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Diffstat (limited to 'thirdparty/misc/polypartition.cpp')
| -rw-r--r-- | thirdparty/misc/polypartition.cpp | 1849 |
1 files changed, 1849 insertions, 0 deletions
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); +} |