReflex(vertices[lastiter->get().index2].p, vertices[k].p, vertices[i].p)) { + w++; + } else { +- top = lastiter->index2; ++ top = lastiter->get().index2; + } + } else { + w++; +@@ -981,11 +978,11 @@ int TPPLPartition::ConvexPartition_OPT(TPPLPoly *poly, TPPLPolyList *parts) { + DiagonalList diagonals, diagonals2; + Diagonal diagonal, newdiagonal; + DiagonalList *pairs = NULL, *pairs2 = NULL; +- DiagonalList::iterator iter, iter2; ++ DiagonalList::Element *iter, *iter2; + int ret; + TPPLPoly newpoly; +- std::vector<long> indices; +- std::vector<long>::iterator iiter; ++ List<long> indices; ++ List<long>::Element *iiter; + bool ijreal, jkreal; + + n = poly->GetNumPoints(); +@@ -1110,35 +1107,35 @@ int TPPLPartition::ConvexPartition_OPT(TPPLPoly *poly, TPPLPolyList *parts) { + newdiagonal.index1 = 0; + newdiagonal.index2 = n - 1; + diagonals.push_front(newdiagonal); +- while (!diagonals.empty()) { +- diagonal = *(diagonals.begin()); ++ while (!diagonals.is_empty()) { ++ diagonal = diagonals.front()->get(); + diagonals.pop_front(); + if ((diagonal.index2 - diagonal.index1) <= 1) { + continue; + } + pairs = &(dpstates[diagonal.index1][diagonal.index2].pairs); +- if (pairs->empty()) { ++ if (pairs->is_empty()) { + ret = 0; + break; + } + if (!vertices[diagonal.index1].isConvex) { +- iter = pairs->end(); ++ iter = pairs->back(); + iter--; +- j = iter->index2; ++ j = iter->get().index2; + newdiagonal.index1 = j; + newdiagonal.index2 = diagonal.index2; + diagonals.push_front(newdiagonal); + if ((j - diagonal.index1) > 1) { +- if (iter->index1 != iter->index2) { ++ if (iter->get().index1 != iter->get().index2) { + pairs2 = &(dpstates[diagonal.index1][j].pairs); + while (1) { +- if (pairs2->empty()) { ++ if (pairs2->is_empty()) { + ret = 0; + break; + } +- iter2 = pairs2->end(); ++ iter2 = pairs2->back(); + iter2--; +- if (iter->index1 != iter2->index1) { ++ if (iter->get().index1 != iter2->get().index1) { + pairs2->pop_back(); + } else { + break; +@@ -1153,21 +1150,21 @@ int TPPLPartition::ConvexPartition_OPT(TPPLPoly *poly, TPPLPolyList *parts) { + diagonals.push_front(newdiagonal); + } + } else { +- iter = pairs->begin(); +- j = iter->index1; ++ iter = pairs->front(); ++ j = iter->get().index1; + newdiagonal.index1 = diagonal.index1; + newdiagonal.index2 = j; + diagonals.push_front(newdiagonal); + if ((diagonal.index2 - j) > 1) { +- if (iter->index1 != iter->index2) { ++ if (iter->get().index1 != iter->get().index2) { + pairs2 = &(dpstates[j][diagonal.index2].pairs); + while (1) { +- if (pairs2->empty()) { ++ if (pairs2->is_empty()) { + ret = 0; + break; + } +- iter2 = pairs2->begin(); +- if (iter->index2 != iter2->index2) { ++ iter2 = pairs2->front(); ++ if (iter->get().index2 != iter2->get().index2) { + pairs2->pop_front(); + } else { + break; +@@ -1197,8 +1194,8 @@ int TPPLPartition::ConvexPartition_OPT(TPPLPoly *poly, TPPLPolyList *parts) { + newdiagonal.index1 = 0; + newdiagonal.index2 = n - 1; + diagonals.push_front(newdiagonal); +- while (!diagonals.empty()) { +- diagonal = *(diagonals.begin()); ++ while (!diagonals.is_empty()) { ++ diagonal = diagonals.front()->get(); + diagonals.pop_front(); + if ((diagonal.index2 - diagonal.index1) <= 1) { + continue; +@@ -1210,8 +1207,8 @@ int TPPLPartition::ConvexPartition_OPT(TPPLPoly *poly, TPPLPolyList *parts) { + indices.push_back(diagonal.index2); + diagonals2.push_front(diagonal); + +- while (!diagonals2.empty()) { +- diagonal = *(diagonals2.begin()); ++ while (!diagonals2.is_empty()) { ++ diagonal = diagonals2.front()->get(); + diagonals2.pop_front(); + if ((diagonal.index2 - diagonal.index1) <= 1) { + continue; +@@ -1220,16 +1217,16 @@ int TPPLPartition::ConvexPartition_OPT(TPPLPoly *poly, TPPLPolyList *parts) { + jkreal = true; + pairs = &(dpstates[diagonal.index1][diagonal.index2].pairs); + if (!vertices[diagonal.index1].isConvex) { +- iter = pairs->end(); ++ iter = pairs->back(); + iter--; +- j = iter->index2; +- if (iter->index1 != iter->index2) { ++ j = iter->get().index2; ++ if (iter->get().index1 != iter->get().index2) { + ijreal = false; + } + } else { +- iter = pairs->begin(); +- j = iter->index1; +- if (iter->index1 != iter->index2) { ++ iter = pairs->front(); ++ j = iter->get().index1; ++ if (iter->get().index1 != iter->get().index2) { + jkreal = false; + } + } +@@ -1253,11 +1250,12 @@ int TPPLPartition::ConvexPartition_OPT(TPPLPoly *poly, TPPLPolyList *parts) { + indices.push_back(j); + } + +- std::sort(indices.begin(), indices.end()); ++ //std::sort(indices.begin(), indices.end()); ++ indices.sort(); + newpoly.Init((long)indices.size()); + k = 0; +- for (iiter = indices.begin(); iiter != indices.end(); iiter++) { +- newpoly[k] = vertices[*iiter].p; ++ for (iiter = indices.front(); iiter != indices.back(); iiter = iiter->next()) { ++ newpoly[k] = vertices[iiter->get()].p; + k++; + } + parts->push_back(newpoly); +@@ -1281,7 +1279,7 @@ int TPPLPartition::ConvexPartition_OPT(TPPLPoly *poly, TPPLPolyList *parts) { + // "Computational Geometry: Algorithms and Applications" + // by Mark de Berg, Otfried Cheong, Marc van Kreveld, and Mark Overmars. + int TPPLPartition::MonotonePartition(TPPLPolyList *inpolys, TPPLPolyList *monotonePolys) { +- TPPLPolyList::iterator iter; ++ TPPLPolyList::Element *iter; + MonotoneVertex *vertices = NULL; + long i, numvertices, vindex, vindex2, newnumvertices, maxnumvertices; + long polystartindex, polyendindex; +@@ -1291,11 +1289,8 @@ int TPPLPartition::MonotonePartition(TPPLPolyList *inpolys, TPPLPolyList *monoto + bool error = false; + + numvertices = 0; +- for (iter = inpolys->begin(); iter != inpolys->end(); iter++) { +- if (!iter->Valid()) { +- return 0; +- } +- numvertices += iter->GetNumPoints(); ++ for (iter = inpolys->front(); iter; iter++) { ++ numvertices += iter->get().GetNumPoints(); + } + + maxnumvertices = numvertices * 3; +@@ -1303,8 +1298,8 @@ int TPPLPartition::MonotonePartition(TPPLPolyList *inpolys, TPPLPolyList *monoto + newnumvertices = numvertices; + + polystartindex = 0; +- for (iter = inpolys->begin(); iter != inpolys->end(); iter++) { +- poly = &(*iter); ++ for (iter = inpolys->front(); iter; iter++) { ++ poly = &(iter->get()); + polyendindex = polystartindex + poly->GetNumPoints() - 1; + for (i = 0; i < poly->GetNumPoints(); i++) { + vertices[i + polystartindex].p = poly->GetPoint(i); +@@ -1360,14 +1355,14 @@ int TPPLPartition::MonotonePartition(TPPLPolyList *inpolys, TPPLPolyList *monoto + // Note that while set doesn't actually have to be implemented as + // a tree, complexity requirements for operations are the same as + // for the balanced binary search tree. +- std::set<ScanLineEdge> edgeTree; ++ Set<ScanLineEdge> edgeTree; + // Store iterators to the edge tree elements. + // This makes deleting existing edges much faster. +- std::set<ScanLineEdge>::iterator *edgeTreeIterators, edgeIter; +- edgeTreeIterators = new std::set<ScanLineEdge>::iterator[maxnumvertices]; +- std::pair<std::set<ScanLineEdge>::iterator, bool> edgeTreeRet; ++ Set<ScanLineEdge>::Element **edgeTreeIterators, *edgeIter; ++ edgeTreeIterators = new Set<ScanLineEdge>::Element *[maxnumvertices]; ++ //Pair<Set<ScanLineEdge>::iterator, bool> edgeTreeRet; + for (i = 0; i < numvertices; i++) { +- edgeTreeIterators[i] = edgeTree.end(); ++ edgeTreeIterators[i] = nullptr; + } + + // For each vertex. +@@ -1387,13 +1382,14 @@ int TPPLPartition::MonotonePartition(TPPLPolyList *inpolys, TPPLPolyList *monoto + newedge.p1 = v->p; + newedge.p2 = vertices[v->next].p; + newedge.index = vindex; +- edgeTreeRet = edgeTree.insert(newedge); +- edgeTreeIterators[vindex] = edgeTreeRet.first; ++ //edgeTreeRet = edgeTree.insert(newedge); ++ //edgeTreeIterators[vindex] = edgeTreeRet.first; ++ edgeTreeIterators[vindex] = edgeTree.insert(newedge); + helpers[vindex] = vindex; + break; + + case TPPL_VERTEXTYPE_END: +- if (edgeTreeIterators[v->previous] == edgeTree.end()) { ++ if (edgeTreeIterators[v->previous] == edgeTree.back()) { + error = true; + break; + } +@@ -1412,29 +1408,30 @@ int TPPLPartition::MonotonePartition(TPPLPolyList *inpolys, TPPLPolyList *monoto + newedge.p1 = v->p; + newedge.p2 = v->p; + edgeIter = edgeTree.lower_bound(newedge); +- if (edgeIter == edgeTree.begin()) { ++ if (edgeIter == edgeTree.front()) { + error = true; + break; + } + edgeIter--; + // Insert the diagonal connecting vi to helper(e_j) in D. +- AddDiagonal(vertices, &newnumvertices, vindex, helpers[edgeIter->index], ++ AddDiagonal(vertices, &newnumvertices, vindex, helpers[edgeIter->get().index], + vertextypes, edgeTreeIterators, &edgeTree, helpers); + vindex2 = newnumvertices - 2; + v2 = &(vertices[vindex2]); + // helper(e_j) in v_i. +- helpers[edgeIter->index] = vindex; ++ helpers[edgeIter->get().index] = vindex; + // Insert e_i in T and set helper(e_i) to v_i. + newedge.p1 = v2->p; + newedge.p2 = vertices[v2->next].p; + newedge.index = vindex2; +- edgeTreeRet = edgeTree.insert(newedge); +- edgeTreeIterators[vindex2] = edgeTreeRet.first; ++ //edgeTreeRet = edgeTree.insert(newedge); ++ //edgeTreeIterators[vindex2] = edgeTreeRet.first; ++ edgeTreeIterators[vindex2] = edgeTree.insert(newedge); + helpers[vindex2] = vindex2; + break; + + case TPPL_VERTEXTYPE_MERGE: +- if (edgeTreeIterators[v->previous] == edgeTree.end()) { ++ if (edgeTreeIterators[v->previous] == edgeTree.back()) { + error = true; + break; + } +@@ -1452,25 +1449,25 @@ int TPPLPartition::MonotonePartition(TPPLPolyList *inpolys, TPPLPolyList *monoto + newedge.p1 = v->p; + newedge.p2 = v->p; + edgeIter = edgeTree.lower_bound(newedge); +- if (edgeIter == edgeTree.begin()) { ++ if (edgeIter == edgeTree.front()) { + error = true; + break; + } + edgeIter--; + // If helper(e_j) is a merge vertex. +- if (vertextypes[helpers[edgeIter->index]] == TPPL_VERTEXTYPE_MERGE) { ++ if (vertextypes[helpers[edgeIter->get().index]] == TPPL_VERTEXTYPE_MERGE) { + // Insert the diagonal connecting v_i to helper(e_j) in D. +- AddDiagonal(vertices, &newnumvertices, vindex2, helpers[edgeIter->index], ++ AddDiagonal(vertices, &newnumvertices, vindex2, helpers[edgeIter->get().index], + vertextypes, edgeTreeIterators, &edgeTree, helpers); + } + // helper(e_j) <- v_i +- helpers[edgeIter->index] = vindex2; ++ helpers[edgeIter->get().index] = vindex2; + break; + + case TPPL_VERTEXTYPE_REGULAR: + // If the interior of P lies to the right of v_i. + if (Below(v->p, vertices[v->previous].p)) { +- if (edgeTreeIterators[v->previous] == edgeTree.end()) { ++ if (edgeTreeIterators[v->previous] == edgeTree.back()) { + error = true; + break; + } +@@ -1488,27 +1485,28 @@ int TPPLPartition::MonotonePartition(TPPLPolyList *inpolys, TPPLPolyList *monoto + newedge.p1 = v2->p; + newedge.p2 = vertices[v2->next].p; + newedge.index = vindex2; +- edgeTreeRet = edgeTree.insert(newedge); +- edgeTreeIterators[vindex2] = edgeTreeRet.first; ++ //edgeTreeRet = edgeTree.insert(newedge); ++ //edgeTreeIterators[vindex2] = edgeTreeRet.first; ++ edgeTreeIterators[vindex2] = edgeTree.insert(newedge); + helpers[vindex2] = vindex; + } else { + // Search in T to find the edge e_j directly left of v_i. + newedge.p1 = v->p; + newedge.p2 = v->p; + edgeIter = edgeTree.lower_bound(newedge); +- if (edgeIter == edgeTree.begin()) { ++ if (edgeIter == edgeTree.front()) { + error = true; + break; + } +- edgeIter--; ++ edgeIter = edgeIter->prev(); + // If helper(e_j) is a merge vertex. +- if (vertextypes[helpers[edgeIter->index]] == TPPL_VERTEXTYPE_MERGE) { ++ if (vertextypes[helpers[edgeIter->get().index]] == TPPL_VERTEXTYPE_MERGE) { + // Insert the diagonal connecting v_i to helper(e_j) in D. +- AddDiagonal(vertices, &newnumvertices, vindex, helpers[edgeIter->index], ++ AddDiagonal(vertices, &newnumvertices, vindex, helpers[edgeIter->get().index], + vertextypes, edgeTreeIterators, &edgeTree, helpers); + } + // helper(e_j) <- v_i. +- helpers[edgeIter->index] = vindex; ++ helpers[edgeIter->get().index] = vindex; + } + break; + } +@@ -1569,8 +1567,8 @@ int TPPLPartition::MonotonePartition(TPPLPolyList *inpolys, TPPLPolyList *monoto + + // Adds a diagonal to the doubly-connected list of vertices. + void TPPLPartition::AddDiagonal(MonotoneVertex *vertices, long *numvertices, long index1, long index2, +- TPPLVertexType *vertextypes, std::set<ScanLineEdge>::iterator *edgeTreeIterators, +- std::set<ScanLineEdge> *edgeTree, long *helpers) { ++ TPPLVertexType *vertextypes, Set<ScanLineEdge>::Element **edgeTreeIterators, ++ Set<ScanLineEdge> *edgeTree, long *helpers) { + long newindex1, newindex2; + + newindex1 = *numvertices; +@@ -1597,14 +1595,14 @@ void TPPLPartition::AddDiagonal(MonotoneVertex *vertices, long *numvertices, lon + vertextypes[newindex1] = vertextypes[index1]; + edgeTreeIterators[newindex1] = edgeTreeIterators[index1]; + helpers[newindex1] = helpers[index1]; +- if (edgeTreeIterators[newindex1] != edgeTree->end()) { +- edgeTreeIterators[newindex1]->index = newindex1; ++ if (edgeTreeIterators[newindex1] != edgeTree->back()) { ++ edgeTreeIterators[newindex1]->get().index = newindex1; + } + vertextypes[newindex2] = vertextypes[index2]; + edgeTreeIterators[newindex2] = edgeTreeIterators[index2]; + helpers[newindex2] = helpers[index2]; +- if (edgeTreeIterators[newindex2] != edgeTree->end()) { +- edgeTreeIterators[newindex2]->index = newindex2; ++ if (edgeTreeIterators[newindex2] != edgeTree->back()) { ++ edgeTreeIterators[newindex2]->get().index = newindex2; + } + } + +@@ -1830,13 +1828,13 @@ int TPPLPartition::TriangulateMonotone(TPPLPoly *inPoly, TPPLPolyList *triangles + + int TPPLPartition::Triangulate_MONO(TPPLPolyList *inpolys, TPPLPolyList *triangles) { + TPPLPolyList monotone; +- TPPLPolyList::iterator iter; ++ TPPLPolyList::Element *iter; + + if (!MonotonePartition(inpolys, &monotone)) { + return 0; + } +- for (iter = monotone.begin(); iter != monotone.end(); iter++) { +- if (!TriangulateMonotone(&(*iter), triangles)) { ++ for (iter = monotone.front(); iter; iter = iter->next()) { ++ if (!TriangulateMonotone(&(iter->get()), triangles)) { + return 0; + } + } +diff --git a/thirdparty/misc/polypartition.h b/thirdparty/misc/polypartition.h +index f163f5d2173f..b2d905a3ef76 100644 +--- a/thirdparty/misc/polypartition.h ++++ b/thirdparty/misc/polypartition.h +@@ -24,8 +24,9 @@ + #ifndef POLYPARTITION_H + #define POLYPARTITION_H + +-#include <list> +-#include <set> ++#include "core/math/vector2.h" ++#include "core/templates/list.h" ++#include "core/templates/set.h" + + typedef double tppl_float; + +@@ -44,49 +45,7 @@ enum TPPLVertexType { + }; + + // 2D point structure. +-struct TPPLPoint { +- tppl_float x; +- tppl_float y; +- // User-specified vertex identifier. Note that this isn't used internally +- // by the library, but will be faithfully copied around. +- int id; +- +- TPPLPoint operator+(const TPPLPoint &p) const { +- TPPLPoint r; +- r.x = x + p.x; +- r.y = y + p.y; +- return r; +- } +- +- TPPLPoint operator-(const TPPLPoint &p) const { +- TPPLPoint r; +- r.x = x - p.x; +- r.y = y - p.y; +- return r; +- } +- +- TPPLPoint operator*(const tppl_float f) const { +- TPPLPoint r; +- r.x = x * f; +- r.y = y * f; +- return r; +- } +- +- TPPLPoint operator/(const tppl_float f) const { +- TPPLPoint r; +- r.x = x / f; +- r.y = y / f; +- return r; +- } +- +- bool operator==(const TPPLPoint &p) const { +- return ((x == p.x) && (y == p.y)); +- } +- +- bool operator!=(const TPPLPoint &p) const { +- return !((x == p.x) && (y == p.y)); +- } +-}; ++typedef Vector2 TPPLPoint; + + // Polygon implemented as an array of points with a "hole" flag. + class TPPLPoly { +@@ -168,9 +127,9 @@ class TPPLPoly { + }; + + #ifdef TPPL_ALLOCATOR +-typedef std::list<TPPLPoly, TPPL_ALLOCATOR(TPPLPoly)> TPPLPolyList; ++typedef List<TPPLPoly, TPPL_ALLOCATOR(TPPLPoly)> TPPLPolyList; + #else +-typedef std::list<TPPLPoly> TPPLPolyList; ++typedef List<TPPLPoly> TPPLPolyList; + #endif + + class TPPLPartition { +@@ -209,9 +168,9 @@ public: + }; + + #ifdef TPPL_ALLOCATOR +- typedef std::list<Diagonal, TPPL_ALLOCATOR(Diagonal)> DiagonalList; ++ typedef List<Diagonal, TPPL_ALLOCATOR(Diagonal)> DiagonalList; + #else +- typedef std::list<Diagonal> DiagonalList; ++ typedef List<Diagonal> DiagonalList; + #endif + + // Dynamic programming state for minimum-weight triangulation. +@@ -265,8 +224,8 @@ public: + // Helper functions for MonotonePartition. + bool Below(TPPLPoint &p1, TPPLPoint &p2); + void AddDiagonal(MonotoneVertex *vertices, long *numvertices, long index1, long index2, +- TPPLVertexType *vertextypes, std::set<ScanLineEdge>::iterator *edgeTreeIterators, +- std::set<ScanLineEdge> *edgeTree, long *helpers); ++ TPPLVertexType *vertextypes, Set<ScanLineEdge>::Element **edgeTreeIterators, ++ Set<ScanLineEdge> *edgeTree, long *helpers); + + // Triangulates a monotone polygon, used in Triangulate_MONO. + int TriangulateMonotone(TPPLPoly *inPoly, TPPLPolyList *triangles); diff --git a/thirdparty/misc/polypartition.cpp b/thirdparty/misc/polypartition.cpp new file mode 100644 index 0000000000..4f1b6dcb21 --- /dev/null +++ b/thirdparty/misc/polypartition.cpp @@ -0,0 +1,1849 @@ +/*************************************************************************/ +/* Copyright (c) 2011-2021 Ivan Fratric and contributors. */ +/* */ +/* Permission is hereby granted, free of charge, to any person obtaining */ +/* a copy of this software and associated documentation files (the */ +/* "Software"), to deal in the Software without restriction, including */ +/* without limitation the rights to use, copy, modify, merge, publish, */ +/* distribute, sublicense, and/or sell copies of the Software, and to */ +/* permit persons to whom the Software is furnished to do so, subject to */ +/* the following conditions: */ +/* */ +/* The above copyright notice and this permission notice shall be */ +/* included in all copies or substantial portions of the Software. */ +/* */ +/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */ +/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */ +/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/ +/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */ +/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */ +/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */ +/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */ +/*************************************************************************/ + +#include "polypartition.h" + +#include <algorithm> + +TPPLPoly::TPPLPoly() { + hole = false; + numpoints = 0; + points = NULL; +} + +TPPLPoly::~TPPLPoly() { + if (points) { + delete[] points; + } +} + +void TPPLPoly::Clear() { + if (points) { + delete[] points; + } + hole = false; + numpoints = 0; + points = NULL; +} + +void TPPLPoly::Init(long numpoints) { + Clear(); + this->numpoints = numpoints; + points = new TPPLPoint[numpoints]; +} + +void TPPLPoly::Triangle(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3) { + Init(3); + points[0] = p1; + points[1] = p2; + points[2] = p3; +} + +TPPLPoly::TPPLPoly(const TPPLPoly &src) : + TPPLPoly() { + hole = src.hole; + numpoints = src.numpoints; + + if (numpoints > 0) { + points = new TPPLPoint[numpoints]; + memcpy(points, src.points, numpoints * sizeof(TPPLPoint)); + } +} + +TPPLPoly &TPPLPoly::operator=(const TPPLPoly &src) { + Clear(); + hole = src.hole; + numpoints = src.numpoints; + + if (numpoints > 0) { + points = new TPPLPoint[numpoints]; + memcpy(points, src.points, numpoints * sizeof(TPPLPoint)); + } + + return *this; +} + +TPPLOrientation TPPLPoly::GetOrientation() const { + long i1, i2; + tppl_float area = 0; + for (i1 = 0; i1 < numpoints; i1++) { + i2 = i1 + 1; + if (i2 == numpoints) { + i2 = 0; + } + area += points[i1].x * points[i2].y - points[i1].y * points[i2].x; + } + if (area > 0) { + return TPPL_ORIENTATION_CCW; + } + if (area < 0) { + return TPPL_ORIENTATION_CW; + } + return TPPL_ORIENTATION_NONE; +} + +void TPPLPoly::SetOrientation(TPPLOrientation orientation) { + TPPLOrientation polyorientation = GetOrientation(); + if (polyorientation != TPPL_ORIENTATION_NONE && polyorientation != orientation) { + Invert(); + } +} + +void TPPLPoly::Invert() { + std::reverse(points, points + numpoints); +} + +TPPLPartition::PartitionVertex::PartitionVertex() : + previous(NULL), next(NULL) { +} + +TPPLPoint TPPLPartition::Normalize(const TPPLPoint &p) { + TPPLPoint r; + tppl_float n = sqrt(p.x * p.x + p.y * p.y); + if (n != 0) { + r = p / n; + } else { + r.x = 0; + r.y = 0; + } + return r; +} + +tppl_float TPPLPartition::Distance(const TPPLPoint &p1, const TPPLPoint &p2) { + tppl_float dx, dy; + dx = p2.x - p1.x; + dy = p2.y - p1.y; + return (sqrt(dx * dx + dy * dy)); +} + +// Checks if two lines intersect. +int TPPLPartition::Intersects(TPPLPoint &p11, TPPLPoint &p12, TPPLPoint &p21, TPPLPoint &p22) { + if ((p11.x == p21.x) && (p11.y == p21.y)) { + return 0; + } + if ((p11.x == p22.x) && (p11.y == p22.y)) { + return 0; + } + if ((p12.x == p21.x) && (p12.y == p21.y)) { + return 0; + } + if ((p12.x == p22.x) && (p12.y == p22.y)) { + return 0; + } + + TPPLPoint v1ort, v2ort, v; + tppl_float dot11, dot12, dot21, dot22; + + v1ort.x = p12.y - p11.y; + v1ort.y = p11.x - p12.x; + + v2ort.x = p22.y - p21.y; + v2ort.y = p21.x - p22.x; + + v = p21 - p11; + dot21 = v.x * v1ort.x + v.y * v1ort.y; + v = p22 - p11; + dot22 = v.x * v1ort.x + v.y * v1ort.y; + + v = p11 - p21; + dot11 = v.x * v2ort.x + v.y * v2ort.y; + v = p12 - p21; + dot12 = v.x * v2ort.x + v.y * v2ort.y; + + if (dot11 * dot12 > 0) { + return 0; + } + if (dot21 * dot22 > 0) { + return 0; + } + + return 1; +} + +// Removes holes from inpolys by merging them with non-holes. +int TPPLPartition::RemoveHoles(TPPLPolyList *inpolys, TPPLPolyList *outpolys) { + TPPLPolyList polys; + TPPLPolyList::Element *holeiter, *polyiter, *iter, *iter2; + long i, i2, holepointindex, polypointindex; + TPPLPoint holepoint, polypoint, bestpolypoint; + TPPLPoint linep1, linep2; + TPPLPoint v1, v2; + TPPLPoly newpoly; + bool hasholes; + bool pointvisible; + bool pointfound; + + // Check for the trivial case of no holes. + hasholes = false; + for (iter = inpolys->front(); iter; iter = iter->next()) { + if (iter->get().IsHole()) { + hasholes = true; + break; + } + } + if (!hasholes) { + for (iter = inpolys->front(); iter; iter = iter->next()) { + outpolys->push_back(iter->get()); + } + return 1; + } + + polys = *inpolys; + + while (1) { + // Find the hole point with the largest x. + hasholes = false; + for (iter = polys.front(); iter; iter = iter->next()) { + if (!iter->get().IsHole()) { + continue; + } + + if (!hasholes) { + hasholes = true; + holeiter = iter; + holepointindex = 0; + } + + for (i = 0; i < iter->get().GetNumPoints(); i++) { + if (iter->get().GetPoint(i).x > holeiter->get().GetPoint(holepointindex).x) { + holeiter = iter; + holepointindex = i; + } + } + } + if (!hasholes) { + break; + } + holepoint = holeiter->get().GetPoint(holepointindex); + + pointfound = false; + for (iter = polys.front(); iter; iter = iter->next()) { + if (iter->get().IsHole()) { + continue; + } + for (i = 0; i < iter->get().GetNumPoints(); i++) { + if (iter->get().GetPoint(i).x <= holepoint.x) { + continue; + } + if (!InCone(iter->get().GetPoint((i + iter->get().GetNumPoints() - 1) % (iter->get().GetNumPoints())), + iter->get().GetPoint(i), + iter->get().GetPoint((i + 1) % (iter->get().GetNumPoints())), + holepoint)) { + continue; + } + polypoint = iter->get().GetPoint(i); + if (pointfound) { + v1 = Normalize(polypoint - holepoint); + v2 = Normalize(bestpolypoint - holepoint); + if (v2.x > v1.x) { + continue; + } + } + pointvisible = true; + for (iter2 = polys.front(); iter2; iter2->next()) { + if (iter2->get().IsHole()) { + continue; + } + for (i2 = 0; i2 < iter2->get().GetNumPoints(); i2++) { + linep1 = iter2->get().GetPoint(i2); + linep2 = iter2->get().GetPoint((i2 + 1) % (iter2->get().GetNumPoints())); + if (Intersects(holepoint, polypoint, linep1, linep2)) { + pointvisible = false; + break; + } + } + if (!pointvisible) { + break; + } + } + if (pointvisible) { + pointfound = true; + bestpolypoint = polypoint; + polyiter = iter; + polypointindex = i; + } + } + } + + if (!pointfound) { + return 0; + } + + newpoly.Init(holeiter->get().GetNumPoints() + polyiter->get().GetNumPoints() + 2); + i2 = 0; + for (i = 0; i <= polypointindex; i++) { + newpoly[i2] = polyiter->get().GetPoint(i); + i2++; + } + for (i = 0; i <= holeiter->get().GetNumPoints(); i++) { + newpoly[i2] = holeiter->get().GetPoint((i + holepointindex) % holeiter->get().GetNumPoints()); + i2++; + } + for (i = polypointindex; i < polyiter->get().GetNumPoints(); i++) { + newpoly[i2] = polyiter->get().GetPoint(i); + i2++; + } + + polys.erase(holeiter); + polys.erase(polyiter); + polys.push_back(newpoly); + } + + for (iter = polys.front(); iter; iter = iter->next()) { + outpolys->push_back(iter->get()); + } + + return 1; +} + +bool TPPLPartition::IsConvex(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3) { + tppl_float tmp; + tmp = (p3.y - p1.y) * (p2.x - p1.x) - (p3.x - p1.x) * (p2.y - p1.y); + if (tmp > 0) { + return 1; + } else { + return 0; + } +} + +bool TPPLPartition::IsReflex(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3) { + tppl_float tmp; + tmp = (p3.y - p1.y) * (p2.x - p1.x) - (p3.x - p1.x) * (p2.y - p1.y); + if (tmp < 0) { + return 1; + } else { + return 0; + } +} + +bool TPPLPartition::IsInside(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3, TPPLPoint &p) { + if (IsConvex(p1, p, p2)) { + return false; + } + if (IsConvex(p2, p, p3)) { + return false; + } + if (IsConvex(p3, p, p1)) { + return false; + } + return true; +} + +bool TPPLPartition::InCone(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3, TPPLPoint &p) { + bool convex; + + convex = IsConvex(p1, p2, p3); + + if (convex) { + if (!IsConvex(p1, p2, p)) { + return false; + } + if (!IsConvex(p2, p3, p)) { + return false; + } + return true; + } else { + if (IsConvex(p1, p2, p)) { + return true; + } + if (IsConvex(p2, p3, p)) { + return true; + } + return false; + } +} + +bool TPPLPartition::InCone(PartitionVertex *v, TPPLPoint &p) { + TPPLPoint p1, p2, p3; + + p1 = v->previous->p; + p2 = v->p; + p3 = v->next->p; + + return InCone(p1, p2, p3, p); +} + +void TPPLPartition::UpdateVertexReflexity(PartitionVertex *v) { + PartitionVertex *v1 = NULL, *v3 = NULL; + v1 = v->previous; + v3 = v->next; + v->isConvex = !IsReflex(v1->p, v->p, v3->p); +} + +void TPPLPartition::UpdateVertex(PartitionVertex *v, PartitionVertex *vertices, long numvertices) { + long i; + PartitionVertex *v1 = NULL, *v3 = NULL; + TPPLPoint vec1, vec3; + + v1 = v->previous; + v3 = v->next; + + v->isConvex = IsConvex(v1->p, v->p, v3->p); + + vec1 = Normalize(v1->p - v->p); + vec3 = Normalize(v3->p - v->p); + v->angle = vec1.x * vec3.x + vec1.y * vec3.y; + + if (v->isConvex) { + v->isEar = true; + for (i = 0; i < numvertices; i++) { + if ((vertices[i].p.x == v->p.x) && (vertices[i].p.y == v->p.y)) { + continue; + } + if ((vertices[i].p.x == v1->p.x) && (vertices[i].p.y == v1->p.y)) { + continue; + } + if ((vertices[i].p.x == v3->p.x) && (vertices[i].p.y == v3->p.y)) { + continue; + } + if (IsInside(v1->p, v->p, v3->p, vertices[i].p)) { + v->isEar = false; + break; + } + } + } else { + v->isEar = false; + } +} + +// Triangulation by ear removal. +int TPPLPartition::Triangulate_EC(TPPLPoly *poly, TPPLPolyList *triangles) { + if (!poly->Valid()) { + return 0; + } + + long numvertices; + PartitionVertex *vertices = NULL; + PartitionVertex *ear = NULL; + TPPLPoly triangle; + long i, j; + bool earfound; + + if (poly->GetNumPoints() < 3) { + return 0; + } + if (poly->GetNumPoints() == 3) { + triangles->push_back(*poly); + return 1; + } + + numvertices = poly->GetNumPoints(); + + vertices = new PartitionVertex[numvertices]; + for (i = 0; i < numvertices; i++) { + vertices[i].isActive = true; + vertices[i].p = poly->GetPoint(i); + if (i == (numvertices - 1)) { + vertices[i].next = &(vertices[0]); + } else { + vertices[i].next = &(vertices[i + 1]); + } + if (i == 0) { + vertices[i].previous = &(vertices[numvertices - 1]); + } else { + vertices[i].previous = &(vertices[i - 1]); + } + } + for (i = 0; i < numvertices; i++) { + UpdateVertex(&vertices[i], vertices, numvertices); + } + + for (i = 0; i < numvertices - 3; i++) { + earfound = false; + // Find the most extruded ear. + for (j = 0; j < numvertices; j++) { + if (!vertices[j].isActive) { + continue; + } + if (!vertices[j].isEar) { + continue; + } + if (!earfound) { + earfound = true; + ear = &(vertices[j]); + } else { + if (vertices[j].angle > ear->angle) { + ear = &(vertices[j]); + } + } + } + if (!earfound) { + delete[] vertices; + return 0; + } + + triangle.Triangle(ear->previous->p, ear->p, ear->next->p); + triangles->push_back(triangle); + + ear->isActive = false; + ear->previous->next = ear->next; + ear->next->previous = ear->previous; + + if (i == numvertices - 4) { + break; + } + + UpdateVertex(ear->previous, vertices, numvertices); + UpdateVertex(ear->next, vertices, numvertices); + } + for (i = 0; i < numvertices; i++) { + if (vertices[i].isActive) { + triangle.Triangle(vertices[i].previous->p, vertices[i].p, vertices[i].next->p); + triangles->push_back(triangle); + break; + } + } + + delete[] vertices; + + return 1; +} + +int TPPLPartition::Triangulate_EC(TPPLPolyList *inpolys, TPPLPolyList *triangles) { + TPPLPolyList outpolys; + TPPLPolyList::Element *iter; + + if (!RemoveHoles(inpolys, &outpolys)) { + return 0; + } + for (iter = outpolys.front(); iter; iter = iter->next()) { + if (!Triangulate_EC(&(iter->get()), triangles)) { + return 0; + } + } + return 1; +} + +int TPPLPartition::ConvexPartition_HM(TPPLPoly *poly, TPPLPolyList *parts) { + if (!poly->Valid()) { + return 0; + } + + TPPLPolyList triangles; + TPPLPolyList::Element *iter1, *iter2; + TPPLPoly *poly1 = NULL, *poly2 = NULL; + TPPLPoly newpoly; + TPPLPoint d1, d2, p1, p2, p3; + long i11, i12, i21, i22, i13, i23, j, k; + bool isdiagonal; + long numreflex; + + // Check if the poly is already convex. + numreflex = 0; + for (i11 = 0; i11 < poly->GetNumPoints(); i11++) { + if (i11 == 0) { + i12 = poly->GetNumPoints() - 1; + } else { + i12 = i11 - 1; + } + if (i11 == (poly->GetNumPoints() - 1)) { + i13 = 0; + } else { + i13 = i11 + 1; + } + if (IsReflex(poly->GetPoint(i12), poly->GetPoint(i11), poly->GetPoint(i13))) { + numreflex = 1; + break; + } + } + if (numreflex == 0) { + parts->push_back(*poly); + return 1; + } + + if (!Triangulate_EC(poly, &triangles)) { + return 0; + } + + for (iter1 = triangles.front(); iter1; iter1 = iter1->next()) { + poly1 = &(iter1->get()); + for (i11 = 0; i11 < poly1->GetNumPoints(); i11++) { + d1 = poly1->GetPoint(i11); + i12 = (i11 + 1) % (poly1->GetNumPoints()); + d2 = poly1->GetPoint(i12); + + isdiagonal = false; + for (iter2 = iter1; iter2; iter2 = iter2->next()) { + if (iter1 == iter2) { + continue; + } + poly2 = &(iter2->get()); + + for (i21 = 0; i21 < poly2->GetNumPoints(); i21++) { + if ((d2.x != poly2->GetPoint(i21).x) || (d2.y != poly2->GetPoint(i21).y)) { + continue; + } + i22 = (i21 + 1) % (poly2->GetNumPoints()); + if ((d1.x != poly2->GetPoint(i22).x) || (d1.y != poly2->GetPoint(i22).y)) { + continue; + } + isdiagonal = true; + break; + } + if (isdiagonal) { + break; + } + } + + if (!isdiagonal) { + continue; + } + + p2 = poly1->GetPoint(i11); + if (i11 == 0) { + i13 = poly1->GetNumPoints() - 1; + } else { + i13 = i11 - 1; + } + p1 = poly1->GetPoint(i13); + if (i22 == (poly2->GetNumPoints() - 1)) { + i23 = 0; + } else { + i23 = i22 + 1; + } + p3 = poly2->GetPoint(i23); + + if (!IsConvex(p1, p2, p3)) { + continue; + } + + p2 = poly1->GetPoint(i12); + if (i12 == (poly1->GetNumPoints() - 1)) { + i13 = 0; + } else { + i13 = i12 + 1; + } + p3 = poly1->GetPoint(i13); + if (i21 == 0) { + i23 = poly2->GetNumPoints() - 1; + } else { + i23 = i21 - 1; + } + p1 = poly2->GetPoint(i23); + + if (!IsConvex(p1, p2, p3)) { + continue; + } + + newpoly.Init(poly1->GetNumPoints() + poly2->GetNumPoints() - 2); + k = 0; + for (j = i12; j != i11; j = (j + 1) % (poly1->GetNumPoints())) { + newpoly[k] = poly1->GetPoint(j); + k++; + } + for (j = i22; j != i21; j = (j + 1) % (poly2->GetNumPoints())) { + newpoly[k] = poly2->GetPoint(j); + k++; + } + + triangles.erase(iter2); + iter1->get() = newpoly; + poly1 = &(iter1->get()); + i11 = -1; + + continue; + } + } + + for (iter1 = triangles.front(); iter1; iter1 = iter1->next()) { + parts->push_back(iter1->get()); + } + + return 1; +} + +int TPPLPartition::ConvexPartition_HM(TPPLPolyList *inpolys, TPPLPolyList *parts) { + TPPLPolyList outpolys; + TPPLPolyList::Element *iter; + + if (!RemoveHoles(inpolys, &outpolys)) { + return 0; + } + for (iter = outpolys.front(); iter; iter = iter->next()) { + if (!ConvexPartition_HM(&(iter->get()), parts)) { + return 0; + } + } + return 1; +} + +// Minimum-weight polygon triangulation by dynamic programming. +// Time complexity: O(n^3) +// Space complexity: O(n^2) +int TPPLPartition::Triangulate_OPT(TPPLPoly *poly, TPPLPolyList *triangles) { + if (!poly->Valid()) { + return 0; + } + + long i, j, k, gap, n; + DPState **dpstates = NULL; + TPPLPoint p1, p2, p3, p4; + long bestvertex; + tppl_float weight, minweight, d1, d2; + Diagonal diagonal, newdiagonal; + DiagonalList diagonals; + TPPLPoly triangle; + int ret = 1; + + n = poly->GetNumPoints(); + dpstates = new DPState *[n]; + for (i = 1; i < n; i++) { + dpstates[i] = new DPState[i]; + } + + // Initialize states and visibility. + for (i = 0; i < (n - 1); i++) { + p1 = poly->GetPoint(i); + for (j = i + 1; j < n; j++) { + dpstates[j][i].visible = true; + dpstates[j][i].weight = 0; + dpstates[j][i].bestvertex = -1; + if (j != (i + 1)) { + p2 = poly->GetPoint(j); + + // Visibility check. + if (i == 0) { + p3 = poly->GetPoint(n - 1); + } else { + p3 = poly->GetPoint(i - 1); + } + if (i == (n - 1)) { + p4 = poly->GetPoint(0); + } else { + p4 = poly->GetPoint(i + 1); + } + if (!InCone(p3, p1, p4, p2)) { + dpstates[j][i].visible = false; + continue; + } + + if (j == 0) { + p3 = poly->GetPoint(n - 1); + } else { + p3 = poly->GetPoint(j - 1); + } + if (j == (n - 1)) { + p4 = poly->GetPoint(0); + } else { + p4 = poly->GetPoint(j + 1); + } + if (!InCone(p3, p2, p4, p1)) { + dpstates[j][i].visible = false; + continue; + } + + for (k = 0; k < n; k++) { + p3 = poly->GetPoint(k); + if (k == (n - 1)) { + p4 = poly->GetPoint(0); + } else { + p4 = poly->GetPoint(k + 1); + } + if (Intersects(p1, p2, p3, p4)) { + dpstates[j][i].visible = false; + break; + } + } + } + } + } + dpstates[n - 1][0].visible = true; + dpstates[n - 1][0].weight = 0; + dpstates[n - 1][0].bestvertex = -1; + + for (gap = 2; gap < n; gap++) { + for (i = 0; i < (n - gap); i++) { + j = i + gap; + if (!dpstates[j][i].visible) { + continue; + } + bestvertex = -1; + for (k = (i + 1); k < j; k++) { + if (!dpstates[k][i].visible) { + continue; + } + if (!dpstates[j][k].visible) { + continue; + } + + if (k <= (i + 1)) { + d1 = 0; + } else { + d1 = Distance(poly->GetPoint(i), poly->GetPoint(k)); + } + if (j <= (k + 1)) { + d2 = 0; + } else { + d2 = Distance(poly->GetPoint(k), poly->GetPoint(j)); + } + + weight = dpstates[k][i].weight + dpstates[j][k].weight + d1 + d2; + + if ((bestvertex == -1) || (weight < minweight)) { + bestvertex = k; + minweight = weight; + } + } + if (bestvertex == -1) { + for (i = 1; i < n; i++) { + delete[] dpstates[i]; + } + delete[] dpstates; + + return 0; + } + + dpstates[j][i].bestvertex = bestvertex; + dpstates[j][i].weight = minweight; + } + } + + newdiagonal.index1 = 0; + newdiagonal.index2 = n - 1; + diagonals.push_back(newdiagonal); + while (!diagonals.is_empty()) { + diagonal = diagonals.front()->get(); + diagonals.pop_front(); + bestvertex = dpstates[diagonal.index2][diagonal.index1].bestvertex; + if (bestvertex == -1) { + ret = 0; + break; + } + triangle.Triangle(poly->GetPoint(diagonal.index1), poly->GetPoint(bestvertex), poly->GetPoint(diagonal.index2)); + triangles->push_back(triangle); + if (bestvertex > (diagonal.index1 + 1)) { + newdiagonal.index1 = diagonal.index1; + newdiagonal.index2 = bestvertex; + diagonals.push_back(newdiagonal); + } + if (diagonal.index2 > (bestvertex + 1)) { + newdiagonal.index1 = bestvertex; + newdiagonal.index2 = diagonal.index2; + diagonals.push_back(newdiagonal); + } + } + + for (i = 1; i < n; i++) { + delete[] dpstates[i]; + } + delete[] dpstates; + + return ret; +} + +void TPPLPartition::UpdateState(long a, long b, long w, long i, long j, DPState2 **dpstates) { + Diagonal newdiagonal; + DiagonalList *pairs = NULL; + long w2; + + w2 = dpstates[a][b].weight; + if (w > w2) { + return; + } + + pairs = &(dpstates[a][b].pairs); + newdiagonal.index1 = i; + newdiagonal.index2 = j; + + if (w < w2) { + pairs->clear(); + pairs->push_front(newdiagonal); + dpstates[a][b].weight = w; + } else { + if ((!pairs->is_empty()) && (i <= pairs->front()->get().index1)) { + return; + } + while ((!pairs->is_empty()) && (pairs->front()->get().index2 >= j)) { + pairs->pop_front(); + } + pairs->push_front(newdiagonal); + } +} + +void TPPLPartition::TypeA(long i, long j, long k, PartitionVertex *vertices, DPState2 **dpstates) { + DiagonalList *pairs = NULL; + DiagonalList::Element *iter, *lastiter; + long top; + long w; + + if (!dpstates[i][j].visible) { + return; + } + top = j; + w = dpstates[i][j].weight; + if (k - j > 1) { + if (!dpstates[j][k].visible) { + return; + } + w += dpstates[j][k].weight + 1; + } + if (j - i > 1) { + pairs = &(dpstates[i][j].pairs); + iter = pairs->back(); + lastiter = pairs->back(); + while (iter != pairs->front()) { + iter--; + if (!IsReflex(vertices[iter->get().index2].p, vertices[j].p, vertices[k].p)) { + lastiter = iter; + } else { + break; + } + } + if (lastiter == pairs->back()) { + w++; + } else { + if (IsReflex(vertices[k].p, vertices[i].p, vertices[lastiter->get().index1].p)) { + w++; + } else { + top = lastiter->get().index1; + } + } + } + UpdateState(i, k, w, top, j, dpstates); +} + +void TPPLPartition::TypeB(long i, long j, long k, PartitionVertex *vertices, DPState2 **dpstates) { + DiagonalList *pairs = NULL; + DiagonalList::Element *iter, *lastiter; + long top; + long w; + + if (!dpstates[j][k].visible) { + return; + } + top = j; + w = dpstates[j][k].weight; + + if (j - i > 1) { + if (!dpstates[i][j].visible) { + return; + } + w += dpstates[i][j].weight + 1; + } + if (k - j > 1) { + pairs = &(dpstates[j][k].pairs); + + iter = pairs->front(); + if ((!pairs->is_empty()) && (!IsReflex(vertices[i].p, vertices[j].p, vertices[iter->get().index1].p))) { + lastiter = iter; + while (iter) { + if (!IsReflex(vertices[i].p, vertices[j].p, vertices[iter->get().index1].p)) { + lastiter = iter; + iter = iter->next(); + } else { + break; + } + } + if (IsReflex(vertices[lastiter->get().index2].p, vertices[k].p, vertices[i].p)) { + w++; + } else { + top = lastiter->get().index2; + } + } else { + w++; + } + } + UpdateState(i, k, w, j, top, dpstates); +} + +int TPPLPartition::ConvexPartition_OPT(TPPLPoly *poly, TPPLPolyList *parts) { + if (!poly->Valid()) { + return 0; + } + + TPPLPoint p1, p2, p3, p4; + PartitionVertex *vertices = NULL; + DPState2 **dpstates = NULL; + long i, j, k, n, gap; + DiagonalList diagonals, diagonals2; + Diagonal diagonal, newdiagonal; + DiagonalList *pairs = NULL, *pairs2 = NULL; + DiagonalList::Element *iter, *iter2; + int ret; + TPPLPoly newpoly; + List<long> indices; + List<long>::Element *iiter; + bool ijreal, jkreal; + + n = poly->GetNumPoints(); + vertices = new PartitionVertex[n]; + + dpstates = new DPState2 *[n]; + for (i = 0; i < n; i++) { + dpstates[i] = new DPState2[n]; + } + + // Initialize vertex information. + for (i = 0; i < n; i++) { + vertices[i].p = poly->GetPoint(i); + vertices[i].isActive = true; + if (i == 0) { + vertices[i].previous = &(vertices[n - 1]); + } else { + vertices[i].previous = &(vertices[i - 1]); + } + if (i == (poly->GetNumPoints() - 1)) { + vertices[i].next = &(vertices[0]); + } else { + vertices[i].next = &(vertices[i + 1]); + } + } + for (i = 1; i < n; i++) { + UpdateVertexReflexity(&(vertices[i])); + } + + // Initialize states and visibility. + for (i = 0; i < (n - 1); i++) { + p1 = poly->GetPoint(i); + for (j = i + 1; j < n; j++) { + dpstates[i][j].visible = true; + if (j == i + 1) { + dpstates[i][j].weight = 0; + } else { + dpstates[i][j].weight = 2147483647; + } + if (j != (i + 1)) { + p2 = poly->GetPoint(j); + + // Visibility check. + if (!InCone(&vertices[i], p2)) { + dpstates[i][j].visible = false; + continue; + } + if (!InCone(&vertices[j], p1)) { + dpstates[i][j].visible = false; + continue; + } + + for (k = 0; k < n; k++) { + p3 = poly->GetPoint(k); + if (k == (n - 1)) { + p4 = poly->GetPoint(0); + } else { + p4 = poly->GetPoint(k + 1); + } + if (Intersects(p1, p2, p3, p4)) { + dpstates[i][j].visible = false; + break; + } + } + } + } + } + for (i = 0; i < (n - 2); i++) { + j = i + 2; + if (dpstates[i][j].visible) { + dpstates[i][j].weight = 0; + newdiagonal.index1 = i + 1; + newdiagonal.index2 = i + 1; + dpstates[i][j].pairs.push_back(newdiagonal); + } + } + + dpstates[0][n - 1].visible = true; + vertices[0].isConvex = false; // By convention. + + for (gap = 3; gap < n; gap++) { + for (i = 0; i < n - gap; i++) { + if (vertices[i].isConvex) { + continue; + } + k = i + gap; + if (dpstates[i][k].visible) { + if (!vertices[k].isConvex) { + for (j = i + 1; j < k; j++) { + TypeA(i, j, k, vertices, dpstates); + } + } else { + for (j = i + 1; j < (k - 1); j++) { + if (vertices[j].isConvex) { + continue; + } + TypeA(i, j, k, vertices, dpstates); + } + TypeA(i, k - 1, k, vertices, dpstates); + } + } + } + for (k = gap; k < n; k++) { + if (vertices[k].isConvex) { + continue; + } + i = k - gap; + if ((vertices[i].isConvex) && (dpstates[i][k].visible)) { + TypeB(i, i + 1, k, vertices, dpstates); + for (j = i + 2; j < k; j++) { + if (vertices[j].isConvex) { + continue; + } + TypeB(i, j, k, vertices, dpstates); + } + } + } + } + + // Recover solution. + ret = 1; + newdiagonal.index1 = 0; + newdiagonal.index2 = n - 1; + diagonals.push_front(newdiagonal); + while (!diagonals.is_empty()) { + diagonal = diagonals.front()->get(); + diagonals.pop_front(); + if ((diagonal.index2 - diagonal.index1) <= 1) { + continue; + } + pairs = &(dpstates[diagonal.index1][diagonal.index2].pairs); + if (pairs->is_empty()) { + ret = 0; + break; + } + if (!vertices[diagonal.index1].isConvex) { + iter = pairs->back(); + iter--; + j = iter->get().index2; + newdiagonal.index1 = j; + newdiagonal.index2 = diagonal.index2; + diagonals.push_front(newdiagonal); + if ((j - diagonal.index1) > 1) { + if (iter->get().index1 != iter->get().index2) { + pairs2 = &(dpstates[diagonal.index1][j].pairs); + while (1) { + if (pairs2->is_empty()) { + ret = 0; + break; + } + iter2 = pairs2->back(); + iter2--; + if (iter->get().index1 != iter2->get().index1) { + pairs2->pop_back(); + } else { + break; + } + } + if (ret == 0) { + break; + } + } + newdiagonal.index1 = diagonal.index1; + newdiagonal.index2 = j; + diagonals.push_front(newdiagonal); + } + } else { + iter = pairs->front(); + j = iter->get().index1; + newdiagonal.index1 = diagonal.index1; + newdiagonal.index2 = j; + diagonals.push_front(newdiagonal); + if ((diagonal.index2 - j) > 1) { + if (iter->get().index1 != iter->get().index2) { + pairs2 = &(dpstates[j][diagonal.index2].pairs); + while (1) { + if (pairs2->is_empty()) { + ret = 0; + break; + } + iter2 = pairs2->front(); + if (iter->get().index2 != iter2->get().index2) { + pairs2->pop_front(); + } else { + break; + } + } + if (ret == 0) { + break; + } + } + newdiagonal.index1 = j; + newdiagonal.index2 = diagonal.index2; + diagonals.push_front(newdiagonal); + } + } + } + + if (ret == 0) { + for (i = 0; i < n; i++) { + delete[] dpstates[i]; + } + delete[] dpstates; + delete[] vertices; + + return ret; + } + + newdiagonal.index1 = 0; + newdiagonal.index2 = n - 1; + diagonals.push_front(newdiagonal); + while (!diagonals.is_empty()) { + diagonal = diagonals.front()->get(); + diagonals.pop_front(); + if ((diagonal.index2 - diagonal.index1) <= 1) { + continue; + } + + indices.clear(); + diagonals2.clear(); + indices.push_back(diagonal.index1); + indices.push_back(diagonal.index2); + diagonals2.push_front(diagonal); + + while (!diagonals2.is_empty()) { + diagonal = diagonals2.front()->get(); + diagonals2.pop_front(); + if ((diagonal.index2 - diagonal.index1) <= 1) { + continue; + } + ijreal = true; + jkreal = true; + pairs = &(dpstates[diagonal.index1][diagonal.index2].pairs); + if (!vertices[diagonal.index1].isConvex) { + iter = pairs->back(); + iter--; + j = iter->get().index2; + if (iter->get().index1 != iter->get().index2) { + ijreal = false; + } + } else { + iter = pairs->front(); + j = iter->get().index1; + if (iter->get().index1 != iter->get().index2) { + jkreal = false; + } + } + + newdiagonal.index1 = diagonal.index1; + newdiagonal.index2 = j; + if (ijreal) { + diagonals.push_back(newdiagonal); + } else { + diagonals2.push_back(newdiagonal); + } + + newdiagonal.index1 = j; + newdiagonal.index2 = diagonal.index2; + if (jkreal) { + diagonals.push_back(newdiagonal); + } else { + diagonals2.push_back(newdiagonal); + } + + indices.push_back(j); + } + + //std::sort(indices.begin(), indices.end()); + indices.sort(); + newpoly.Init((long)indices.size()); + k = 0; + for (iiter = indices.front(); iiter != indices.back(); iiter = iiter->next()) { + newpoly[k] = vertices[iiter->get()].p; + k++; + } + parts->push_back(newpoly); + } + + for (i = 0; i < n; i++) { + delete[] dpstates[i]; + } + delete[] dpstates; + delete[] vertices; + + return ret; +} + +// Creates a monotone partition of a list of polygons that +// can contain holes. Triangulates a set of polygons by +// first partitioning them into monotone polygons. +// Time complexity: O(n*log(n)), n is the number of vertices. +// Space complexity: O(n) +// The algorithm used here is outlined in the book +// "Computational Geometry: Algorithms and Applications" +// by Mark de Berg, Otfried Cheong, Marc van Kreveld, and Mark Overmars. +int TPPLPartition::MonotonePartition(TPPLPolyList *inpolys, TPPLPolyList *monotonePolys) { + TPPLPolyList::Element *iter; + MonotoneVertex *vertices = NULL; + long i, numvertices, vindex, vindex2, newnumvertices, maxnumvertices; + long polystartindex, polyendindex; + TPPLPoly *poly = NULL; + MonotoneVertex *v = NULL, *v2 = NULL, *vprev = NULL, *vnext = NULL; + ScanLineEdge newedge; + bool error = false; + + numvertices = 0; + for (iter = inpolys->front(); iter; iter++) { + numvertices += iter->get().GetNumPoints(); + } + + maxnumvertices = numvertices * 3; + vertices = new MonotoneVertex[maxnumvertices]; + newnumvertices = numvertices; + + polystartindex = 0; + for (iter = inpolys->front(); iter; iter++) { + poly = &(iter->get()); + polyendindex = polystartindex + poly->GetNumPoints() - 1; + for (i = 0; i < poly->GetNumPoints(); i++) { + vertices[i + polystartindex].p = poly->GetPoint(i); + if (i == 0) { + vertices[i + polystartindex].previous = polyendindex; + } else { + vertices[i + polystartindex].previous = i + polystartindex - 1; + } + if (i == (poly->GetNumPoints() - 1)) { + vertices[i + polystartindex].next = polystartindex; + } else { + vertices[i + polystartindex].next = i + polystartindex + 1; + } + } + polystartindex = polyendindex + 1; + } + + // Construct the priority queue. + long *priority = new long[numvertices]; + for (i = 0; i < numvertices; i++) { + priority[i] = i; + } + std::sort(priority, &(priority[numvertices]), VertexSorter(vertices)); + + // Determine vertex types. + TPPLVertexType *vertextypes = new TPPLVertexType[maxnumvertices]; + for (i = 0; i < numvertices; i++) { + v = &(vertices[i]); + vprev = &(vertices[v->previous]); + vnext = &(vertices[v->next]); + + if (Below(vprev->p, v->p) && Below(vnext->p, v->p)) { + if (IsConvex(vnext->p, vprev->p, v->p)) { + vertextypes[i] = TPPL_VERTEXTYPE_START; + } else { + vertextypes[i] = TPPL_VERTEXTYPE_SPLIT; + } + } else if (Below(v->p, vprev->p) && Below(v->p, vnext->p)) { + if (IsConvex(vnext->p, vprev->p, v->p)) { + vertextypes[i] = TPPL_VERTEXTYPE_END; + } else { + vertextypes[i] = TPPL_VERTEXTYPE_MERGE; + } + } else { + vertextypes[i] = TPPL_VERTEXTYPE_REGULAR; + } + } + + // Helpers. + long *helpers = new long[maxnumvertices]; + + // Binary search tree that holds edges intersecting the scanline. + // Note that while set doesn't actually have to be implemented as + // a tree, complexity requirements for operations are the same as + // for the balanced binary search tree. + Set<ScanLineEdge> edgeTree; + // Store iterators to the edge tree elements. + // This makes deleting existing edges much faster. + Set<ScanLineEdge>::Element **edgeTreeIterators, *edgeIter; + edgeTreeIterators = new Set<ScanLineEdge>::Element *[maxnumvertices]; + //Pair<Set<ScanLineEdge>::iterator, bool> edgeTreeRet; + for (i = 0; i < numvertices; i++) { + edgeTreeIterators[i] = nullptr; + } + + // For each vertex. + for (i = 0; i < numvertices; i++) { + vindex = priority[i]; + v = &(vertices[vindex]); + vindex2 = vindex; + v2 = v; + + // Depending on the vertex type, do the appropriate action. + // Comments in the following sections are copied from + // "Computational Geometry: Algorithms and Applications". + // Notation: e_i = e subscript i, v_i = v subscript i, etc. + switch (vertextypes[vindex]) { + case TPPL_VERTEXTYPE_START: + // Insert e_i in T and set helper(e_i) to v_i. + newedge.p1 = v->p; + newedge.p2 = vertices[v->next].p; + newedge.index = vindex; + //edgeTreeRet = edgeTree.insert(newedge); + //edgeTreeIterators[vindex] = edgeTreeRet.first; + edgeTreeIterators[vindex] = edgeTree.insert(newedge); + helpers[vindex] = vindex; + break; + + case TPPL_VERTEXTYPE_END: + if (edgeTreeIterators[v->previous] == edgeTree.back()) { + error = true; + break; + } + // If helper(e_i - 1) is a merge vertex + if (vertextypes[helpers[v->previous]] == TPPL_VERTEXTYPE_MERGE) { + // Insert the diagonal connecting vi to helper(e_i - 1) in D. + AddDiagonal(vertices, &newnumvertices, vindex, helpers[v->previous], + vertextypes, edgeTreeIterators, &edgeTree, helpers); + } + // Delete e_i - 1 from T + edgeTree.erase(edgeTreeIterators[v->previous]); + break; + + case TPPL_VERTEXTYPE_SPLIT: + // Search in T to find the edge e_j directly left of v_i. + newedge.p1 = v->p; + newedge.p2 = v->p; + edgeIter = edgeTree.lower_bound(newedge); + if (edgeIter == edgeTree.front()) { + error = true; + break; + } + edgeIter--; + // Insert the diagonal connecting vi to helper(e_j) in D. + AddDiagonal(vertices, &newnumvertices, vindex, helpers[edgeIter->get().index], + vertextypes, edgeTreeIterators, &edgeTree, helpers); + vindex2 = newnumvertices - 2; + v2 = &(vertices[vindex2]); + // helper(e_j) in v_i. + helpers[edgeIter->get().index] = vindex; + // Insert e_i in T and set helper(e_i) to v_i. + newedge.p1 = v2->p; + newedge.p2 = vertices[v2->next].p; + newedge.index = vindex2; + //edgeTreeRet = edgeTree.insert(newedge); + //edgeTreeIterators[vindex2] = edgeTreeRet.first; + edgeTreeIterators[vindex2] = edgeTree.insert(newedge); + helpers[vindex2] = vindex2; + break; + + case TPPL_VERTEXTYPE_MERGE: + if (edgeTreeIterators[v->previous] == edgeTree.back()) { + error = true; + break; + } + // if helper(e_i - 1) is a merge vertex + if (vertextypes[helpers[v->previous]] == TPPL_VERTEXTYPE_MERGE) { + // Insert the diagonal connecting vi to helper(e_i - 1) in D. + AddDiagonal(vertices, &newnumvertices, vindex, helpers[v->previous], + vertextypes, edgeTreeIterators, &edgeTree, helpers); + vindex2 = newnumvertices - 2; + v2 = &(vertices[vindex2]); + } + // Delete e_i - 1 from T. + edgeTree.erase(edgeTreeIterators[v->previous]); + // Search in T to find the edge e_j directly left of v_i. + newedge.p1 = v->p; + newedge.p2 = v->p; + edgeIter = edgeTree.lower_bound(newedge); + if (edgeIter == edgeTree.front()) { + error = true; + break; + } + edgeIter--; + // If helper(e_j) is a merge vertex. + if (vertextypes[helpers[edgeIter->get().index]] == TPPL_VERTEXTYPE_MERGE) { + // Insert the diagonal connecting v_i to helper(e_j) in D. + AddDiagonal(vertices, &newnumvertices, vindex2, helpers[edgeIter->get().index], + vertextypes, edgeTreeIterators, &edgeTree, helpers); + } + // helper(e_j) <- v_i + helpers[edgeIter->get().index] = vindex2; + break; + + case TPPL_VERTEXTYPE_REGULAR: + // If the interior of P lies to the right of v_i. + if (Below(v->p, vertices[v->previous].p)) { + if (edgeTreeIterators[v->previous] == edgeTree.back()) { + error = true; + break; + } + // If helper(e_i - 1) is a merge vertex. + if (vertextypes[helpers[v->previous]] == TPPL_VERTEXTYPE_MERGE) { + // Insert the diagonal connecting v_i to helper(e_i - 1) in D. + AddDiagonal(vertices, &newnumvertices, vindex, helpers[v->previous], + vertextypes, edgeTreeIterators, &edgeTree, helpers); + vindex2 = newnumvertices - 2; + v2 = &(vertices[vindex2]); + } + // Delete e_i - 1 from T. + edgeTree.erase(edgeTreeIterators[v->previous]); + // Insert e_i in T and set helper(e_i) to v_i. + newedge.p1 = v2->p; + newedge.p2 = vertices[v2->next].p; + newedge.index = vindex2; + //edgeTreeRet = edgeTree.insert(newedge); + //edgeTreeIterators[vindex2] = edgeTreeRet.first; + edgeTreeIterators[vindex2] = edgeTree.insert(newedge); + helpers[vindex2] = vindex; + } else { + // Search in T to find the edge e_j directly left of v_i. + newedge.p1 = v->p; + newedge.p2 = v->p; + edgeIter = edgeTree.lower_bound(newedge); + if (edgeIter == edgeTree.front()) { + error = true; + break; + } + edgeIter = edgeIter->prev(); + // If helper(e_j) is a merge vertex. + if (vertextypes[helpers[edgeIter->get().index]] == TPPL_VERTEXTYPE_MERGE) { + // Insert the diagonal connecting v_i to helper(e_j) in D. + AddDiagonal(vertices, &newnumvertices, vindex, helpers[edgeIter->get().index], + vertextypes, edgeTreeIterators, &edgeTree, helpers); + } + // helper(e_j) <- v_i. + helpers[edgeIter->get().index] = vindex; + } + break; + } + + if (error) + break; + } + + char *used = new char[newnumvertices]; + memset(used, 0, newnumvertices * sizeof(char)); + + if (!error) { + // Return result. + long size; + TPPLPoly mpoly; + for (i = 0; i < newnumvertices; i++) { + if (used[i]) { + continue; + } + v = &(vertices[i]); + vnext = &(vertices[v->next]); + size = 1; + while (vnext != v) { + vnext = &(vertices[vnext->next]); + size++; + } + mpoly.Init(size); + v = &(vertices[i]); + mpoly[0] = v->p; + vnext = &(vertices[v->next]); + size = 1; + used[i] = 1; + used[v->next] = 1; + while (vnext != v) { + mpoly[size] = vnext->p; + used[vnext->next] = 1; + vnext = &(vertices[vnext->next]); + size++; + } + monotonePolys->push_back(mpoly); + } + } + + // Cleanup. + delete[] vertices; + delete[] priority; + delete[] vertextypes; + delete[] edgeTreeIterators; + delete[] helpers; + delete[] used; + + if (error) { + return 0; + } else { + return 1; + } +} + +// Adds a diagonal to the doubly-connected list of vertices. +void TPPLPartition::AddDiagonal(MonotoneVertex *vertices, long *numvertices, long index1, long index2, + TPPLVertexType *vertextypes, Set<ScanLineEdge>::Element **edgeTreeIterators, + Set<ScanLineEdge> *edgeTree, long *helpers) { + long newindex1, newindex2; + + newindex1 = *numvertices; + (*numvertices)++; + newindex2 = *numvertices; + (*numvertices)++; + + vertices[newindex1].p = vertices[index1].p; + vertices[newindex2].p = vertices[index2].p; + + vertices[newindex2].next = vertices[index2].next; + vertices[newindex1].next = vertices[index1].next; + + vertices[vertices[index2].next].previous = newindex2; + vertices[vertices[index1].next].previous = newindex1; + + vertices[index1].next = newindex2; + vertices[newindex2].previous = index1; + + vertices[index2].next = newindex1; + vertices[newindex1].previous = index2; + + // Update all relevant structures. + vertextypes[newindex1] = vertextypes[index1]; + edgeTreeIterators[newindex1] = edgeTreeIterators[index1]; + helpers[newindex1] = helpers[index1]; + if (edgeTreeIterators[newindex1] != edgeTree->back()) { + edgeTreeIterators[newindex1]->get().index = newindex1; + } + vertextypes[newindex2] = vertextypes[index2]; + edgeTreeIterators[newindex2] = edgeTreeIterators[index2]; + helpers[newindex2] = helpers[index2]; + if (edgeTreeIterators[newindex2] != edgeTree->back()) { + edgeTreeIterators[newindex2]->get().index = newindex2; + } +} + +bool TPPLPartition::Below(TPPLPoint &p1, TPPLPoint &p2) { + if (p1.y < p2.y) { + return true; + } else if (p1.y == p2.y) { + if (p1.x < p2.x) { + return true; + } + } + return false; +} + +// Sorts in the falling order of y values, if y is equal, x is used instead. +bool TPPLPartition::VertexSorter::operator()(long index1, long index2) { + if (vertices[index1].p.y > vertices[index2].p.y) { + return true; + } else if (vertices[index1].p.y == vertices[index2].p.y) { + if (vertices[index1].p.x > vertices[index2].p.x) { + return true; + } + } + return false; +} + +bool TPPLPartition::ScanLineEdge::IsConvex(const TPPLPoint &p1, const TPPLPoint &p2, const TPPLPoint &p3) const { + tppl_float tmp; + tmp = (p3.y - p1.y) * (p2.x - p1.x) - (p3.x - p1.x) * (p2.y - p1.y); + if (tmp > 0) { + return 1; + } + + return 0; +} + +bool TPPLPartition::ScanLineEdge::operator<(const ScanLineEdge &other) const { + if (other.p1.y == other.p2.y) { + if (p1.y == p2.y) { + return (p1.y < other.p1.y); + } + return IsConvex(p1, p2, other.p1); + } else if (p1.y == p2.y) { + return !IsConvex(other.p1, other.p2, p1); + } else if (p1.y < other.p1.y) { + return !IsConvex(other.p1, other.p2, p1); + } else { + return IsConvex(p1, p2, other.p1); + } +} + +// Triangulates monotone polygon. +// Time complexity: O(n) +// Space complexity: O(n) +int TPPLPartition::TriangulateMonotone(TPPLPoly *inPoly, TPPLPolyList *triangles) { + if (!inPoly->Valid()) { + return 0; + } + + long i, i2, j, topindex, bottomindex, leftindex, rightindex, vindex; + TPPLPoint *points = NULL; + long numpoints; + TPPLPoly triangle; + + numpoints = inPoly->GetNumPoints(); + points = inPoly->GetPoints(); + + // Trivial case. + if (numpoints == 3) { + triangles->push_back(*inPoly); + return 1; + } + + topindex = 0; + bottomindex = 0; + for (i = 1; i < numpoints; i++) { + if (Below(points[i], points[bottomindex])) { + bottomindex = i; + } + if (Below(points[topindex], points[i])) { + topindex = i; + } + } + + // Check if the poly is really monotone. + i = topindex; + while (i != bottomindex) { + i2 = i + 1; + if (i2 >= numpoints) { + i2 = 0; + } + if (!Below(points[i2], points[i])) { + return 0; + } + i = i2; + } + i = bottomindex; + while (i != topindex) { + i2 = i + 1; + if (i2 >= numpoints) { + i2 = 0; + } + if (!Below(points[i], points[i2])) { + return 0; + } + i = i2; + } + + char *vertextypes = new char[numpoints]; + long *priority = new long[numpoints]; + + // Merge left and right vertex chains. + priority[0] = topindex; + vertextypes[topindex] = 0; + leftindex = topindex + 1; + if (leftindex >= numpoints) { + leftindex = 0; + } + rightindex = topindex - 1; + if (rightindex < 0) { + rightindex = numpoints - 1; + } + for (i = 1; i < (numpoints - 1); i++) { + if (leftindex == bottomindex) { + priority[i] = rightindex; + rightindex--; + if (rightindex < 0) { + rightindex = numpoints - 1; + } + vertextypes[priority[i]] = -1; + } else if (rightindex == bottomindex) { + priority[i] = leftindex; + leftindex++; + if (leftindex >= numpoints) { + leftindex = 0; + } + vertextypes[priority[i]] = 1; + } else { + if (Below(points[leftindex], points[rightindex])) { + priority[i] = rightindex; + rightindex--; + if (rightindex < 0) { + rightindex = numpoints - 1; + } + vertextypes[priority[i]] = -1; + } else { + priority[i] = leftindex; + leftindex++; + if (leftindex >= numpoints) { + leftindex = 0; + } + vertextypes[priority[i]] = 1; + } + } + } + priority[i] = bottomindex; + vertextypes[bottomindex] = 0; + + long *stack = new long[numpoints]; + long stackptr = 0; + + stack[0] = priority[0]; + stack[1] = priority[1]; + stackptr = 2; + + // For each vertex from top to bottom trim as many triangles as possible. + for (i = 2; i < (numpoints - 1); i++) { + vindex = priority[i]; + if (vertextypes[vindex] != vertextypes[stack[stackptr - 1]]) { + for (j = 0; j < (stackptr - 1); j++) { + if (vertextypes[vindex] == 1) { + triangle.Triangle(points[stack[j + 1]], points[stack[j]], points[vindex]); + } else { + triangle.Triangle(points[stack[j]], points[stack[j + 1]], points[vindex]); + } + triangles->push_back(triangle); + } + stack[0] = priority[i - 1]; + stack[1] = priority[i]; + stackptr = 2; + } else { + stackptr--; + while (stackptr > 0) { + if (vertextypes[vindex] == 1) { + if (IsConvex(points[vindex], points[stack[stackptr - 1]], points[stack[stackptr]])) { + triangle.Triangle(points[vindex], points[stack[stackptr - 1]], points[stack[stackptr]]); + triangles->push_back(triangle); + stackptr--; + } else { + break; + } + } else { + if (IsConvex(points[vindex], points[stack[stackptr]], points[stack[stackptr - 1]])) { + triangle.Triangle(points[vindex], points[stack[stackptr]], points[stack[stackptr - 1]]); + triangles->push_back(triangle); + stackptr--; + } else { + break; + } + } + } + stackptr++; + stack[stackptr] = vindex; + stackptr++; + } + } + vindex = priority[i]; + for (j = 0; j < (stackptr - 1); j++) { + if (vertextypes[stack[j + 1]] == 1) { + triangle.Triangle(points[stack[j]], points[stack[j + 1]], points[vindex]); + } else { + triangle.Triangle(points[stack[j + 1]], points[stack[j]], points[vindex]); + } + triangles->push_back(triangle); + } + + delete[] priority; + delete[] vertextypes; + delete[] stack; + + return 1; +} + +int TPPLPartition::Triangulate_MONO(TPPLPolyList *inpolys, TPPLPolyList *triangles) { + TPPLPolyList monotone; + TPPLPolyList::Element *iter; + + if (!MonotonePartition(inpolys, &monotone)) { + return 0; + } + for (iter = monotone.front(); iter; iter = iter->next()) { + if (!TriangulateMonotone(&(iter->get()), triangles)) { + return 0; + } + } + return 1; +} + +int TPPLPartition::Triangulate_MONO(TPPLPoly *poly, TPPLPolyList *triangles) { + TPPLPolyList polys; + polys.push_back(*poly); + + return Triangulate_MONO(&polys, triangles); +} diff --git a/thirdparty/misc/polypartition.h b/thirdparty/misc/polypartition.h new file mode 100644 index 0000000000..b2d905a3ef --- /dev/null +++ b/thirdparty/misc/polypartition.h @@ -0,0 +1,378 @@ +/*************************************************************************/ +/* Copyright (c) 2011-2021 Ivan Fratric and contributors. */ +/* */ +/* Permission is hereby granted, free of charge, to any person obtaining */ +/* a copy of this software and associated documentation files (the */ +/* "Software"), to deal in the Software without restriction, including */ +/* without limitation the rights to use, copy, modify, merge, publish, */ +/* distribute, sublicense, and/or sell copies of the Software, and to */ +/* permit persons to whom the Software is furnished to do so, subject to */ +/* the following conditions: */ +/* */ +/* The above copyright notice and this permission notice shall be */ +/* included in all copies or substantial portions of the Software. */ +/* */ +/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */ +/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */ +/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/ +/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */ +/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */ +/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */ +/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */ +/*************************************************************************/ + +#ifndef POLYPARTITION_H +#define POLYPARTITION_H + +#include "core/math/vector2.h" +#include "core/templates/list.h" +#include "core/templates/set.h" + +typedef double tppl_float; + +enum TPPLOrientation { + TPPL_ORIENTATION_CW = -1, + TPPL_ORIENTATION_NONE = 0, + TPPL_ORIENTATION_CCW = 1, +}; + +enum TPPLVertexType { + TPPL_VERTEXTYPE_REGULAR = 0, + TPPL_VERTEXTYPE_START = 1, + TPPL_VERTEXTYPE_END = 2, + TPPL_VERTEXTYPE_SPLIT = 3, + TPPL_VERTEXTYPE_MERGE = 4, +}; + +// 2D point structure. +typedef Vector2 TPPLPoint; + +// Polygon implemented as an array of points with a "hole" flag. +class TPPLPoly { + protected: + TPPLPoint *points; + long numpoints; + bool hole; + + public: + // Constructors and destructors. + TPPLPoly(); + ~TPPLPoly(); + + TPPLPoly(const TPPLPoly &src); + TPPLPoly &operator=(const TPPLPoly &src); + + // Getters and setters. + long GetNumPoints() const { + return numpoints; + } + + bool IsHole() const { + return hole; + } + + void SetHole(bool hole) { + this->hole = hole; + } + + TPPLPoint &GetPoint(long i) { + return points[i]; + } + + const TPPLPoint &GetPoint(long i) const { + return points[i]; + } + + TPPLPoint *GetPoints() { + return points; + } + + TPPLPoint &operator[](int i) { + return points[i]; + } + + const TPPLPoint &operator[](int i) const { + return points[i]; + } + + // Clears the polygon points. + void Clear(); + + // Inits the polygon with numpoints vertices. + void Init(long numpoints); + + // Creates a triangle with points p1, p2, and p3. + void Triangle(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3); + + // Inverts the orfer of vertices. + void Invert(); + + // Returns the orientation of the polygon. + // Possible values: + // TPPL_ORIENTATION_CCW: Polygon vertices are in counter-clockwise order. + // TPPL_ORIENTATION_CW: Polygon vertices are in clockwise order. + // TPPL_ORIENTATION_NONE: The polygon has no (measurable) area. + TPPLOrientation GetOrientation() const; + + // Sets the polygon orientation. + // Possible values: + // TPPL_ORIENTATION_CCW: Sets vertices in counter-clockwise order. + // TPPL_ORIENTATION_CW: Sets vertices in clockwise order. + // TPPL_ORIENTATION_NONE: Reverses the orientation of the vertices if there + // is one, otherwise does nothing (if orientation is already NONE). + void SetOrientation(TPPLOrientation orientation); + + // Checks whether a polygon is valid or not. + inline bool Valid() const { return this->numpoints >= 3; } +}; + +#ifdef TPPL_ALLOCATOR +typedef List<TPPLPoly, TPPL_ALLOCATOR(TPPLPoly)> TPPLPolyList; +#else +typedef List<TPPLPoly> TPPLPolyList; +#endif + +class TPPLPartition { + protected: + struct PartitionVertex { + bool isActive; + bool isConvex; + bool isEar; + + TPPLPoint p; + tppl_float angle; + PartitionVertex *previous; + PartitionVertex *next; + + PartitionVertex(); + }; + + struct MonotoneVertex { + TPPLPoint p; + long previous; + long next; + }; + + class VertexSorter { + MonotoneVertex *vertices; + +public: + VertexSorter(MonotoneVertex *v) : + vertices(v) {} + bool operator()(long index1, long index2); + }; + + struct Diagonal { + long index1; + long index2; + }; + +#ifdef TPPL_ALLOCATOR + typedef List<Diagonal, TPPL_ALLOCATOR(Diagonal)> DiagonalList; +#else + typedef List<Diagonal> DiagonalList; +#endif + + // Dynamic programming state for minimum-weight triangulation. + struct DPState { + bool visible; + tppl_float weight; + long bestvertex; + }; + + // Dynamic programming state for convex partitioning. + struct DPState2 { + bool visible; + long weight; + DiagonalList pairs; + }; + + // Edge that intersects the scanline. + struct ScanLineEdge { + mutable long index; + TPPLPoint p1; + TPPLPoint p2; + + // Determines if the edge is to the left of another edge. + bool operator<(const ScanLineEdge &other) const; + + bool IsConvex(const TPPLPoint &p1, const TPPLPoint &p2, const TPPLPoint &p3) const; + }; + + // Standard helper functions. + bool IsConvex(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3); + bool IsReflex(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3); + bool IsInside(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3, TPPLPoint &p); + + bool InCone(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3, TPPLPoint &p); + bool InCone(PartitionVertex *v, TPPLPoint &p); + + int Intersects(TPPLPoint &p11, TPPLPoint &p12, TPPLPoint &p21, TPPLPoint &p22); + + TPPLPoint Normalize(const TPPLPoint &p); + tppl_float Distance(const TPPLPoint &p1, const TPPLPoint &p2); + + // Helper functions for Triangulate_EC. + void UpdateVertexReflexity(PartitionVertex *v); + void UpdateVertex(PartitionVertex *v, PartitionVertex *vertices, long numvertices); + + // Helper functions for ConvexPartition_OPT. + void UpdateState(long a, long b, long w, long i, long j, DPState2 **dpstates); + void TypeA(long i, long j, long k, PartitionVertex *vertices, DPState2 **dpstates); + void TypeB(long i, long j, long k, PartitionVertex *vertices, DPState2 **dpstates); + + // Helper functions for MonotonePartition. + bool Below(TPPLPoint &p1, TPPLPoint &p2); + void AddDiagonal(MonotoneVertex *vertices, long *numvertices, long index1, long index2, + TPPLVertexType *vertextypes, Set<ScanLineEdge>::Element **edgeTreeIterators, + Set<ScanLineEdge> *edgeTree, long *helpers); + + // Triangulates a monotone polygon, used in Triangulate_MONO. + int TriangulateMonotone(TPPLPoly *inPoly, TPPLPolyList *triangles); + + public: + // Simple heuristic procedure for removing holes from a list of polygons. + // It works by creating a diagonal from the right-most hole vertex + // to some other visible vertex. + // Time complexity: O(h*(n^2)), h is the # of holes, n is the # of vertices. + // Space complexity: O(n) + // params: + // inpolys: + // A list of polygons that can contain holes. + // Vertices of all non-hole polys have to be in counter-clockwise order. + // Vertices of all hole polys have to be in clockwise order. + // outpolys: + // A list of polygons without holes. + // Returns 1 on success, 0 on failure. + int RemoveHoles(TPPLPolyList *inpolys, TPPLPolyList *outpolys); + + // Triangulates a polygon by ear clipping. + // Time complexity: O(n^2), n is the number of vertices. + // Space complexity: O(n) + // params: + // poly: + // An input polygon to be triangulated. + // Vertices have to be in counter-clockwise order. + // triangles: + // A list of triangles (result). + // Returns 1 on success, 0 on failure. + int Triangulate_EC(TPPLPoly *poly, TPPLPolyList *triangles); + + // Triangulates a list of polygons that may contain holes by ear clipping + // algorithm. It first calls RemoveHoles to get rid of the holes, and then + // calls Triangulate_EC for each resulting polygon. + // Time complexity: O(h*(n^2)), h is the # of holes, n is the # of vertices. + // Space complexity: O(n) + // params: + // inpolys: + // A list of polygons to be triangulated (can contain holes). + // Vertices of all non-hole polys have to be in counter-clockwise order. + // Vertices of all hole polys have to be in clockwise order. + // triangles: + // A list of triangles (result). + // Returns 1 on success, 0 on failure. + int Triangulate_EC(TPPLPolyList *inpolys, TPPLPolyList *triangles); + + // Creates an optimal polygon triangulation in terms of minimal edge length. + // Time complexity: O(n^3), n is the number of vertices + // Space complexity: O(n^2) + // params: + // poly: + // An input polygon to be triangulated. + // Vertices have to be in counter-clockwise order. + // triangles: + // A list of triangles (result). + // Returns 1 on success, 0 on failure. + int Triangulate_OPT(TPPLPoly *poly, TPPLPolyList *triangles); + + // Triangulates a polygon by first partitioning it into monotone polygons. + // Time complexity: O(n*log(n)), n is the number of vertices. + // Space complexity: O(n) + // params: + // poly: + // An input polygon to be triangulated. + // Vertices have to be in counter-clockwise order. + // triangles: + // A list of triangles (result). + // Returns 1 on success, 0 on failure. + int Triangulate_MONO(TPPLPoly *poly, TPPLPolyList *triangles); + + // Triangulates a list of polygons by first + // partitioning them into monotone polygons. + // Time complexity: O(n*log(n)), n is the number of vertices. + // Space complexity: O(n) + // params: + // inpolys: + // A list of polygons to be triangulated (can contain holes). + // Vertices of all non-hole polys have to be in counter-clockwise order. + // Vertices of all hole polys have to be in clockwise order. + // triangles: + // A list of triangles (result). + // Returns 1 on success, 0 on failure. + int Triangulate_MONO(TPPLPolyList *inpolys, TPPLPolyList *triangles); + + // Creates a monotone partition of a list of polygons that + // can contain holes. Triangulates a set of polygons by + // first partitioning them into monotone polygons. + // Time complexity: O(n*log(n)), n is the number of vertices. + // Space complexity: O(n) + // params: + // inpolys: + // A list of polygons to be triangulated (can contain holes). + // Vertices of all non-hole polys have to be in counter-clockwise order. + // Vertices of all hole polys have to be in clockwise order. + // monotonePolys: + // A list of monotone polygons (result). + // Returns 1 on success, 0 on failure. + int MonotonePartition(TPPLPolyList *inpolys, TPPLPolyList *monotonePolys); + + // Partitions a polygon into convex polygons by using the + // Hertel-Mehlhorn algorithm. The algorithm gives at most four times + // the number of parts as the optimal algorithm, however, in practice + // it works much better than that and often gives optimal partition. + // It uses triangulation obtained by ear clipping as intermediate result. + // Time complexity O(n^2), n is the number of vertices. + // Space complexity: O(n) + // params: + // poly: + // An input polygon to be partitioned. + // Vertices have to be in counter-clockwise order. + // parts: + // Resulting list of convex polygons. + // Returns 1 on success, 0 on failure. + int ConvexPartition_HM(TPPLPoly *poly, TPPLPolyList *parts); + + // Partitions a list of polygons into convex parts by using the + // Hertel-Mehlhorn algorithm. The algorithm gives at most four times + // the number of parts as the optimal algorithm, however, in practice + // it works much better than that and often gives optimal partition. + // It uses triangulation obtained by ear clipping as intermediate result. + // Time complexity O(n^2), n is the number of vertices. + // Space complexity: O(n) + // params: + // inpolys: + // An input list of polygons to be partitioned. Vertices of + // all non-hole polys have to be in counter-clockwise order. + // Vertices of all hole polys have to be in clockwise order. + // parts: + // Resulting list of convex polygons. + // Returns 1 on success, 0 on failure. + int ConvexPartition_HM(TPPLPolyList *inpolys, TPPLPolyList *parts); + + // Optimal convex partitioning (in terms of number of resulting + // convex polygons) using the Keil-Snoeyink algorithm. + // For reference, see M. Keil, J. Snoeyink, "On the time bound for + // convex decomposition of simple polygons", 1998. + // Time complexity O(n^3), n is the number of vertices. + // Space complexity: O(n^3) + // params: + // poly: + // An input polygon to be partitioned. + // Vertices have to be in counter-clockwise order. + // parts: + // Resulting list of convex polygons. + // Returns 1 on success, 0 on failure. + int ConvexPartition_OPT(TPPLPoly *poly, TPPLPolyList *parts); +}; + +#endif diff --git a/thirdparty/misc/triangulator.cpp b/thirdparty/misc/triangulator.cpp deleted file mode 100644 index d6b63c6638..0000000000 --- a/thirdparty/misc/triangulator.cpp +++ /dev/null @@ -1,1550 +0,0 @@ -//Copyright (C) 2011 by Ivan Fratric -// -//Permission is hereby granted, free of charge, to any person obtaining a copy -//of this software and associated documentation files (the "Software"), to deal -//in the Software without restriction, including without limitation the rights -//to use, copy, modify, merge, publish, distribute, sublicense, and/or sell -//copies of the Software, and to permit persons to whom the Software is -//furnished to do so, subject to the following conditions: -// -//The above copyright notice and this permission notice shall be included in -//all copies or substantial portions of the Software. -// -//THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR -//IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, -//FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE -//AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER -//LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, -//OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN -//THE SOFTWARE. - - -#include <stdio.h> -#include <string.h> -#include <math.h> - -#include "triangulator.h" - - -#define TRIANGULATOR_VERTEXTYPE_REGULAR 0 -#define TRIANGULATOR_VERTEXTYPE_START 1 -#define TRIANGULATOR_VERTEXTYPE_END 2 -#define TRIANGULATOR_VERTEXTYPE_SPLIT 3 -#define TRIANGULATOR_VERTEXTYPE_MERGE 4 - -TriangulatorPoly::TriangulatorPoly() { - hole = false; - numpoints = 0; - points = NULL; -} - -TriangulatorPoly::~TriangulatorPoly() { - if(points) delete [] points; -} - -void TriangulatorPoly::Clear() { - if(points) delete [] points; - hole = false; - numpoints = 0; - points = NULL; -} - -void TriangulatorPoly::Init(long numpoints) { - Clear(); - this->numpoints = numpoints; - points = new Vector2[numpoints]; -} - -void TriangulatorPoly::Triangle(Vector2 &p1, Vector2 &p2, Vector2 &p3) { - Init(3); - points[0] = p1; - points[1] = p2; - points[2] = p3; -} - -TriangulatorPoly::TriangulatorPoly(const TriangulatorPoly &src) { - hole = src.hole; - numpoints = src.numpoints; - points = new Vector2[numpoints]; - memcpy(points, src.points, numpoints*sizeof(Vector2)); -} - -TriangulatorPoly& TriangulatorPoly::operator=(const TriangulatorPoly &src) { - Clear(); - hole = src.hole; - numpoints = src.numpoints; - points = new Vector2[numpoints]; - memcpy(points, src.points, numpoints*sizeof(Vector2)); - return *this; -} - -int TriangulatorPoly::GetOrientation() { - long i1,i2; - real_t area = 0; - for(i1=0; i1<numpoints; i1++) { - i2 = i1+1; - if(i2 == numpoints) i2 = 0; - area += points[i1].x * points[i2].y - points[i1].y * points[i2].x; - } - if(area>0) return TRIANGULATOR_CCW; - if(area<0) return TRIANGULATOR_CW; - return 0; -} - -void TriangulatorPoly::SetOrientation(int orientation) { - int polyorientation = GetOrientation(); - if(polyorientation&&(polyorientation!=orientation)) { - Invert(); - } -} - -void TriangulatorPoly::Invert() { - long i; - Vector2 *invpoints; - - invpoints = new Vector2[numpoints]; - for(i=0;i<numpoints;i++) { - invpoints[i] = points[numpoints-i-1]; - } - - delete [] points; - points = invpoints; -} - -Vector2 TriangulatorPartition::Normalize(const Vector2 &p) { - Vector2 r; - real_t n = sqrt(p.x*p.x + p.y*p.y); - if(n!=0) { - r = p/n; - } else { - r.x = 0; - r.y = 0; - } - return r; -} - -real_t TriangulatorPartition::Distance(const Vector2 &p1, const Vector2 &p2) { - real_t dx,dy; - dx = p2.x - p1.x; - dy = p2.y - p1.y; - return(sqrt(dx*dx + dy*dy)); -} - -//checks if two lines intersect -int TriangulatorPartition::Intersects(Vector2 &p11, Vector2 &p12, Vector2 &p21, Vector2 &p22) { - if((p11.x == p21.x)&&(p11.y == p21.y)) return 0; - if((p11.x == p22.x)&&(p11.y == p22.y)) return 0; - if((p12.x == p21.x)&&(p12.y == p21.y)) return 0; - if((p12.x == p22.x)&&(p12.y == p22.y)) return 0; - - Vector2 v1ort,v2ort,v; - real_t dot11,dot12,dot21,dot22; - - v1ort.x = p12.y-p11.y; - v1ort.y = p11.x-p12.x; - - v2ort.x = p22.y-p21.y; - v2ort.y = p21.x-p22.x; - - v = p21-p11; - dot21 = v.x*v1ort.x + v.y*v1ort.y; - v = p22-p11; - dot22 = v.x*v1ort.x + v.y*v1ort.y; - - v = p11-p21; - dot11 = v.x*v2ort.x + v.y*v2ort.y; - v = p12-p21; - dot12 = v.x*v2ort.x + v.y*v2ort.y; - - if(dot11*dot12>0) return 0; - if(dot21*dot22>0) return 0; - - return 1; -} - -//removes holes from inpolys by merging them with non-holes -int TriangulatorPartition::RemoveHoles(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *outpolys) { - List<TriangulatorPoly> polys; - List<TriangulatorPoly>::Element *holeiter,*polyiter,*iter,*iter2; - long i,i2,holepointindex,polypointindex; - Vector2 holepoint,polypoint,bestpolypoint; - Vector2 linep1,linep2; - Vector2 v1,v2; - TriangulatorPoly newpoly; - bool hasholes; - bool pointvisible; - bool pointfound; - - //check for trivial case (no holes) - hasholes = false; - for(iter = inpolys->front(); iter; iter=iter->next()) { - if(iter->get().IsHole()) { - hasholes = true; - break; - } - } - if(!hasholes) { - for(iter = inpolys->front(); iter; iter=iter->next()) { - outpolys->push_back(iter->get()); - } - return 1; - } - - polys = *inpolys; - - while(1) { - //find the hole point with the largest x - hasholes = false; - for(iter = polys.front(); iter; iter=iter->next()) { - if(!iter->get().IsHole()) continue; - - if(!hasholes) { - hasholes = true; - holeiter = iter; - holepointindex = 0; - } - - for(i=0; i < iter->get().GetNumPoints(); i++) { - if(iter->get().GetPoint(i).x > holeiter->get().GetPoint(holepointindex).x) { - holeiter = iter; - holepointindex = i; - } - } - } - if(!hasholes) break; - holepoint = holeiter->get().GetPoint(holepointindex); - - pointfound = false; - for(iter = polys.front(); iter; iter=iter->next()) { - if(iter->get().IsHole()) continue; - for(i=0; i < iter->get().GetNumPoints(); i++) { - if(iter->get().GetPoint(i).x <= holepoint.x) continue; - if(!InCone(iter->get().GetPoint((i+iter->get().GetNumPoints()-1)%(iter->get().GetNumPoints())), - iter->get().GetPoint(i), - iter->get().GetPoint((i+1)%(iter->get().GetNumPoints())), - holepoint)) - continue; - polypoint = iter->get().GetPoint(i); - if(pointfound) { - v1 = Normalize(polypoint-holepoint); - v2 = Normalize(bestpolypoint-holepoint); - if(v2.x > v1.x) continue; - } - pointvisible = true; - for(iter2 = polys.front(); iter2; iter2=iter2->next()) { - if(iter2->get().IsHole()) continue; - for(i2=0; i2 < iter2->get().GetNumPoints(); i2++) { - linep1 = iter2->get().GetPoint(i2); - linep2 = iter2->get().GetPoint((i2+1)%(iter2->get().GetNumPoints())); - if(Intersects(holepoint,polypoint,linep1,linep2)) { - pointvisible = false; - break; - } - } - if(!pointvisible) break; - } - if(pointvisible) { - pointfound = true; - bestpolypoint = polypoint; - polyiter = iter; - polypointindex = i; - } - } - } - - if(!pointfound) return 0; - - newpoly.Init(holeiter->get().GetNumPoints() + polyiter->get().GetNumPoints() + 2); - i2 = 0; - for(i=0;i<=polypointindex;i++) { - newpoly[i2] = polyiter->get().GetPoint(i); - i2++; - } - for(i=0;i<=holeiter->get().GetNumPoints();i++) { - newpoly[i2] = holeiter->get().GetPoint((i+holepointindex)%holeiter->get().GetNumPoints()); - i2++; - } - for(i=polypointindex;i<polyiter->get().GetNumPoints();i++) { - newpoly[i2] = polyiter->get().GetPoint(i); - i2++; - } - - polys.erase(holeiter); - polys.erase(polyiter); - polys.push_back(newpoly); - } - - for(iter = polys.front(); iter; iter=iter->next()) { - outpolys->push_back(iter->get()); - } - - return 1; -} - -bool TriangulatorPartition::IsConvex(Vector2& p1, Vector2& p2, Vector2& p3) { - real_t tmp; - tmp = (p3.y-p1.y)*(p2.x-p1.x)-(p3.x-p1.x)*(p2.y-p1.y); - if(tmp>0) return 1; - else return 0; -} - -bool TriangulatorPartition::IsReflex(Vector2& p1, Vector2& p2, Vector2& p3) { - real_t tmp; - tmp = (p3.y-p1.y)*(p2.x-p1.x)-(p3.x-p1.x)*(p2.y-p1.y); - if(tmp<0) return 1; - else return 0; -} - -bool TriangulatorPartition::IsInside(Vector2& p1, Vector2& p2, Vector2& p3, Vector2 &p) { - if(IsConvex(p1,p,p2)) return false; - if(IsConvex(p2,p,p3)) return false; - if(IsConvex(p3,p,p1)) return false; - return true; -} - -bool TriangulatorPartition::InCone(Vector2 &p1, Vector2 &p2, Vector2 &p3, Vector2 &p) { - bool convex; - - convex = IsConvex(p1,p2,p3); - - if(convex) { - if(!IsConvex(p1,p2,p)) return false; - if(!IsConvex(p2,p3,p)) return false; - return true; - } else { - if(IsConvex(p1,p2,p)) return true; - if(IsConvex(p2,p3,p)) return true; - return false; - } -} - -bool TriangulatorPartition::InCone(PartitionVertex *v, Vector2 &p) { - Vector2 p1,p2,p3; - - p1 = v->previous->p; - p2 = v->p; - p3 = v->next->p; - - return InCone(p1,p2,p3,p); -} - -void TriangulatorPartition::UpdateVertexReflexity(PartitionVertex *v) { - PartitionVertex *v1,*v3; - v1 = v->previous; - v3 = v->next; - v->isConvex = !IsReflex(v1->p,v->p,v3->p); -} - -void TriangulatorPartition::UpdateVertex(PartitionVertex *v, PartitionVertex *vertices, long numvertices) { - long i; - PartitionVertex *v1,*v3; - Vector2 vec1,vec3; - - v1 = v->previous; - v3 = v->next; - - v->isConvex = IsConvex(v1->p,v->p,v3->p); - - vec1 = Normalize(v1->p - v->p); - vec3 = Normalize(v3->p - v->p); - v->angle = vec1.x*vec3.x + vec1.y*vec3.y; - - if(v->isConvex) { - v->isEar = true; - for(i=0;i<numvertices;i++) { - if((vertices[i].p.x==v->p.x)&&(vertices[i].p.y==v->p.y)) continue; - if((vertices[i].p.x==v1->p.x)&&(vertices[i].p.y==v1->p.y)) continue; - if((vertices[i].p.x==v3->p.x)&&(vertices[i].p.y==v3->p.y)) continue; - if(IsInside(v1->p,v->p,v3->p,vertices[i].p)) { - v->isEar = false; - break; - } - } - } else { - v->isEar = false; - } -} - -//triangulation by ear removal -int TriangulatorPartition::Triangulate_EC(TriangulatorPoly *poly, List<TriangulatorPoly> *triangles) { - long numvertices; - PartitionVertex *vertices; - PartitionVertex *ear; - TriangulatorPoly triangle; - long i,j; - bool earfound; - - if(poly->GetNumPoints() < 3) return 0; - if(poly->GetNumPoints() == 3) { - triangles->push_back(*poly); - return 1; - } - - numvertices = poly->GetNumPoints(); - - vertices = new PartitionVertex[numvertices]; - for(i=0;i<numvertices;i++) { - vertices[i].isActive = true; - vertices[i].p = poly->GetPoint(i); - if(i==(numvertices-1)) vertices[i].next=&(vertices[0]); - else vertices[i].next=&(vertices[i+1]); - if(i==0) vertices[i].previous = &(vertices[numvertices-1]); - else vertices[i].previous = &(vertices[i-1]); - } - for(i=0;i<numvertices;i++) { - UpdateVertex(&vertices[i],vertices,numvertices); - } - - for(i=0;i<numvertices-3;i++) { - earfound = false; - //find the most extruded ear - for(j=0;j<numvertices;j++) { - if(!vertices[j].isActive) continue; - if(!vertices[j].isEar) continue; - if(!earfound) { - earfound = true; - ear = &(vertices[j]); - } else { - if(vertices[j].angle > ear->angle) { - ear = &(vertices[j]); - } - } - } - if(!earfound) { - delete [] vertices; - return 0; - } - - triangle.Triangle(ear->previous->p,ear->p,ear->next->p); - triangles->push_back(triangle); - - ear->isActive = false; - ear->previous->next = ear->next; - ear->next->previous = ear->previous; - - if(i==numvertices-4) break; - - UpdateVertex(ear->previous,vertices,numvertices); - UpdateVertex(ear->next,vertices,numvertices); - } - for(i=0;i<numvertices;i++) { - if(vertices[i].isActive) { - triangle.Triangle(vertices[i].previous->p,vertices[i].p,vertices[i].next->p); - triangles->push_back(triangle); - break; - } - } - - delete [] vertices; - - return 1; -} - -int TriangulatorPartition::Triangulate_EC(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *triangles) { - List<TriangulatorPoly> outpolys; - List<TriangulatorPoly>::Element*iter; - - if(!RemoveHoles(inpolys,&outpolys)) return 0; - for(iter=outpolys.front();iter;iter=iter->next()) { - if(!Triangulate_EC(&(iter->get()),triangles)) return 0; - } - return 1; -} - -int TriangulatorPartition::ConvexPartition_HM(TriangulatorPoly *poly, List<TriangulatorPoly> *parts) { - List<TriangulatorPoly> triangles; - List<TriangulatorPoly>::Element *iter1,*iter2; - TriangulatorPoly *poly1,*poly2; - TriangulatorPoly newpoly; - Vector2 d1,d2,p1,p2,p3; - long i11,i12,i21,i22,i13,i23,j,k; - bool isdiagonal; - long numreflex; - - //check if the poly is already convex - numreflex = 0; - for(i11=0;i11<poly->GetNumPoints();i11++) { - if(i11==0) i12 = poly->GetNumPoints()-1; - else i12=i11-1; - if(i11==(poly->GetNumPoints()-1)) i13=0; - else i13=i11+1; - if(IsReflex(poly->GetPoint(i12),poly->GetPoint(i11),poly->GetPoint(i13))) { - numreflex = 1; - break; - } - } - if(numreflex == 0) { - parts->push_back(*poly); - return 1; - } - - if(!Triangulate_EC(poly,&triangles)) return 0; - - for(iter1 = triangles.front(); iter1 ; iter1=iter1->next()) { - poly1 = &(iter1->get()); - for(i11=0;i11<poly1->GetNumPoints();i11++) { - d1 = poly1->GetPoint(i11); - i12 = (i11+1)%(poly1->GetNumPoints()); - d2 = poly1->GetPoint(i12); - - isdiagonal = false; - for(iter2 = iter1; iter2 ; iter2=iter2->next()) { - if(iter1 == iter2) continue; - poly2 = &(iter2->get()); - - for(i21=0;i21<poly2->GetNumPoints();i21++) { - if((d2.x != poly2->GetPoint(i21).x)||(d2.y != poly2->GetPoint(i21).y)) continue; - i22 = (i21+1)%(poly2->GetNumPoints()); - if((d1.x != poly2->GetPoint(i22).x)||(d1.y != poly2->GetPoint(i22).y)) continue; - isdiagonal = true; - break; - } - if(isdiagonal) break; - } - - if(!isdiagonal) continue; - - p2 = poly1->GetPoint(i11); - if(i11 == 0) i13 = poly1->GetNumPoints()-1; - else i13 = i11-1; - p1 = poly1->GetPoint(i13); - if(i22 == (poly2->GetNumPoints()-1)) i23 = 0; - else i23 = i22+1; - p3 = poly2->GetPoint(i23); - - if(!IsConvex(p1,p2,p3)) continue; - - p2 = poly1->GetPoint(i12); - if(i12 == (poly1->GetNumPoints()-1)) i13 = 0; - else i13 = i12+1; - p3 = poly1->GetPoint(i13); - if(i21 == 0) i23 = poly2->GetNumPoints()-1; - else i23 = i21-1; - p1 = poly2->GetPoint(i23); - - if(!IsConvex(p1,p2,p3)) continue; - - newpoly.Init(poly1->GetNumPoints()+poly2->GetNumPoints()-2); - k = 0; - for(j=i12;j!=i11;j=(j+1)%(poly1->GetNumPoints())) { - newpoly[k] = poly1->GetPoint(j); - k++; - } - for(j=i22;j!=i21;j=(j+1)%(poly2->GetNumPoints())) { - newpoly[k] = poly2->GetPoint(j); - k++; - } - - triangles.erase(iter2); - iter1->get() = newpoly; - poly1 = &(iter1->get()); - i11 = -1; - - continue; - } - } - - for(iter1 = triangles.front(); iter1 ; iter1=iter1->next()) { - parts->push_back(iter1->get()); - } - - return 1; -} - -int TriangulatorPartition::ConvexPartition_HM(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *parts) { - List<TriangulatorPoly> outpolys; - List<TriangulatorPoly>::Element* iter; - - if(!RemoveHoles(inpolys,&outpolys)) return 0; - for(iter=outpolys.front();iter;iter=iter->next()) { - if(!ConvexPartition_HM(&(iter->get()),parts)) return 0; - } - return 1; -} - -//minimum-weight polygon triangulation by dynamic programming -//O(n^3) time complexity -//O(n^2) space complexity -int TriangulatorPartition::Triangulate_OPT(TriangulatorPoly *poly, List<TriangulatorPoly> *triangles) { - long i,j,k,gap,n; - DPState **dpstates; - Vector2 p1,p2,p3,p4; - long bestvertex; - real_t weight,minweight,d1,d2; - Diagonal diagonal,newdiagonal; - List<Diagonal> diagonals; - TriangulatorPoly triangle; - int ret = 1; - - n = poly->GetNumPoints(); - dpstates = new DPState *[n]; - for(i=1;i<n;i++) { - dpstates[i] = new DPState[i]; - } - - //init states and visibility - for(i=0;i<(n-1);i++) { - p1 = poly->GetPoint(i); - for(j=i+1;j<n;j++) { - dpstates[j][i].visible = true; - dpstates[j][i].weight = 0; - dpstates[j][i].bestvertex = -1; - if(j!=(i+1)) { - p2 = poly->GetPoint(j); - - //visibility check - if(i==0) p3 = poly->GetPoint(n-1); - else p3 = poly->GetPoint(i-1); - if(i==(n-1)) p4 = poly->GetPoint(0); - else p4 = poly->GetPoint(i+1); - if(!InCone(p3,p1,p4,p2)) { - dpstates[j][i].visible = false; - continue; - } - - if(j==0) p3 = poly->GetPoint(n-1); - else p3 = poly->GetPoint(j-1); - if(j==(n-1)) p4 = poly->GetPoint(0); - else p4 = poly->GetPoint(j+1); - if(!InCone(p3,p2,p4,p1)) { - dpstates[j][i].visible = false; - continue; - } - - for(k=0;k<n;k++) { - p3 = poly->GetPoint(k); - if(k==(n-1)) p4 = poly->GetPoint(0); - else p4 = poly->GetPoint(k+1); - if(Intersects(p1,p2,p3,p4)) { - dpstates[j][i].visible = false; - break; - } - } - } - } - } - dpstates[n-1][0].visible = true; - dpstates[n-1][0].weight = 0; - dpstates[n-1][0].bestvertex = -1; - - for(gap = 2; gap<n; gap++) { - for(i=0; i<(n-gap); i++) { - j = i+gap; - if(!dpstates[j][i].visible) continue; - bestvertex = -1; - for(k=(i+1);k<j;k++) { - if(!dpstates[k][i].visible) continue; - if(!dpstates[j][k].visible) continue; - - if(k<=(i+1)) d1=0; - else d1 = Distance(poly->GetPoint(i),poly->GetPoint(k)); - if(j<=(k+1)) d2=0; - else d2 = Distance(poly->GetPoint(k),poly->GetPoint(j)); - - weight = dpstates[k][i].weight + dpstates[j][k].weight + d1 + d2; - - if((bestvertex == -1)||(weight<minweight)) { - bestvertex = k; - minweight = weight; - } - } - if(bestvertex == -1) { - for(i=1;i<n;i++) { - delete [] dpstates[i]; - } - delete [] dpstates; - - return 0; - } - - dpstates[j][i].bestvertex = bestvertex; - dpstates[j][i].weight = minweight; - } - } - - newdiagonal.index1 = 0; - newdiagonal.index2 = n-1; - diagonals.push_back(newdiagonal); - while(!diagonals.is_empty()) { - diagonal = (diagonals.front()->get()); - diagonals.pop_front(); - bestvertex = dpstates[diagonal.index2][diagonal.index1].bestvertex; - if(bestvertex == -1) { - ret = 0; - break; - } - triangle.Triangle(poly->GetPoint(diagonal.index1),poly->GetPoint(bestvertex),poly->GetPoint(diagonal.index2)); - triangles->push_back(triangle); - if(bestvertex > (diagonal.index1+1)) { - newdiagonal.index1 = diagonal.index1; - newdiagonal.index2 = bestvertex; - diagonals.push_back(newdiagonal); - } - if(diagonal.index2 > (bestvertex+1)) { - newdiagonal.index1 = bestvertex; - newdiagonal.index2 = diagonal.index2; - diagonals.push_back(newdiagonal); - } - } - - for(i=1;i<n;i++) { - delete [] dpstates[i]; - } - delete [] dpstates; - - return ret; -} - -void TriangulatorPartition::UpdateState(long a, long b, long w, long i, long j, DPState2 **dpstates) { - Diagonal newdiagonal; - List<Diagonal> *pairs; - long w2; - - w2 = dpstates[a][b].weight; - if(w>w2) return; - - pairs = &(dpstates[a][b].pairs); - newdiagonal.index1 = i; - newdiagonal.index2 = j; - - if(w<w2) { - pairs->clear(); - pairs->push_front(newdiagonal); - dpstates[a][b].weight = w; - } else { - if((!pairs->is_empty())&&(i <= pairs->front()->get().index1)) return; - while((!pairs->is_empty())&&(pairs->front()->get().index2 >= j)) pairs->pop_front(); - pairs->push_front(newdiagonal); - } -} - -void TriangulatorPartition::TypeA(long i, long j, long k, PartitionVertex *vertices, DPState2 **dpstates) { - List<Diagonal> *pairs; - List<Diagonal>::Element *iter,*lastiter; - long top; - long w; - - if(!dpstates[i][j].visible) return; - top = j; - w = dpstates[i][j].weight; - if(k-j > 1) { - if (!dpstates[j][k].visible) return; - w += dpstates[j][k].weight + 1; - } - if(j-i > 1) { - pairs = &(dpstates[i][j].pairs); - iter = NULL; - lastiter = NULL; - while(iter!=pairs->front()) { - if (!iter) - iter=pairs->back(); - else - iter=iter->prev(); - - if(!IsReflex(vertices[iter->get().index2].p,vertices[j].p,vertices[k].p)) lastiter = iter; - else break; - } - if(lastiter == NULL) w++; - else { - if(IsReflex(vertices[k].p,vertices[i].p,vertices[lastiter->get().index1].p)) w++; - else top = lastiter->get().index1; - } - } - UpdateState(i,k,w,top,j,dpstates); -} - -void TriangulatorPartition::TypeB(long i, long j, long k, PartitionVertex *vertices, DPState2 **dpstates) { - List<Diagonal> *pairs; - List<Diagonal>::Element* iter,*lastiter; - long top; - long w; - - if(!dpstates[j][k].visible) return; - top = j; - w = dpstates[j][k].weight; - - if (j-i > 1) { - if (!dpstates[i][j].visible) return; - w += dpstates[i][j].weight + 1; - } - if (k-j > 1) { - pairs = &(dpstates[j][k].pairs); - - iter = pairs->front(); - if((!pairs->is_empty())&&(!IsReflex(vertices[i].p,vertices[j].p,vertices[iter->get().index1].p))) { - lastiter = iter; - while(iter!=NULL) { - if(!IsReflex(vertices[i].p,vertices[j].p,vertices[iter->get().index1].p)) { - lastiter = iter; - iter=iter->next(); - } - else break; - } - if(IsReflex(vertices[lastiter->get().index2].p,vertices[k].p,vertices[i].p)) w++; - else top = lastiter->get().index2; - } else w++; - } - UpdateState(i,k,w,j,top,dpstates); -} - -int TriangulatorPartition::ConvexPartition_OPT(TriangulatorPoly *poly, List<TriangulatorPoly> *parts) { - Vector2 p1,p2,p3,p4; - PartitionVertex *vertices; - DPState2 **dpstates; - long i,j,k,n,gap; - List<Diagonal> diagonals,diagonals2; - Diagonal diagonal,newdiagonal; - List<Diagonal> *pairs,*pairs2; - List<Diagonal>::Element* iter,*iter2; - int ret; - TriangulatorPoly newpoly; - List<long> indices; - List<long>::Element* iiter; - bool ijreal,jkreal; - - n = poly->GetNumPoints(); - vertices = new PartitionVertex[n]; - - dpstates = new DPState2 *[n]; - for(i=0;i<n;i++) { - dpstates[i] = new DPState2[n]; - } - - //init vertex information - for(i=0;i<n;i++) { - vertices[i].p = poly->GetPoint(i); - vertices[i].isActive = true; - if(i==0) vertices[i].previous = &(vertices[n-1]); - else vertices[i].previous = &(vertices[i-1]); - if(i==(poly->GetNumPoints()-1)) vertices[i].next = &(vertices[0]); - else vertices[i].next = &(vertices[i+1]); - } - for(i=1;i<n;i++) { - UpdateVertexReflexity(&(vertices[i])); - } - - //init states and visibility - for(i=0;i<(n-1);i++) { - p1 = poly->GetPoint(i); - for(j=i+1;j<n;j++) { - dpstates[i][j].visible = true; - if(j==i+1) { - dpstates[i][j].weight = 0; - } else { - dpstates[i][j].weight = 2147483647; - } - if(j!=(i+1)) { - p2 = poly->GetPoint(j); - - //visibility check - if(!InCone(&vertices[i],p2)) { - dpstates[i][j].visible = false; - continue; - } - if(!InCone(&vertices[j],p1)) { - dpstates[i][j].visible = false; - continue; - } - - for(k=0;k<n;k++) { - p3 = poly->GetPoint(k); - if(k==(n-1)) p4 = poly->GetPoint(0); - else p4 = poly->GetPoint(k+1); - if(Intersects(p1,p2,p3,p4)) { - dpstates[i][j].visible = false; - break; - } - } - } - } - } - for(i=0;i<(n-2);i++) { - j = i+2; - if(dpstates[i][j].visible) { - dpstates[i][j].weight = 0; - newdiagonal.index1 = i+1; - newdiagonal.index2 = i+1; - dpstates[i][j].pairs.push_back(newdiagonal); - } - } - - dpstates[0][n-1].visible = true; - vertices[0].isConvex = false; //by convention - - for(gap=3; gap<n; gap++) { - for(i=0;i<n-gap;i++) { - if(vertices[i].isConvex) continue; - k = i+gap; - if(dpstates[i][k].visible) { - if(!vertices[k].isConvex) { - for(j=i+1;j<k;j++) TypeA(i,j,k,vertices,dpstates); - } else { - for(j=i+1;j<(k-1);j++) { - if(vertices[j].isConvex) continue; - TypeA(i,j,k,vertices,dpstates); - } - TypeA(i,k-1,k,vertices,dpstates); - } - } - } - for(k=gap;k<n;k++) { - if(vertices[k].isConvex) continue; - i = k-gap; - if((vertices[i].isConvex)&&(dpstates[i][k].visible)) { - TypeB(i,i+1,k,vertices,dpstates); - for(j=i+2;j<k;j++) { - if(vertices[j].isConvex) continue; - TypeB(i,j,k,vertices,dpstates); - } - } - } - } - - - //recover solution - ret = 1; - newdiagonal.index1 = 0; - newdiagonal.index2 = n-1; - diagonals.push_front(newdiagonal); - while(!diagonals.is_empty()) { - diagonal = (diagonals.front()->get()); - diagonals.pop_front(); - if((diagonal.index2 - diagonal.index1) <=1) continue; - pairs = &(dpstates[diagonal.index1][diagonal.index2].pairs); - if(pairs->is_empty()) { - ret = 0; - break; - } - if(!vertices[diagonal.index1].isConvex) { - iter = pairs->back(); - - j = iter->get().index2; - newdiagonal.index1 = j; - newdiagonal.index2 = diagonal.index2; - diagonals.push_front(newdiagonal); - if((j - diagonal.index1)>1) { - if(iter->get().index1 != iter->get().index2) { - pairs2 = &(dpstates[diagonal.index1][j].pairs); - while(1) { - if(pairs2->is_empty()) { - ret = 0; - break; - } - iter2 = pairs2->back(); - - if(iter->get().index1 != iter2->get().index1) pairs2->pop_back(); - else break; - } - if(ret == 0) break; - } - newdiagonal.index1 = diagonal.index1; - newdiagonal.index2 = j; - diagonals.push_front(newdiagonal); - } - } else { - iter = pairs->front(); - j = iter->get().index1; - newdiagonal.index1 = diagonal.index1; - newdiagonal.index2 = j; - diagonals.push_front(newdiagonal); - if((diagonal.index2 - j) > 1) { - if(iter->get().index1 != iter->get().index2) { - pairs2 = &(dpstates[j][diagonal.index2].pairs); - while(1) { - if(pairs2->is_empty()) { - ret = 0; - break; - } - iter2 = pairs2->front(); - if(iter->get().index2 != iter2->get().index2) pairs2->pop_front(); - else break; - } - if(ret == 0) break; - } - newdiagonal.index1 = j; - newdiagonal.index2 = diagonal.index2; - diagonals.push_front(newdiagonal); - } - } - } - - if(ret == 0) { - for(i=0;i<n;i++) { - delete [] dpstates[i]; - } - delete [] dpstates; - delete [] vertices; - - return ret; - } - - newdiagonal.index1 = 0; - newdiagonal.index2 = n-1; - diagonals.push_front(newdiagonal); - while(!diagonals.is_empty()) { - diagonal = (diagonals.front())->get(); - diagonals.pop_front(); - if((diagonal.index2 - diagonal.index1) <= 1) continue; - - indices.clear(); - diagonals2.clear(); - indices.push_back(diagonal.index1); - indices.push_back(diagonal.index2); - diagonals2.push_front(diagonal); - - while(!diagonals2.is_empty()) { - diagonal = (diagonals2.front()->get()); - diagonals2.pop_front(); - if((diagonal.index2 - diagonal.index1) <= 1) continue; - ijreal = true; - jkreal = true; - pairs = &(dpstates[diagonal.index1][diagonal.index2].pairs); - if(!vertices[diagonal.index1].isConvex) { - iter = pairs->back(); - j = iter->get().index2; - if(iter->get().index1 != iter->get().index2) ijreal = false; - } else { - iter = pairs->front(); - j = iter->get().index1; - if(iter->get().index1 != iter->get().index2) jkreal = false; - } - - newdiagonal.index1 = diagonal.index1; - newdiagonal.index2 = j; - if(ijreal) { - diagonals.push_back(newdiagonal); - } else { - diagonals2.push_back(newdiagonal); - } - - newdiagonal.index1 = j; - newdiagonal.index2 = diagonal.index2; - if(jkreal) { - diagonals.push_back(newdiagonal); - } else { - diagonals2.push_back(newdiagonal); - } - - indices.push_back(j); - } - - indices.sort(); - newpoly.Init((long)indices.size()); - k=0; - for(iiter = indices.front();iiter;iiter=iiter->next()) { - newpoly[k] = vertices[iiter->get()].p; - k++; - } - parts->push_back(newpoly); - } - - for(i=0;i<n;i++) { - delete [] dpstates[i]; - } - delete [] dpstates; - delete [] vertices; - - return ret; -} - -//triangulates a set of polygons by first partitioning them into monotone polygons -//O(n*log(n)) time complexity, O(n) space complexity -//the algorithm used here is outlined in the book -//"Computational Geometry: Algorithms and Applications" -//by Mark de Berg, Otfried Cheong, Marc van Kreveld and Mark Overmars -int TriangulatorPartition::MonotonePartition(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *monotonePolys) { - List<TriangulatorPoly>::Element *iter; - MonotoneVertex *vertices; - long i,numvertices,vindex,vindex2,newnumvertices,maxnumvertices; - long polystartindex, polyendindex; - TriangulatorPoly *poly; - MonotoneVertex *v,*v2,*vprev,*vnext; - ScanLineEdge newedge; - bool error = false; - - numvertices = 0; - for(iter = inpolys->front(); iter ; iter=iter->next()) { - numvertices += iter->get().GetNumPoints(); - } - - maxnumvertices = numvertices*3; - vertices = new MonotoneVertex[maxnumvertices]; - newnumvertices = numvertices; - - polystartindex = 0; - for(iter = inpolys->front(); iter ; iter=iter->next()) { - poly = &(iter->get()); - polyendindex = polystartindex + poly->GetNumPoints()-1; - for(i=0;i<poly->GetNumPoints();i++) { - vertices[i+polystartindex].p = poly->GetPoint(i); - if(i==0) vertices[i+polystartindex].previous = polyendindex; - else vertices[i+polystartindex].previous = i+polystartindex-1; - if(i==(poly->GetNumPoints()-1)) vertices[i+polystartindex].next = polystartindex; - else vertices[i+polystartindex].next = i+polystartindex+1; - } - polystartindex = polyendindex+1; - } - - //construct the priority queue - long *priority = new long [numvertices]; - for(i=0;i<numvertices;i++) priority[i] = i; - SortArray<long,VertexSorter> sorter; - sorter.compare.vertices=vertices; - sorter.sort(priority,numvertices); - - //determine vertex types - char *vertextypes = new char[maxnumvertices]; - for(i=0;i<numvertices;i++) { - v = &(vertices[i]); - vprev = &(vertices[v->previous]); - vnext = &(vertices[v->next]); - - if(Below(vprev->p,v->p)&&Below(vnext->p,v->p)) { - if(IsConvex(vnext->p,vprev->p,v->p)) { - vertextypes[i] = TRIANGULATOR_VERTEXTYPE_START; - } else { - vertextypes[i] = TRIANGULATOR_VERTEXTYPE_SPLIT; - } - } else if(Below(v->p,vprev->p)&&Below(v->p,vnext->p)) { - if(IsConvex(vnext->p,vprev->p,v->p)) - { - vertextypes[i] = TRIANGULATOR_VERTEXTYPE_END; - } else { - vertextypes[i] = TRIANGULATOR_VERTEXTYPE_MERGE; - } - } else { - vertextypes[i] = TRIANGULATOR_VERTEXTYPE_REGULAR; - } - } - - //helpers - long *helpers = new long[maxnumvertices]; - - //binary search tree that holds edges intersecting the scanline - //note that while set doesn't actually have to be implemented as a tree - //complexity requirements for operations are the same as for the balanced binary search tree - Set<ScanLineEdge> edgeTree; - //store iterators to the edge tree elements - //this makes deleting existing edges much faster - Set<ScanLineEdge>::Element **edgeTreeIterators,*edgeIter; - edgeTreeIterators = new Set<ScanLineEdge>::Element*[maxnumvertices]; - //Pair<Set<ScanLineEdge>::Element*,bool> edgeTreeRet; - for(i = 0; i<numvertices; i++) edgeTreeIterators[i] = NULL; - - //for each vertex - for(i=0;i<numvertices;i++) { - vindex = priority[i]; - v = &(vertices[vindex]); - vindex2 = vindex; - v2 = v; - - //depending on the vertex type, do the appropriate action - //comments in the following sections are copied from "Computational Geometry: Algorithms and Applications" - switch(vertextypes[vindex]) { - case TRIANGULATOR_VERTEXTYPE_START: - //Insert ei in T and set helper(ei) to vi. - newedge.p1 = v->p; - newedge.p2 = vertices[v->next].p; - newedge.index = vindex; - edgeTreeIterators[vindex] = edgeTree.insert(newedge); - helpers[vindex] = vindex; - break; - - case TRIANGULATOR_VERTEXTYPE_END: - //if helper(ei-1) is a merge vertex - if(vertextypes[helpers[v->previous]]==TRIANGULATOR_VERTEXTYPE_MERGE) { - //Insert the diagonal connecting vi to helper(ei-1) in D. - AddDiagonal(vertices,&newnumvertices,vindex,helpers[v->previous], - vertextypes, edgeTreeIterators, &edgeTree, helpers); - } - //Delete ei-1 from T - edgeTree.erase(edgeTreeIterators[v->previous]); - break; - - case TRIANGULATOR_VERTEXTYPE_SPLIT: - //Search in T to find the edge e j directly left of vi. - newedge.p1 = v->p; - newedge.p2 = v->p; - edgeIter = edgeTree.lower_bound(newedge); - if(edgeIter == edgeTree.front()) { - error = true; - break; - } - edgeIter=edgeIter->prev(); - //Insert the diagonal connecting vi to helper(ej) in D. - AddDiagonal(vertices,&newnumvertices,vindex,helpers[edgeIter->get().index], - vertextypes, edgeTreeIterators, &edgeTree, helpers); - vindex2 = newnumvertices-2; - v2 = &(vertices[vindex2]); - //helper(e j)�vi - helpers[edgeIter->get().index] = vindex; - //Insert ei in T and set helper(ei) to vi. - newedge.p1 = v2->p; - newedge.p2 = vertices[v2->next].p; - newedge.index = vindex2; - - edgeTreeIterators[vindex2] = edgeTree.insert(newedge); - helpers[vindex2] = vindex2; - break; - - case TRIANGULATOR_VERTEXTYPE_MERGE: - //if helper(ei-1) is a merge vertex - if(vertextypes[helpers[v->previous]]==TRIANGULATOR_VERTEXTYPE_MERGE) { - //Insert the diagonal connecting vi to helper(ei-1) in D. - AddDiagonal(vertices,&newnumvertices,vindex,helpers[v->previous], - vertextypes, edgeTreeIterators, &edgeTree, helpers); - vindex2 = newnumvertices-2; - v2 = &(vertices[vindex2]); - } - //Delete ei-1 from T. - edgeTree.erase(edgeTreeIterators[v->previous]); - //Search in T to find the edge e j directly left of vi. - newedge.p1 = v->p; - newedge.p2 = v->p; - edgeIter = edgeTree.lower_bound(newedge); - if(edgeIter == edgeTree.front()) { - error = true; - break; - } - edgeIter=edgeIter->prev(); - //if helper(ej) is a merge vertex - if(vertextypes[helpers[edgeIter->get().index]]==TRIANGULATOR_VERTEXTYPE_MERGE) { - //Insert the diagonal connecting vi to helper(e j) in D. - AddDiagonal(vertices,&newnumvertices,vindex2,helpers[edgeIter->get().index], - vertextypes, edgeTreeIterators, &edgeTree, helpers); - } - //helper(e j)�vi - helpers[edgeIter->get().index] = vindex2; - break; - - case TRIANGULATOR_VERTEXTYPE_REGULAR: - //if the interior of P lies to the right of vi - if(Below(v->p,vertices[v->previous].p)) { - //if helper(ei-1) is a merge vertex - if(vertextypes[helpers[v->previous]]==TRIANGULATOR_VERTEXTYPE_MERGE) { - //Insert the diagonal connecting vi to helper(ei-1) in D. - AddDiagonal(vertices,&newnumvertices,vindex,helpers[v->previous], - vertextypes, edgeTreeIterators, &edgeTree, helpers); - vindex2 = newnumvertices-2; - v2 = &(vertices[vindex2]); - } - //Delete ei-1 from T. - edgeTree.erase(edgeTreeIterators[v->previous]); - //Insert ei in T and set helper(ei) to vi. - newedge.p1 = v2->p; - newedge.p2 = vertices[v2->next].p; - newedge.index = vindex2; - edgeTreeIterators[vindex2] = edgeTree.insert(newedge); - helpers[vindex2] = vindex; - } else { - //Search in T to find the edge ej directly left of vi. - newedge.p1 = v->p; - newedge.p2 = v->p; - edgeIter = edgeTree.lower_bound(newedge); - if(edgeIter == edgeTree.front()) { - error = true; - break; - } - edgeIter=edgeIter->prev(); - //if helper(ej) is a merge vertex - if(vertextypes[helpers[edgeIter->get().index]]==TRIANGULATOR_VERTEXTYPE_MERGE) { - //Insert the diagonal connecting vi to helper(e j) in D. - AddDiagonal(vertices,&newnumvertices,vindex,helpers[edgeIter->get().index], - vertextypes, edgeTreeIterators, &edgeTree, helpers); - } - //helper(e j)�vi - helpers[edgeIter->get().index] = vindex; - } - break; - } - - if(error) break; - } - - char *used = new char[newnumvertices]; - memset(used,0,newnumvertices*sizeof(char)); - - if(!error) { - //return result - long size; - TriangulatorPoly mpoly; - for(i=0;i<newnumvertices;i++) { - if(used[i]) continue; - v = &(vertices[i]); - vnext = &(vertices[v->next]); - size = 1; - while(vnext!=v) { - vnext = &(vertices[vnext->next]); - size++; - } - mpoly.Init(size); - v = &(vertices[i]); - mpoly[0] = v->p; - vnext = &(vertices[v->next]); - size = 1; - used[i] = 1; - used[v->next] = 1; - while(vnext!=v) { - mpoly[size] = vnext->p; - used[vnext->next] = 1; - vnext = &(vertices[vnext->next]); - size++; - } - monotonePolys->push_back(mpoly); - } - } - - //cleanup - delete [] vertices; - delete [] priority; - delete [] vertextypes; - delete [] edgeTreeIterators; - delete [] helpers; - delete [] used; - - if(error) { - return 0; - } else { - return 1; - } -} - -//adds a diagonal to the doubly-connected list of vertices -void TriangulatorPartition::AddDiagonal(MonotoneVertex *vertices, long *numvertices, long index1, long index2, - char *vertextypes, Set<ScanLineEdge>::Element **edgeTreeIterators, - Set<ScanLineEdge> *edgeTree, long *helpers) -{ - long newindex1,newindex2; - - newindex1 = *numvertices; - (*numvertices)++; - newindex2 = *numvertices; - (*numvertices)++; - - vertices[newindex1].p = vertices[index1].p; - vertices[newindex2].p = vertices[index2].p; - - vertices[newindex2].next = vertices[index2].next; - vertices[newindex1].next = vertices[index1].next; - - vertices[vertices[index2].next].previous = newindex2; - vertices[vertices[index1].next].previous = newindex1; - - vertices[index1].next = newindex2; - vertices[newindex2].previous = index1; - - vertices[index2].next = newindex1; - vertices[newindex1].previous = index2; - - //update all relevant structures - vertextypes[newindex1] = vertextypes[index1]; - edgeTreeIterators[newindex1] = edgeTreeIterators[index1]; - helpers[newindex1] = helpers[index1]; - if(edgeTreeIterators[newindex1] != NULL) - edgeTreeIterators[newindex1]->get().index = newindex1; - vertextypes[newindex2] = vertextypes[index2]; - edgeTreeIterators[newindex2] = edgeTreeIterators[index2]; - helpers[newindex2] = helpers[index2]; - if(edgeTreeIterators[newindex2] != NULL) - edgeTreeIterators[newindex2]->get().index = newindex2; -} - -bool TriangulatorPartition::Below(Vector2 &p1, Vector2 &p2) { - if(p1.y < p2.y) return true; - else if(p1.y == p2.y) { - if(p1.x < p2.x) return true; - } - return false; -} - - - - - -//sorts in the falling order of y values, if y is equal, x is used instead -bool TriangulatorPartition::VertexSorter::operator() (long index1, long index2) const { - if(vertices[index1].p.y > vertices[index2].p.y) return true; - else if(vertices[index1].p.y == vertices[index2].p.y) { - if(vertices[index1].p.x > vertices[index2].p.x) return true; - } - return false; -} - -bool TriangulatorPartition::ScanLineEdge::IsConvex(const Vector2& p1, const Vector2& p2, const Vector2& p3) const { - real_t tmp; - tmp = (p3.y-p1.y)*(p2.x-p1.x)-(p3.x-p1.x)*(p2.y-p1.y); - if(tmp>0) return 1; - else return 0; -} - -bool TriangulatorPartition::ScanLineEdge::operator < (const ScanLineEdge & other) const { - if(other.p1.y == other.p2.y) { - if(p1.y == p2.y) { - if(p1.y < other.p1.y) return true; - else return false; - } - if(IsConvex(p1,p2,other.p1)) return true; - else return false; - } else if(p1.y == p2.y) { - if(IsConvex(other.p1,other.p2,p1)) return false; - else return true; - } else if(p1.y < other.p1.y) { - if(IsConvex(other.p1,other.p2,p1)) return false; - else return true; - } else { - if(IsConvex(p1,p2,other.p1)) return true; - else return false; - } -} - -//triangulates monotone polygon -//O(n) time, O(n) space complexity -int TriangulatorPartition::TriangulateMonotone(TriangulatorPoly *inPoly, List<TriangulatorPoly> *triangles) { - long i,i2,j,topindex,bottomindex,leftindex,rightindex,vindex; - Vector2 *points; - long numpoints; - TriangulatorPoly triangle; - - numpoints = inPoly->GetNumPoints(); - points = inPoly->GetPoints(); - - //trivial calses - if(numpoints < 3) return 0; - if(numpoints == 3) { - triangles->push_back(*inPoly); - } - - topindex = 0; bottomindex=0; - for(i=1;i<numpoints;i++) { - if(Below(points[i],points[bottomindex])) bottomindex = i; - if(Below(points[topindex],points[i])) topindex = i; - } - - //check if the poly is really monotone - i = topindex; - while(i!=bottomindex) { - i2 = i+1; if(i2>=numpoints) i2 = 0; - if(!Below(points[i2],points[i])) return 0; - i = i2; - } - i = bottomindex; - while(i!=topindex) { - i2 = i+1; if(i2>=numpoints) i2 = 0; - if(!Below(points[i],points[i2])) return 0; - i = i2; - } - - char *vertextypes = new char[numpoints]; - long *priority = new long[numpoints]; - - //merge left and right vertex chains - priority[0] = topindex; - vertextypes[topindex] = 0; - leftindex = topindex+1; if(leftindex>=numpoints) leftindex = 0; - rightindex = topindex-1; if(rightindex<0) rightindex = numpoints-1; - for(i=1;i<(numpoints-1);i++) { - if(leftindex==bottomindex) { - priority[i] = rightindex; - rightindex--; if(rightindex<0) rightindex = numpoints-1; - vertextypes[priority[i]] = -1; - } else if(rightindex==bottomindex) { - priority[i] = leftindex; - leftindex++; if(leftindex>=numpoints) leftindex = 0; - vertextypes[priority[i]] = 1; - } else { - if(Below(points[leftindex],points[rightindex])) { - priority[i] = rightindex; - rightindex--; if(rightindex<0) rightindex = numpoints-1; - vertextypes[priority[i]] = -1; - } else { - priority[i] = leftindex; - leftindex++; if(leftindex>=numpoints) leftindex = 0; - vertextypes[priority[i]] = 1; - } - } - } - priority[i] = bottomindex; - vertextypes[bottomindex] = 0; - - long *stack = new long[numpoints]; - long stackptr = 0; - - stack[0] = priority[0]; - stack[1] = priority[1]; - stackptr = 2; - - //for each vertex from top to bottom trim as many triangles as possible - for(i=2;i<(numpoints-1);i++) { - vindex = priority[i]; - if(vertextypes[vindex]!=vertextypes[stack[stackptr-1]]) { - for(j=0;j<(stackptr-1);j++) { - if(vertextypes[vindex]==1) { - triangle.Triangle(points[stack[j+1]],points[stack[j]],points[vindex]); - } else { - triangle.Triangle(points[stack[j]],points[stack[j+1]],points[vindex]); - } - triangles->push_back(triangle); - } - stack[0] = priority[i-1]; - stack[1] = priority[i]; - stackptr = 2; - } else { - stackptr--; - while(stackptr>0) { - if(vertextypes[vindex]==1) { - if(IsConvex(points[vindex],points[stack[stackptr-1]],points[stack[stackptr]])) { - triangle.Triangle(points[vindex],points[stack[stackptr-1]],points[stack[stackptr]]); - triangles->push_back(triangle); - stackptr--; - } else { - break; - } - } else { - if(IsConvex(points[vindex],points[stack[stackptr]],points[stack[stackptr-1]])) { - triangle.Triangle(points[vindex],points[stack[stackptr]],points[stack[stackptr-1]]); - triangles->push_back(triangle); - stackptr--; - } else { - break; - } - } - } - stackptr++; - stack[stackptr] = vindex; - stackptr++; - } - } - vindex = priority[i]; - for(j=0;j<(stackptr-1);j++) { - if(vertextypes[stack[j+1]]==1) { - triangle.Triangle(points[stack[j]],points[stack[j+1]],points[vindex]); - } else { - triangle.Triangle(points[stack[j+1]],points[stack[j]],points[vindex]); - } - triangles->push_back(triangle); - } - - delete [] priority; - delete [] vertextypes; - delete [] stack; - - return 1; -} - -int TriangulatorPartition::Triangulate_MONO(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *triangles) { - List<TriangulatorPoly> monotone; - List<TriangulatorPoly>::Element* iter; - - if(!MonotonePartition(inpolys,&monotone)) return 0; - for(iter = monotone.front(); iter;iter=iter->next()) { - if(!TriangulateMonotone(&(iter->get()),triangles)) return 0; - } - return 1; -} - -int TriangulatorPartition::Triangulate_MONO(TriangulatorPoly *poly, List<TriangulatorPoly> *triangles) { - List<TriangulatorPoly> polys; - polys.push_back(*poly); - - return Triangulate_MONO(&polys, triangles); -} diff --git a/thirdparty/misc/triangulator.h b/thirdparty/misc/triangulator.h deleted file mode 100644 index 24b79e7d34..0000000000 --- a/thirdparty/misc/triangulator.h +++ /dev/null @@ -1,306 +0,0 @@ -//Copyright (C) 2011 by Ivan Fratric -// -//Permission is hereby granted, free of charge, to any person obtaining a copy -//of this software and associated documentation files (the "Software"), to deal -//in the Software without restriction, including without limitation the rights -//to use, copy, modify, merge, publish, distribute, sublicense, and/or sell -//copies of the Software, and to permit persons to whom the Software is -//furnished to do so, subject to the following conditions: -// -//The above copyright notice and this permission notice shall be included in -//all copies or substantial portions of the Software. -// -//THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR -//IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, -//FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE -//AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER -//LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, -//OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN -//THE SOFTWARE. - -#ifndef TRIANGULATOR_H -#define TRIANGULATOR_H - -#include "core/templates/list.h" -#include "core/math/vector2.h" -#include "core/templates/set.h" - -//2D point structure - -#define TRIANGULATOR_CCW 1 -#define TRIANGULATOR_CW -1 -//Polygon implemented as an array of points with a 'hole' flag -class TriangulatorPoly { -protected: - - - - Vector2 *points; - long numpoints; - bool hole; - -public: - - //constructors/destructors - TriangulatorPoly(); - ~TriangulatorPoly(); - - TriangulatorPoly(const TriangulatorPoly &src); - TriangulatorPoly& operator=(const TriangulatorPoly &src); - - //getters and setters - long GetNumPoints() { - return numpoints; - } - - bool IsHole() { - return hole; - } - - void SetHole(bool hole) { - this->hole = hole; - } - - Vector2 &GetPoint(long i) { - return points[i]; - } - - Vector2 *GetPoints() { - return points; - } - - Vector2& operator[] (int i) { - return points[i]; - } - - //clears the polygon points - void Clear(); - - //inits the polygon with numpoints vertices - void Init(long numpoints); - - //creates a triangle with points p1,p2,p3 - void Triangle(Vector2 &p1, Vector2 &p2, Vector2 &p3); - - //inverts the orfer of vertices - void Invert(); - - //returns the orientation of the polygon - //possible values: - // Triangulator_CCW : polygon vertices are in counter-clockwise order - // Triangulator_CW : polygon vertices are in clockwise order - // 0 : the polygon has no (measurable) area - int GetOrientation(); - - //sets the polygon orientation - //orientation can be - // Triangulator_CCW : sets vertices in counter-clockwise order - // Triangulator_CW : sets vertices in clockwise order - void SetOrientation(int orientation); -}; - -class TriangulatorPartition { -protected: - struct PartitionVertex { - bool isActive; - bool isConvex; - bool isEar; - - Vector2 p; - real_t angle; - PartitionVertex *previous; - PartitionVertex *next; - }; - - struct MonotoneVertex { - Vector2 p; - long previous; - long next; - }; - - struct VertexSorter{ - mutable MonotoneVertex *vertices; - bool operator() (long index1, long index2) const; - }; - - struct Diagonal { - long index1; - long index2; - }; - - //dynamic programming state for minimum-weight triangulation - struct DPState { - bool visible; - real_t weight; - long bestvertex; - }; - - //dynamic programming state for convex partitioning - struct DPState2 { - bool visible; - long weight; - List<Diagonal> pairs; - }; - - //edge that intersects the scanline - struct ScanLineEdge { - mutable long index; - Vector2 p1; - Vector2 p2; - - //determines if the edge is to the left of another edge - bool operator< (const ScanLineEdge & other) const; - - bool IsConvex(const Vector2& p1, const Vector2& p2, const Vector2& p3) const; - }; - - //standard helper functions - bool IsConvex(Vector2& p1, Vector2& p2, Vector2& p3); - bool IsReflex(Vector2& p1, Vector2& p2, Vector2& p3); - bool IsInside(Vector2& p1, Vector2& p2, Vector2& p3, Vector2 &p); - - bool InCone(Vector2 &p1, Vector2 &p2, Vector2 &p3, Vector2 &p); - bool InCone(PartitionVertex *v, Vector2 &p); - - int Intersects(Vector2 &p11, Vector2 &p12, Vector2 &p21, Vector2 &p22); - - Vector2 Normalize(const Vector2 &p); - real_t Distance(const Vector2 &p1, const Vector2 &p2); - - //helper functions for Triangulate_EC - void UpdateVertexReflexity(PartitionVertex *v); - void UpdateVertex(PartitionVertex *v,PartitionVertex *vertices, long numvertices); - - //helper functions for ConvexPartition_OPT - void UpdateState(long a, long b, long w, long i, long j, DPState2 **dpstates); - void TypeA(long i, long j, long k, PartitionVertex *vertices, DPState2 **dpstates); - void TypeB(long i, long j, long k, PartitionVertex *vertices, DPState2 **dpstates); - - //helper functions for MonotonePartition - bool Below(Vector2 &p1, Vector2 &p2); - void AddDiagonal(MonotoneVertex *vertices, long *numvertices, long index1, long index2, - char *vertextypes, Set<ScanLineEdge>::Element **edgeTreeIterators, - Set<ScanLineEdge> *edgeTree, long *helpers); - - //triangulates a monotone polygon, used in Triangulate_MONO - int TriangulateMonotone(TriangulatorPoly *inPoly, List<TriangulatorPoly> *triangles); - -public: - - //simple heuristic procedure for removing holes from a list of polygons - //works by creating a diagonal from the rightmost hole vertex to some visible vertex - //time complexity: O(h*(n^2)), h is the number of holes, n is the number of vertices - //space complexity: O(n) - //params: - // inpolys : a list of polygons that can contain holes - // vertices of all non-hole polys have to be in counter-clockwise order - // vertices of all hole polys have to be in clockwise order - // outpolys : a list of polygons without holes - //returns 1 on success, 0 on failure - int RemoveHoles(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *outpolys); - - //triangulates a polygon by ear clipping - //time complexity O(n^2), n is the number of vertices - //space complexity: O(n) - //params: - // poly : an input polygon to be triangulated - // vertices have to be in counter-clockwise order - // triangles : a list of triangles (result) - //returns 1 on success, 0 on failure - int Triangulate_EC(TriangulatorPoly *poly, List<TriangulatorPoly> *triangles); - - //triangulates a list of polygons that may contain holes by ear clipping algorithm - //first calls RemoveHoles to get rid of the holes, and then Triangulate_EC for each resulting polygon - //time complexity: O(h*(n^2)), h is the number of holes, n is the number of vertices - //space complexity: O(n) - //params: - // inpolys : a list of polygons to be triangulated (can contain holes) - // vertices of all non-hole polys have to be in counter-clockwise order - // vertices of all hole polys have to be in clockwise order - // triangles : a list of triangles (result) - //returns 1 on success, 0 on failure - int Triangulate_EC(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *triangles); - - //creates an optimal polygon triangulation in terms of minimal edge length - //time complexity: O(n^3), n is the number of vertices - //space complexity: O(n^2) - //params: - // poly : an input polygon to be triangulated - // vertices have to be in counter-clockwise order - // triangles : a list of triangles (result) - //returns 1 on success, 0 on failure - int Triangulate_OPT(TriangulatorPoly *poly, List<TriangulatorPoly> *triangles); - - //triangulates a polygons by firstly partitioning it into monotone polygons - //time complexity: O(n*log(n)), n is the number of vertices - //space complexity: O(n) - //params: - // poly : an input polygon to be triangulated - // vertices have to be in counter-clockwise order - // triangles : a list of triangles (result) - //returns 1 on success, 0 on failure - int Triangulate_MONO(TriangulatorPoly *poly, List<TriangulatorPoly> *triangles); - - //triangulates a list of polygons by firstly partitioning them into monotone polygons - //time complexity: O(n*log(n)), n is the number of vertices - //space complexity: O(n) - //params: - // inpolys : a list of polygons to be triangulated (can contain holes) - // vertices of all non-hole polys have to be in counter-clockwise order - // vertices of all hole polys have to be in clockwise order - // triangles : a list of triangles (result) - //returns 1 on success, 0 on failure - int Triangulate_MONO(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *triangles); - - //creates a monotone partition of a list of polygons that can contain holes - //time complexity: O(n*log(n)), n is the number of vertices - //space complexity: O(n) - //params: - // inpolys : a list of polygons to be triangulated (can contain holes) - // vertices of all non-hole polys have to be in counter-clockwise order - // vertices of all hole polys have to be in clockwise order - // monotonePolys : a list of monotone polygons (result) - //returns 1 on success, 0 on failure - int MonotonePartition(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *monotonePolys); - - //partitions a polygon into convex polygons by using Hertel-Mehlhorn algorithm - //the algorithm gives at most four times the number of parts as the optimal algorithm - //however, in practice it works much better than that and often gives optimal partition - //uses triangulation obtained by ear clipping as intermediate result - //time complexity O(n^2), n is the number of vertices - //space complexity: O(n) - //params: - // poly : an input polygon to be partitioned - // vertices have to be in counter-clockwise order - // parts : resulting list of convex polygons - //returns 1 on success, 0 on failure - int ConvexPartition_HM(TriangulatorPoly *poly, List<TriangulatorPoly> *parts); - - //partitions a list of polygons into convex parts by using Hertel-Mehlhorn algorithm - //the algorithm gives at most four times the number of parts as the optimal algorithm - //however, in practice it works much better than that and often gives optimal partition - //uses triangulation obtained by ear clipping as intermediate result - //time complexity O(n^2), n is the number of vertices - //space complexity: O(n) - //params: - // inpolys : an input list of polygons to be partitioned - // vertices of all non-hole polys have to be in counter-clockwise order - // vertices of all hole polys have to be in clockwise order - // parts : resulting list of convex polygons - //returns 1 on success, 0 on failure - int ConvexPartition_HM(List<TriangulatorPoly> *inpolys, List<TriangulatorPoly> *parts); - - //optimal convex partitioning (in terms of number of resulting convex polygons) - //using the Keil-Snoeyink algorithm - //M. Keil, J. Snoeyink, "On the time bound for convex decomposition of simple polygons", 1998 - //time complexity O(n^3), n is the number of vertices - //space complexity: O(n^3) - // poly : an input polygon to be partitioned - // vertices have to be in counter-clockwise order - // parts : resulting list of convex polygons - //returns 1 on success, 0 on failure - int ConvexPartition_OPT(TriangulatorPoly *poly, List<TriangulatorPoly> *parts); -}; - - -#endif |