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Diffstat (limited to 'thirdparty/bullet/src/Bullet3Geometry/b3ConvexHullComputer.cpp')
| -rw-r--r-- | thirdparty/bullet/src/Bullet3Geometry/b3ConvexHullComputer.cpp | 2755 |
1 files changed, 2755 insertions, 0 deletions
diff --git a/thirdparty/bullet/src/Bullet3Geometry/b3ConvexHullComputer.cpp b/thirdparty/bullet/src/Bullet3Geometry/b3ConvexHullComputer.cpp new file mode 100644 index 0000000000..18835c38d5 --- /dev/null +++ b/thirdparty/bullet/src/Bullet3Geometry/b3ConvexHullComputer.cpp @@ -0,0 +1,2755 @@ +/* +Copyright (c) 2011 Ole Kniemeyer, MAXON, www.maxon.net + +This software is provided 'as-is', without any express or implied warranty. +In no event will the authors be held liable for any damages arising from the use of this software. +Permission is granted to anyone to use this software for any purpose, +including commercial applications, and to alter it and redistribute it freely, +subject to the following restrictions: + +1. The origin of this software must not be misrepresented; you must not claim that you wrote the original software. If you use this software in a product, an acknowledgment in the product documentation would be appreciated but is not required. +2. Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software. +3. This notice may not be removed or altered from any source distribution. +*/ + +#include <string.h> + +#include "b3ConvexHullComputer.h" +#include "Bullet3Common/b3AlignedObjectArray.h" +#include "Bullet3Common/b3MinMax.h" +#include "Bullet3Common/b3Vector3.h" + +#ifdef __GNUC__ + #include <stdint.h> + typedef int32_t btInt32_t; + typedef int64_t btInt64_t; + typedef uint32_t btUint32_t; + typedef uint64_t btUint64_t; +#elif defined(_MSC_VER) + typedef __int32 btInt32_t; + typedef __int64 btInt64_t; + typedef unsigned __int32 btUint32_t; + typedef unsigned __int64 btUint64_t; +#else + typedef int btInt32_t; + typedef long long int btInt64_t; + typedef unsigned int btUint32_t; + typedef unsigned long long int btUint64_t; +#endif + + +//The definition of USE_X86_64_ASM is moved into the build system. You can enable it manually by commenting out the following lines +//#if (defined(__GNUC__) && defined(__x86_64__) && !defined(__ICL)) // || (defined(__ICL) && defined(_M_X64)) bug in Intel compiler, disable inline assembly +// #define USE_X86_64_ASM +//#endif + + +//#define DEBUG_CONVEX_HULL +//#define SHOW_ITERATIONS + +#if defined(DEBUG_CONVEX_HULL) || defined(SHOW_ITERATIONS) + #include <stdio.h> +#endif + +// Convex hull implementation based on Preparata and Hong +// Ole Kniemeyer, MAXON Computer GmbH +class b3ConvexHullInternal +{ + public: + + class Point64 + { + public: + btInt64_t x; + btInt64_t y; + btInt64_t z; + + Point64(btInt64_t x, btInt64_t y, btInt64_t z): x(x), y(y), z(z) + { + } + + bool isZero() + { + return (x == 0) && (y == 0) && (z == 0); + } + + btInt64_t dot(const Point64& b) const + { + return x * b.x + y * b.y + z * b.z; + } + }; + + class Point32 + { + public: + btInt32_t x; + btInt32_t y; + btInt32_t z; + int index; + + Point32() + { + } + + Point32(btInt32_t x, btInt32_t y, btInt32_t z): x(x), y(y), z(z), index(-1) + { + } + + bool operator==(const Point32& b) const + { + return (x == b.x) && (y == b.y) && (z == b.z); + } + + bool operator!=(const Point32& b) const + { + return (x != b.x) || (y != b.y) || (z != b.z); + } + + bool isZero() + { + return (x == 0) && (y == 0) && (z == 0); + } + + Point64 cross(const Point32& b) const + { + return Point64(y * b.z - z * b.y, z * b.x - x * b.z, x * b.y - y * b.x); + } + + Point64 cross(const Point64& b) const + { + return Point64(y * b.z - z * b.y, z * b.x - x * b.z, x * b.y - y * b.x); + } + + btInt64_t dot(const Point32& b) const + { + return x * b.x + y * b.y + z * b.z; + } + + btInt64_t dot(const Point64& b) const + { + return x * b.x + y * b.y + z * b.z; + } + + Point32 operator+(const Point32& b) const + { + return Point32(x + b.x, y + b.y, z + b.z); + } + + Point32 operator-(const Point32& b) const + { + return Point32(x - b.x, y - b.y, z - b.z); + } + }; + + class Int128 + { + public: + btUint64_t low; + btUint64_t high; + + Int128() + { + } + + Int128(btUint64_t low, btUint64_t high): low(low), high(high) + { + } + + Int128(btUint64_t low): low(low), high(0) + { + } + + Int128(btInt64_t value): low(value), high((value >= 0) ? 0 : (btUint64_t) -1LL) + { + } + + static Int128 mul(btInt64_t a, btInt64_t b); + + static Int128 mul(btUint64_t a, btUint64_t b); + + Int128 operator-() const + { + return Int128((btUint64_t) -(btInt64_t)low, ~high + (low == 0)); + } + + Int128 operator+(const Int128& b) const + { +#ifdef USE_X86_64_ASM + Int128 result; + __asm__ ("addq %[bl], %[rl]\n\t" + "adcq %[bh], %[rh]\n\t" + : [rl] "=r" (result.low), [rh] "=r" (result.high) + : "0"(low), "1"(high), [bl] "g"(b.low), [bh] "g"(b.high) + : "cc" ); + return result; +#else + btUint64_t lo = low + b.low; + return Int128(lo, high + b.high + (lo < low)); +#endif + } + + Int128 operator-(const Int128& b) const + { +#ifdef USE_X86_64_ASM + Int128 result; + __asm__ ("subq %[bl], %[rl]\n\t" + "sbbq %[bh], %[rh]\n\t" + : [rl] "=r" (result.low), [rh] "=r" (result.high) + : "0"(low), "1"(high), [bl] "g"(b.low), [bh] "g"(b.high) + : "cc" ); + return result; +#else + return *this + -b; +#endif + } + + Int128& operator+=(const Int128& b) + { +#ifdef USE_X86_64_ASM + __asm__ ("addq %[bl], %[rl]\n\t" + "adcq %[bh], %[rh]\n\t" + : [rl] "=r" (low), [rh] "=r" (high) + : "0"(low), "1"(high), [bl] "g"(b.low), [bh] "g"(b.high) + : "cc" ); +#else + btUint64_t lo = low + b.low; + if (lo < low) + { + ++high; + } + low = lo; + high += b.high; +#endif + return *this; + } + + Int128& operator++() + { + if (++low == 0) + { + ++high; + } + return *this; + } + + Int128 operator*(btInt64_t b) const; + + b3Scalar toScalar() const + { + return ((btInt64_t) high >= 0) ? b3Scalar(high) * (b3Scalar(0x100000000LL) * b3Scalar(0x100000000LL)) + b3Scalar(low) + : -(-*this).toScalar(); + } + + int getSign() const + { + return ((btInt64_t) high < 0) ? -1 : (high || low) ? 1 : 0; + } + + bool operator<(const Int128& b) const + { + return (high < b.high) || ((high == b.high) && (low < b.low)); + } + + int ucmp(const Int128&b) const + { + if (high < b.high) + { + return -1; + } + if (high > b.high) + { + return 1; + } + if (low < b.low) + { + return -1; + } + if (low > b.low) + { + return 1; + } + return 0; + } + }; + + + class Rational64 + { + private: + btUint64_t m_numerator; + btUint64_t m_denominator; + int sign; + + public: + Rational64(btInt64_t numerator, btInt64_t denominator) + { + if (numerator > 0) + { + sign = 1; + m_numerator = (btUint64_t) numerator; + } + else if (numerator < 0) + { + sign = -1; + m_numerator = (btUint64_t) -numerator; + } + else + { + sign = 0; + m_numerator = 0; + } + if (denominator > 0) + { + m_denominator = (btUint64_t) denominator; + } + else if (denominator < 0) + { + sign = -sign; + m_denominator = (btUint64_t) -denominator; + } + else + { + m_denominator = 0; + } + } + + bool isNegativeInfinity() const + { + return (sign < 0) && (m_denominator == 0); + } + + bool isNaN() const + { + return (sign == 0) && (m_denominator == 0); + } + + int compare(const Rational64& b) const; + + b3Scalar toScalar() const + { + return sign * ((m_denominator == 0) ? B3_INFINITY : (b3Scalar) m_numerator / m_denominator); + } + }; + + + class Rational128 + { + private: + Int128 numerator; + Int128 denominator; + int sign; + bool isInt64; + + public: + Rational128(btInt64_t value) + { + if (value > 0) + { + sign = 1; + this->numerator = value; + } + else if (value < 0) + { + sign = -1; + this->numerator = -value; + } + else + { + sign = 0; + this->numerator = (btUint64_t) 0; + } + this->denominator = (btUint64_t) 1; + isInt64 = true; + } + + Rational128(const Int128& numerator, const Int128& denominator) + { + sign = numerator.getSign(); + if (sign >= 0) + { + this->numerator = numerator; + } + else + { + this->numerator = -numerator; + } + int dsign = denominator.getSign(); + if (dsign >= 0) + { + this->denominator = denominator; + } + else + { + sign = -sign; + this->denominator = -denominator; + } + isInt64 = false; + } + + int compare(const Rational128& b) const; + + int compare(btInt64_t b) const; + + b3Scalar toScalar() const + { + return sign * ((denominator.getSign() == 0) ? B3_INFINITY : numerator.toScalar() / denominator.toScalar()); + } + }; + + class PointR128 + { + public: + Int128 x; + Int128 y; + Int128 z; + Int128 denominator; + + PointR128() + { + } + + PointR128(Int128 x, Int128 y, Int128 z, Int128 denominator): x(x), y(y), z(z), denominator(denominator) + { + } + + b3Scalar xvalue() const + { + return x.toScalar() / denominator.toScalar(); + } + + b3Scalar yvalue() const + { + return y.toScalar() / denominator.toScalar(); + } + + b3Scalar zvalue() const + { + return z.toScalar() / denominator.toScalar(); + } + }; + + + class Edge; + class Face; + + class Vertex + { + public: + Vertex* next; + Vertex* prev; + Edge* edges; + Face* firstNearbyFace; + Face* lastNearbyFace; + PointR128 point128; + Point32 point; + int copy; + + Vertex(): next(NULL), prev(NULL), edges(NULL), firstNearbyFace(NULL), lastNearbyFace(NULL), copy(-1) + { + } + +#ifdef DEBUG_CONVEX_HULL + void print() + { + b3Printf("V%d (%d, %d, %d)", point.index, point.x, point.y, point.z); + } + + void printGraph(); +#endif + + Point32 operator-(const Vertex& b) const + { + return point - b.point; + } + + Rational128 dot(const Point64& b) const + { + return (point.index >= 0) ? Rational128(point.dot(b)) + : Rational128(point128.x * b.x + point128.y * b.y + point128.z * b.z, point128.denominator); + } + + b3Scalar xvalue() const + { + return (point.index >= 0) ? b3Scalar(point.x) : point128.xvalue(); + } + + b3Scalar yvalue() const + { + return (point.index >= 0) ? b3Scalar(point.y) : point128.yvalue(); + } + + b3Scalar zvalue() const + { + return (point.index >= 0) ? b3Scalar(point.z) : point128.zvalue(); + } + + void receiveNearbyFaces(Vertex* src) + { + if (lastNearbyFace) + { + lastNearbyFace->nextWithSameNearbyVertex = src->firstNearbyFace; + } + else + { + firstNearbyFace = src->firstNearbyFace; + } + if (src->lastNearbyFace) + { + lastNearbyFace = src->lastNearbyFace; + } + for (Face* f = src->firstNearbyFace; f; f = f->nextWithSameNearbyVertex) + { + b3Assert(f->nearbyVertex == src); + f->nearbyVertex = this; + } + src->firstNearbyFace = NULL; + src->lastNearbyFace = NULL; + } + }; + + + class Edge + { + public: + Edge* next; + Edge* prev; + Edge* reverse; + Vertex* target; + Face* face; + int copy; + + ~Edge() + { + next = NULL; + prev = NULL; + reverse = NULL; + target = NULL; + face = NULL; + } + + void link(Edge* n) + { + b3Assert(reverse->target == n->reverse->target); + next = n; + n->prev = this; + } + +#ifdef DEBUG_CONVEX_HULL + void print() + { + b3Printf("E%p : %d -> %d, n=%p p=%p (0 %d\t%d\t%d) -> (%d %d %d)", this, reverse->target->point.index, target->point.index, next, prev, + reverse->target->point.x, reverse->target->point.y, reverse->target->point.z, target->point.x, target->point.y, target->point.z); + } +#endif + }; + + class Face + { + public: + Face* next; + Vertex* nearbyVertex; + Face* nextWithSameNearbyVertex; + Point32 origin; + Point32 dir0; + Point32 dir1; + + Face(): next(NULL), nearbyVertex(NULL), nextWithSameNearbyVertex(NULL) + { + } + + void init(Vertex* a, Vertex* b, Vertex* c) + { + nearbyVertex = a; + origin = a->point; + dir0 = *b - *a; + dir1 = *c - *a; + if (a->lastNearbyFace) + { + a->lastNearbyFace->nextWithSameNearbyVertex = this; + } + else + { + a->firstNearbyFace = this; + } + a->lastNearbyFace = this; + } + + Point64 getNormal() + { + return dir0.cross(dir1); + } + }; + + template<typename UWord, typename UHWord> class DMul + { + private: + static btUint32_t high(btUint64_t value) + { + return (btUint32_t) (value >> 32); + } + + static btUint32_t low(btUint64_t value) + { + return (btUint32_t) value; + } + + static btUint64_t mul(btUint32_t a, btUint32_t b) + { + return (btUint64_t) a * (btUint64_t) b; + } + + static void shlHalf(btUint64_t& value) + { + value <<= 32; + } + + static btUint64_t high(Int128 value) + { + return value.high; + } + + static btUint64_t low(Int128 value) + { + return value.low; + } + + static Int128 mul(btUint64_t a, btUint64_t b) + { + return Int128::mul(a, b); + } + + static void shlHalf(Int128& value) + { + value.high = value.low; + value.low = 0; + } + + public: + + static void mul(UWord a, UWord b, UWord& resLow, UWord& resHigh) + { + UWord p00 = mul(low(a), low(b)); + UWord p01 = mul(low(a), high(b)); + UWord p10 = mul(high(a), low(b)); + UWord p11 = mul(high(a), high(b)); + UWord p0110 = UWord(low(p01)) + UWord(low(p10)); + p11 += high(p01); + p11 += high(p10); + p11 += high(p0110); + shlHalf(p0110); + p00 += p0110; + if (p00 < p0110) + { + ++p11; + } + resLow = p00; + resHigh = p11; + } + }; + + private: + + class IntermediateHull + { + public: + Vertex* minXy; + Vertex* maxXy; + Vertex* minYx; + Vertex* maxYx; + + IntermediateHull(): minXy(NULL), maxXy(NULL), minYx(NULL), maxYx(NULL) + { + } + + void print(); + }; + + enum Orientation {NONE, CLOCKWISE, COUNTER_CLOCKWISE}; + + template <typename T> class PoolArray + { + private: + T* array; + int size; + + public: + PoolArray<T>* next; + + PoolArray(int size): size(size), next(NULL) + { + array = (T*) b3AlignedAlloc(sizeof(T) * size, 16); + } + + ~PoolArray() + { + b3AlignedFree(array); + } + + T* init() + { + T* o = array; + for (int i = 0; i < size; i++, o++) + { + o->next = (i+1 < size) ? o + 1 : NULL; + } + return array; + } + }; + + template <typename T> class Pool + { + private: + PoolArray<T>* arrays; + PoolArray<T>* nextArray; + T* freeObjects; + int arraySize; + + public: + Pool(): arrays(NULL), nextArray(NULL), freeObjects(NULL), arraySize(256) + { + } + + ~Pool() + { + while (arrays) + { + PoolArray<T>* p = arrays; + arrays = p->next; + p->~PoolArray<T>(); + b3AlignedFree(p); + } + } + + void reset() + { + nextArray = arrays; + freeObjects = NULL; + } + + void setArraySize(int arraySize) + { + this->arraySize = arraySize; + } + + T* newObject() + { + T* o = freeObjects; + if (!o) + { + PoolArray<T>* p = nextArray; + if (p) + { + nextArray = p->next; + } + else + { + p = new(b3AlignedAlloc(sizeof(PoolArray<T>), 16)) PoolArray<T>(arraySize); + p->next = arrays; + arrays = p; + } + o = p->init(); + } + freeObjects = o->next; + return new(o) T(); + }; + + void freeObject(T* object) + { + object->~T(); + object->next = freeObjects; + freeObjects = object; + } + }; + + b3Vector3 scaling; + b3Vector3 center; + Pool<Vertex> vertexPool; + Pool<Edge> edgePool; + Pool<Face> facePool; + b3AlignedObjectArray<Vertex*> originalVertices; + int mergeStamp; + int minAxis; + int medAxis; + int maxAxis; + int usedEdgePairs; + int maxUsedEdgePairs; + + static Orientation getOrientation(const Edge* prev, const Edge* next, const Point32& s, const Point32& t); + Edge* findMaxAngle(bool ccw, const Vertex* start, const Point32& s, const Point64& rxs, const Point64& sxrxs, Rational64& minCot); + void findEdgeForCoplanarFaces(Vertex* c0, Vertex* c1, Edge*& e0, Edge*& e1, Vertex* stop0, Vertex* stop1); + + Edge* newEdgePair(Vertex* from, Vertex* to); + + void removeEdgePair(Edge* edge) + { + Edge* n = edge->next; + Edge* r = edge->reverse; + + b3Assert(edge->target && r->target); + + if (n != edge) + { + n->prev = edge->prev; + edge->prev->next = n; + r->target->edges = n; + } + else + { + r->target->edges = NULL; + } + + n = r->next; + + if (n != r) + { + n->prev = r->prev; + r->prev->next = n; + edge->target->edges = n; + } + else + { + edge->target->edges = NULL; + } + + edgePool.freeObject(edge); + edgePool.freeObject(r); + usedEdgePairs--; + } + + void computeInternal(int start, int end, IntermediateHull& result); + + bool mergeProjection(IntermediateHull& h0, IntermediateHull& h1, Vertex*& c0, Vertex*& c1); + + void merge(IntermediateHull& h0, IntermediateHull& h1); + + b3Vector3 toBtVector(const Point32& v); + + b3Vector3 getBtNormal(Face* face); + + bool shiftFace(Face* face, b3Scalar amount, b3AlignedObjectArray<Vertex*> stack); + + public: + Vertex* vertexList; + + void compute(const void* coords, bool doubleCoords, int stride, int count); + + b3Vector3 getCoordinates(const Vertex* v); + + b3Scalar shrink(b3Scalar amount, b3Scalar clampAmount); +}; + + +b3ConvexHullInternal::Int128 b3ConvexHullInternal::Int128::operator*(btInt64_t b) const +{ + bool negative = (btInt64_t) high < 0; + Int128 a = negative ? -*this : *this; + if (b < 0) + { + negative = !negative; + b = -b; + } + Int128 result = mul(a.low, (btUint64_t) b); + result.high += a.high * (btUint64_t) b; + return negative ? -result : result; +} + +b3ConvexHullInternal::Int128 b3ConvexHullInternal::Int128::mul(btInt64_t a, btInt64_t b) +{ + Int128 result; + +#ifdef USE_X86_64_ASM + __asm__ ("imulq %[b]" + : "=a" (result.low), "=d" (result.high) + : "0"(a), [b] "r"(b) + : "cc" ); + return result; + +#else + bool negative = a < 0; + if (negative) + { + a = -a; + } + if (b < 0) + { + negative = !negative; + b = -b; + } + DMul<btUint64_t, btUint32_t>::mul((btUint64_t) a, (btUint64_t) b, result.low, result.high); + return negative ? -result : result; +#endif +} + +b3ConvexHullInternal::Int128 b3ConvexHullInternal::Int128::mul(btUint64_t a, btUint64_t b) +{ + Int128 result; + +#ifdef USE_X86_64_ASM + __asm__ ("mulq %[b]" + : "=a" (result.low), "=d" (result.high) + : "0"(a), [b] "r"(b) + : "cc" ); + +#else + DMul<btUint64_t, btUint32_t>::mul(a, b, result.low, result.high); +#endif + + return result; +} + +int b3ConvexHullInternal::Rational64::compare(const Rational64& b) const +{ + if (sign != b.sign) + { + return sign - b.sign; + } + else if (sign == 0) + { + return 0; + } + + // return (numerator * b.denominator > b.numerator * denominator) ? sign : (numerator * b.denominator < b.numerator * denominator) ? -sign : 0; + +#ifdef USE_X86_64_ASM + + int result; + btInt64_t tmp; + btInt64_t dummy; + __asm__ ("mulq %[bn]\n\t" + "movq %%rax, %[tmp]\n\t" + "movq %%rdx, %%rbx\n\t" + "movq %[tn], %%rax\n\t" + "mulq %[bd]\n\t" + "subq %[tmp], %%rax\n\t" + "sbbq %%rbx, %%rdx\n\t" // rdx:rax contains 128-bit-difference "numerator*b.denominator - b.numerator*denominator" + "setnsb %%bh\n\t" // bh=1 if difference is non-negative, bh=0 otherwise + "orq %%rdx, %%rax\n\t" + "setnzb %%bl\n\t" // bl=1 if difference if non-zero, bl=0 if it is zero + "decb %%bh\n\t" // now bx=0x0000 if difference is zero, 0xff01 if it is negative, 0x0001 if it is positive (i.e., same sign as difference) + "shll $16, %%ebx\n\t" // ebx has same sign as difference + : "=&b"(result), [tmp] "=&r"(tmp), "=a"(dummy) + : "a"(denominator), [bn] "g"(b.numerator), [tn] "g"(numerator), [bd] "g"(b.denominator) + : "%rdx", "cc" ); + return result ? result ^ sign // if sign is +1, only bit 0 of result is inverted, which does not change the sign of result (and cannot result in zero) + // if sign is -1, all bits of result are inverted, which changes the sign of result (and again cannot result in zero) + : 0; + +#else + + return sign * Int128::mul(m_numerator, b.m_denominator).ucmp(Int128::mul(m_denominator, b.m_numerator)); + +#endif +} + +int b3ConvexHullInternal::Rational128::compare(const Rational128& b) const +{ + if (sign != b.sign) + { + return sign - b.sign; + } + else if (sign == 0) + { + return 0; + } + if (isInt64) + { + return -b.compare(sign * (btInt64_t) numerator.low); + } + + Int128 nbdLow, nbdHigh, dbnLow, dbnHigh; + DMul<Int128, btUint64_t>::mul(numerator, b.denominator, nbdLow, nbdHigh); + DMul<Int128, btUint64_t>::mul(denominator, b.numerator, dbnLow, dbnHigh); + + int cmp = nbdHigh.ucmp(dbnHigh); + if (cmp) + { + return cmp * sign; + } + return nbdLow.ucmp(dbnLow) * sign; +} + +int b3ConvexHullInternal::Rational128::compare(btInt64_t b) const +{ + if (isInt64) + { + btInt64_t a = sign * (btInt64_t) numerator.low; + return (a > b) ? 1 : (a < b) ? -1 : 0; + } + if (b > 0) + { + if (sign <= 0) + { + return -1; + } + } + else if (b < 0) + { + if (sign >= 0) + { + return 1; + } + b = -b; + } + else + { + return sign; + } + + return numerator.ucmp(denominator * b) * sign; +} + + +b3ConvexHullInternal::Edge* b3ConvexHullInternal::newEdgePair(Vertex* from, Vertex* to) +{ + b3Assert(from && to); + Edge* e = edgePool.newObject(); + Edge* r = edgePool.newObject(); + e->reverse = r; + r->reverse = e; + e->copy = mergeStamp; + r->copy = mergeStamp; + e->target = to; + r->target = from; + e->face = NULL; + r->face = NULL; + usedEdgePairs++; + if (usedEdgePairs > maxUsedEdgePairs) + { + maxUsedEdgePairs = usedEdgePairs; + } + return e; +} + +bool b3ConvexHullInternal::mergeProjection(IntermediateHull& h0, IntermediateHull& h1, Vertex*& c0, Vertex*& c1) +{ + Vertex* v0 = h0.maxYx; + Vertex* v1 = h1.minYx; + if ((v0->point.x == v1->point.x) && (v0->point.y == v1->point.y)) + { + b3Assert(v0->point.z < v1->point.z); + Vertex* v1p = v1->prev; + if (v1p == v1) + { + c0 = v0; + if (v1->edges) + { + b3Assert(v1->edges->next == v1->edges); + v1 = v1->edges->target; + b3Assert(v1->edges->next == v1->edges); + } + c1 = v1; + return false; + } + Vertex* v1n = v1->next; + v1p->next = v1n; + v1n->prev = v1p; + if (v1 == h1.minXy) + { + if ((v1n->point.x < v1p->point.x) || ((v1n->point.x == v1p->point.x) && (v1n->point.y < v1p->point.y))) + { + h1.minXy = v1n; + } + else + { + h1.minXy = v1p; + } + } + if (v1 == h1.maxXy) + { + if ((v1n->point.x > v1p->point.x) || ((v1n->point.x == v1p->point.x) && (v1n->point.y > v1p->point.y))) + { + h1.maxXy = v1n; + } + else + { + h1.maxXy = v1p; + } + } + } + + v0 = h0.maxXy; + v1 = h1.maxXy; + Vertex* v00 = NULL; + Vertex* v10 = NULL; + btInt32_t sign = 1; + + for (int side = 0; side <= 1; side++) + { + btInt32_t dx = (v1->point.x - v0->point.x) * sign; + if (dx > 0) + { + while (true) + { + btInt32_t dy = v1->point.y - v0->point.y; + + Vertex* w0 = side ? v0->next : v0->prev; + if (w0 != v0) + { + btInt32_t dx0 = (w0->point.x - v0->point.x) * sign; + btInt32_t dy0 = w0->point.y - v0->point.y; + if ((dy0 <= 0) && ((dx0 == 0) || ((dx0 < 0) && (dy0 * dx <= dy * dx0)))) + { + v0 = w0; + dx = (v1->point.x - v0->point.x) * sign; + continue; + } + } + + Vertex* w1 = side ? v1->next : v1->prev; + if (w1 != v1) + { + btInt32_t dx1 = (w1->point.x - v1->point.x) * sign; + btInt32_t dy1 = w1->point.y - v1->point.y; + btInt32_t dxn = (w1->point.x - v0->point.x) * sign; + if ((dxn > 0) && (dy1 < 0) && ((dx1 == 0) || ((dx1 < 0) && (dy1 * dx < dy * dx1)))) + { + v1 = w1; + dx = dxn; + continue; + } + } + + break; + } + } + else if (dx < 0) + { + while (true) + { + btInt32_t dy = v1->point.y - v0->point.y; + + Vertex* w1 = side ? v1->prev : v1->next; + if (w1 != v1) + { + btInt32_t dx1 = (w1->point.x - v1->point.x) * sign; + btInt32_t dy1 = w1->point.y - v1->point.y; + if ((dy1 >= 0) && ((dx1 == 0) || ((dx1 < 0) && (dy1 * dx <= dy * dx1)))) + { + v1 = w1; + dx = (v1->point.x - v0->point.x) * sign; + continue; + } + } + + Vertex* w0 = side ? v0->prev : v0->next; + if (w0 != v0) + { + btInt32_t dx0 = (w0->point.x - v0->point.x) * sign; + btInt32_t dy0 = w0->point.y - v0->point.y; + btInt32_t dxn = (v1->point.x - w0->point.x) * sign; + if ((dxn < 0) && (dy0 > 0) && ((dx0 == 0) || ((dx0 < 0) && (dy0 * dx < dy * dx0)))) + { + v0 = w0; + dx = dxn; + continue; + } + } + + break; + } + } + else + { + btInt32_t x = v0->point.x; + btInt32_t y0 = v0->point.y; + Vertex* w0 = v0; + Vertex* t; + while (((t = side ? w0->next : w0->prev) != v0) && (t->point.x == x) && (t->point.y <= y0)) + { + w0 = t; + y0 = t->point.y; + } + v0 = w0; + + btInt32_t y1 = v1->point.y; + Vertex* w1 = v1; + while (((t = side ? w1->prev : w1->next) != v1) && (t->point.x == x) && (t->point.y >= y1)) + { + w1 = t; + y1 = t->point.y; + } + v1 = w1; + } + + if (side == 0) + { + v00 = v0; + v10 = v1; + + v0 = h0.minXy; + v1 = h1.minXy; + sign = -1; + } + } + + v0->prev = v1; + v1->next = v0; + + v00->next = v10; + v10->prev = v00; + + if (h1.minXy->point.x < h0.minXy->point.x) + { + h0.minXy = h1.minXy; + } + if (h1.maxXy->point.x >= h0.maxXy->point.x) + { + h0.maxXy = h1.maxXy; + } + + h0.maxYx = h1.maxYx; + + c0 = v00; + c1 = v10; + + return true; +} + +void b3ConvexHullInternal::computeInternal(int start, int end, IntermediateHull& result) +{ + int n = end - start; + switch (n) + { + case 0: + result.minXy = NULL; + result.maxXy = NULL; + result.minYx = NULL; + result.maxYx = NULL; + return; + case 2: + { + Vertex* v = originalVertices[start]; + Vertex* w = v + 1; + if (v->point != w->point) + { + btInt32_t dx = v->point.x - w->point.x; + btInt32_t dy = v->point.y - w->point.y; + + if ((dx == 0) && (dy == 0)) + { + if (v->point.z > w->point.z) + { + Vertex* t = w; + w = v; + v = t; + } + b3Assert(v->point.z < w->point.z); + v->next = v; + v->prev = v; + result.minXy = v; + result.maxXy = v; + result.minYx = v; + result.maxYx = v; + } + else + { + v->next = w; + v->prev = w; + w->next = v; + w->prev = v; + + if ((dx < 0) || ((dx == 0) && (dy < 0))) + { + result.minXy = v; + result.maxXy = w; + } + else + { + result.minXy = w; + result.maxXy = v; + } + + if ((dy < 0) || ((dy == 0) && (dx < 0))) + { + result.minYx = v; + result.maxYx = w; + } + else + { + result.minYx = w; + result.maxYx = v; + } + } + + Edge* e = newEdgePair(v, w); + e->link(e); + v->edges = e; + + e = e->reverse; + e->link(e); + w->edges = e; + + return; + } + } + // lint -fallthrough + case 1: + { + Vertex* v = originalVertices[start]; + v->edges = NULL; + v->next = v; + v->prev = v; + + result.minXy = v; + result.maxXy = v; + result.minYx = v; + result.maxYx = v; + + return; + } + } + + int split0 = start + n / 2; + Point32 p = originalVertices[split0-1]->point; + int split1 = split0; + while ((split1 < end) && (originalVertices[split1]->point == p)) + { + split1++; + } + computeInternal(start, split0, result); + IntermediateHull hull1; + computeInternal(split1, end, hull1); +#ifdef DEBUG_CONVEX_HULL + b3Printf("\n\nMerge\n"); + result.print(); + hull1.print(); +#endif + merge(result, hull1); +#ifdef DEBUG_CONVEX_HULL + b3Printf("\n Result\n"); + result.print(); +#endif +} + +#ifdef DEBUG_CONVEX_HULL +void b3ConvexHullInternal::IntermediateHull::print() +{ + b3Printf(" Hull\n"); + for (Vertex* v = minXy; v; ) + { + b3Printf(" "); + v->print(); + if (v == maxXy) + { + b3Printf(" maxXy"); + } + if (v == minYx) + { + b3Printf(" minYx"); + } + if (v == maxYx) + { + b3Printf(" maxYx"); + } + if (v->next->prev != v) + { + b3Printf(" Inconsistency"); + } + b3Printf("\n"); + v = v->next; + if (v == minXy) + { + break; + } + } + if (minXy) + { + minXy->copy = (minXy->copy == -1) ? -2 : -1; + minXy->printGraph(); + } +} + +void b3ConvexHullInternal::Vertex::printGraph() +{ + print(); + b3Printf("\nEdges\n"); + Edge* e = edges; + if (e) + { + do + { + e->print(); + b3Printf("\n"); + e = e->next; + } while (e != edges); + do + { + Vertex* v = e->target; + if (v->copy != copy) + { + v->copy = copy; + v->printGraph(); + } + e = e->next; + } while (e != edges); + } +} +#endif + +b3ConvexHullInternal::Orientation b3ConvexHullInternal::getOrientation(const Edge* prev, const Edge* next, const Point32& s, const Point32& t) +{ + b3Assert(prev->reverse->target == next->reverse->target); + if (prev->next == next) + { + if (prev->prev == next) + { + Point64 n = t.cross(s); + Point64 m = (*prev->target - *next->reverse->target).cross(*next->target - *next->reverse->target); + b3Assert(!m.isZero()); + btInt64_t dot = n.dot(m); + b3Assert(dot != 0); + return (dot > 0) ? COUNTER_CLOCKWISE : CLOCKWISE; + } + return COUNTER_CLOCKWISE; + } + else if (prev->prev == next) + { + return CLOCKWISE; + } + else + { + return NONE; + } +} + +b3ConvexHullInternal::Edge* b3ConvexHullInternal::findMaxAngle(bool ccw, const Vertex* start, const Point32& s, const Point64& rxs, const Point64& sxrxs, Rational64& minCot) +{ + Edge* minEdge = NULL; + +#ifdef DEBUG_CONVEX_HULL + b3Printf("find max edge for %d\n", start->point.index); +#endif + Edge* e = start->edges; + if (e) + { + do + { + if (e->copy > mergeStamp) + { + Point32 t = *e->target - *start; + Rational64 cot(t.dot(sxrxs), t.dot(rxs)); +#ifdef DEBUG_CONVEX_HULL + b3Printf(" Angle is %f (%d) for ", (float) b3Atan(cot.toScalar()), (int) cot.isNaN()); + e->print(); +#endif + if (cot.isNaN()) + { + b3Assert(ccw ? (t.dot(s) < 0) : (t.dot(s) > 0)); + } + else + { + int cmp; + if (minEdge == NULL) + { + minCot = cot; + minEdge = e; + } + else if ((cmp = cot.compare(minCot)) < 0) + { + minCot = cot; + minEdge = e; + } + else if ((cmp == 0) && (ccw == (getOrientation(minEdge, e, s, t) == COUNTER_CLOCKWISE))) + { + minEdge = e; + } + } +#ifdef DEBUG_CONVEX_HULL + b3Printf("\n"); +#endif + } + e = e->next; + } while (e != start->edges); + } + return minEdge; +} + +void b3ConvexHullInternal::findEdgeForCoplanarFaces(Vertex* c0, Vertex* c1, Edge*& e0, Edge*& e1, Vertex* stop0, Vertex* stop1) +{ + Edge* start0 = e0; + Edge* start1 = e1; + Point32 et0 = start0 ? start0->target->point : c0->point; + Point32 et1 = start1 ? start1->target->point : c1->point; + Point32 s = c1->point - c0->point; + Point64 normal = ((start0 ? start0 : start1)->target->point - c0->point).cross(s); + btInt64_t dist = c0->point.dot(normal); + b3Assert(!start1 || (start1->target->point.dot(normal) == dist)); + Point64 perp = s.cross(normal); + b3Assert(!perp.isZero()); + +#ifdef DEBUG_CONVEX_HULL + b3Printf(" Advancing %d %d (%p %p, %d %d)\n", c0->point.index, c1->point.index, start0, start1, start0 ? start0->target->point.index : -1, start1 ? start1->target->point.index : -1); +#endif + + btInt64_t maxDot0 = et0.dot(perp); + if (e0) + { + while (e0->target != stop0) + { + Edge* e = e0->reverse->prev; + if (e->target->point.dot(normal) < dist) + { + break; + } + b3Assert(e->target->point.dot(normal) == dist); + if (e->copy == mergeStamp) + { + break; + } + btInt64_t dot = e->target->point.dot(perp); + if (dot <= maxDot0) + { + break; + } + maxDot0 = dot; + e0 = e; + et0 = e->target->point; + } + } + + btInt64_t maxDot1 = et1.dot(perp); + if (e1) + { + while (e1->target != stop1) + { + Edge* e = e1->reverse->next; + if (e->target->point.dot(normal) < dist) + { + break; + } + b3Assert(e->target->point.dot(normal) == dist); + if (e->copy == mergeStamp) + { + break; + } + btInt64_t dot = e->target->point.dot(perp); + if (dot <= maxDot1) + { + break; + } + maxDot1 = dot; + e1 = e; + et1 = e->target->point; + } + } + +#ifdef DEBUG_CONVEX_HULL + b3Printf(" Starting at %d %d\n", et0.index, et1.index); +#endif + + btInt64_t dx = maxDot1 - maxDot0; + if (dx > 0) + { + while (true) + { + btInt64_t dy = (et1 - et0).dot(s); + + if (e0 && (e0->target != stop0)) + { + Edge* f0 = e0->next->reverse; + if (f0->copy > mergeStamp) + { + btInt64_t dx0 = (f0->target->point - et0).dot(perp); + btInt64_t dy0 = (f0->target->point - et0).dot(s); + if ((dx0 == 0) ? (dy0 < 0) : ((dx0 < 0) && (Rational64(dy0, dx0).compare(Rational64(dy, dx)) >= 0))) + { + et0 = f0->target->point; + dx = (et1 - et0).dot(perp); + e0 = (e0 == start0) ? NULL : f0; + continue; + } + } + } + + if (e1 && (e1->target != stop1)) + { + Edge* f1 = e1->reverse->next; + if (f1->copy > mergeStamp) + { + Point32 d1 = f1->target->point - et1; + if (d1.dot(normal) == 0) + { + btInt64_t dx1 = d1.dot(perp); + btInt64_t dy1 = d1.dot(s); + btInt64_t dxn = (f1->target->point - et0).dot(perp); + if ((dxn > 0) && ((dx1 == 0) ? (dy1 < 0) : ((dx1 < 0) && (Rational64(dy1, dx1).compare(Rational64(dy, dx)) > 0)))) + { + e1 = f1; + et1 = e1->target->point; + dx = dxn; + continue; + } + } + else + { + b3Assert((e1 == start1) && (d1.dot(normal) < 0)); + } + } + } + + break; + } + } + else if (dx < 0) + { + while (true) + { + btInt64_t dy = (et1 - et0).dot(s); + + if (e1 && (e1->target != stop1)) + { + Edge* f1 = e1->prev->reverse; + if (f1->copy > mergeStamp) + { + btInt64_t dx1 = (f1->target->point - et1).dot(perp); + btInt64_t dy1 = (f1->target->point - et1).dot(s); + if ((dx1 == 0) ? (dy1 > 0) : ((dx1 < 0) && (Rational64(dy1, dx1).compare(Rational64(dy, dx)) <= 0))) + { + et1 = f1->target->point; + dx = (et1 - et0).dot(perp); + e1 = (e1 == start1) ? NULL : f1; + continue; + } + } + } + + if (e0 && (e0->target != stop0)) + { + Edge* f0 = e0->reverse->prev; + if (f0->copy > mergeStamp) + { + Point32 d0 = f0->target->point - et0; + if (d0.dot(normal) == 0) + { + btInt64_t dx0 = d0.dot(perp); + btInt64_t dy0 = d0.dot(s); + btInt64_t dxn = (et1 - f0->target->point).dot(perp); + if ((dxn < 0) && ((dx0 == 0) ? (dy0 > 0) : ((dx0 < 0) && (Rational64(dy0, dx0).compare(Rational64(dy, dx)) < 0)))) + { + e0 = f0; + et0 = e0->target->point; + dx = dxn; + continue; + } + } + else + { + b3Assert((e0 == start0) && (d0.dot(normal) < 0)); + } + } + } + + break; + } + } +#ifdef DEBUG_CONVEX_HULL + b3Printf(" Advanced edges to %d %d\n", et0.index, et1.index); +#endif +} + + +void b3ConvexHullInternal::merge(IntermediateHull& h0, IntermediateHull& h1) +{ + if (!h1.maxXy) + { + return; + } + if (!h0.maxXy) + { + h0 = h1; + return; + } + + mergeStamp--; + + Vertex* c0 = NULL; + Edge* toPrev0 = NULL; + Edge* firstNew0 = NULL; + Edge* pendingHead0 = NULL; + Edge* pendingTail0 = NULL; + Vertex* c1 = NULL; + Edge* toPrev1 = NULL; + Edge* firstNew1 = NULL; + Edge* pendingHead1 = NULL; + Edge* pendingTail1 = NULL; + Point32 prevPoint; + + if (mergeProjection(h0, h1, c0, c1)) + { + Point32 s = *c1 - *c0; + Point64 normal = Point32(0, 0, -1).cross(s); + Point64 t = s.cross(normal); + b3Assert(!t.isZero()); + + Edge* e = c0->edges; + Edge* start0 = NULL; + if (e) + { + do + { + btInt64_t dot = (*e->target - *c0).dot(normal); + b3Assert(dot <= 0); + if ((dot == 0) && ((*e->target - *c0).dot(t) > 0)) + { + if (!start0 || (getOrientation(start0, e, s, Point32(0, 0, -1)) == CLOCKWISE)) + { + start0 = e; + } + } + e = e->next; + } while (e != c0->edges); + } + + e = c1->edges; + Edge* start1 = NULL; + if (e) + { + do + { + btInt64_t dot = (*e->target - *c1).dot(normal); + b3Assert(dot <= 0); + if ((dot == 0) && ((*e->target - *c1).dot(t) > 0)) + { + if (!start1 || (getOrientation(start1, e, s, Point32(0, 0, -1)) == COUNTER_CLOCKWISE)) + { + start1 = e; + } + } + e = e->next; + } while (e != c1->edges); + } + + if (start0 || start1) + { + findEdgeForCoplanarFaces(c0, c1, start0, start1, NULL, NULL); + if (start0) + { + c0 = start0->target; + } + if (start1) + { + c1 = start1->target; + } + } + + prevPoint = c1->point; + prevPoint.z++; + } + else + { + prevPoint = c1->point; + prevPoint.x++; + } + + Vertex* first0 = c0; + Vertex* first1 = c1; + bool firstRun = true; + + while (true) + { + Point32 s = *c1 - *c0; + Point32 r = prevPoint - c0->point; + Point64 rxs = r.cross(s); + Point64 sxrxs = s.cross(rxs); + +#ifdef DEBUG_CONVEX_HULL + b3Printf("\n Checking %d %d\n", c0->point.index, c1->point.index); +#endif + Rational64 minCot0(0, 0); + Edge* min0 = findMaxAngle(false, c0, s, rxs, sxrxs, minCot0); + Rational64 minCot1(0, 0); + Edge* min1 = findMaxAngle(true, c1, s, rxs, sxrxs, minCot1); + if (!min0 && !min1) + { + Edge* e = newEdgePair(c0, c1); + e->link(e); + c0->edges = e; + + e = e->reverse; + e->link(e); + c1->edges = e; + return; + } + else + { + int cmp = !min0 ? 1 : !min1 ? -1 : minCot0.compare(minCot1); +#ifdef DEBUG_CONVEX_HULL + b3Printf(" -> Result %d\n", cmp); +#endif + if (firstRun || ((cmp >= 0) ? !minCot1.isNegativeInfinity() : !minCot0.isNegativeInfinity())) + { + Edge* e = newEdgePair(c0, c1); + if (pendingTail0) + { + pendingTail0->prev = e; + } + else + { + pendingHead0 = e; + } + e->next = pendingTail0; + pendingTail0 = e; + + e = e->reverse; + if (pendingTail1) + { + pendingTail1->next = e; + } + else + { + pendingHead1 = e; + } + e->prev = pendingTail1; + pendingTail1 = e; + } + + Edge* e0 = min0; + Edge* e1 = min1; + +#ifdef DEBUG_CONVEX_HULL + b3Printf(" Found min edges to %d %d\n", e0 ? e0->target->point.index : -1, e1 ? e1->target->point.index : -1); +#endif + + if (cmp == 0) + { + findEdgeForCoplanarFaces(c0, c1, e0, e1, NULL, NULL); + } + + if ((cmp >= 0) && e1) + { + if (toPrev1) + { + for (Edge* e = toPrev1->next, *n = NULL; e != min1; e = n) + { + n = e->next; + removeEdgePair(e); + } + } + + if (pendingTail1) + { + if (toPrev1) + { + toPrev1->link(pendingHead1); + } + else + { + min1->prev->link(pendingHead1); + firstNew1 = pendingHead1; + } + pendingTail1->link(min1); + pendingHead1 = NULL; + pendingTail1 = NULL; + } + else if (!toPrev1) + { + firstNew1 = min1; + } + + prevPoint = c1->point; + c1 = e1->target; + toPrev1 = e1->reverse; + } + + if ((cmp <= 0) && e0) + { + if (toPrev0) + { + for (Edge* e = toPrev0->prev, *n = NULL; e != min0; e = n) + { + n = e->prev; + removeEdgePair(e); + } + } + + if (pendingTail0) + { + if (toPrev0) + { + pendingHead0->link(toPrev0); + } + else + { + pendingHead0->link(min0->next); + firstNew0 = pendingHead0; + } + min0->link(pendingTail0); + pendingHead0 = NULL; + pendingTail0 = NULL; + } + else if (!toPrev0) + { + firstNew0 = min0; + } + + prevPoint = c0->point; + c0 = e0->target; + toPrev0 = e0->reverse; + } + } + + if ((c0 == first0) && (c1 == first1)) + { + if (toPrev0 == NULL) + { + pendingHead0->link(pendingTail0); + c0->edges = pendingTail0; + } + else + { + for (Edge* e = toPrev0->prev, *n = NULL; e != firstNew0; e = n) + { + n = e->prev; + removeEdgePair(e); + } + if (pendingTail0) + { + pendingHead0->link(toPrev0); + firstNew0->link(pendingTail0); + } + } + + if (toPrev1 == NULL) + { + pendingTail1->link(pendingHead1); + c1->edges = pendingTail1; + } + else + { + for (Edge* e = toPrev1->next, *n = NULL; e != firstNew1; e = n) + { + n = e->next; + removeEdgePair(e); + } + if (pendingTail1) + { + toPrev1->link(pendingHead1); + pendingTail1->link(firstNew1); + } + } + + return; + } + + firstRun = false; + } +} + + +static bool b3PointCmp(const b3ConvexHullInternal::Point32& p, const b3ConvexHullInternal::Point32& q) +{ + return (p.y < q.y) || ((p.y == q.y) && ((p.x < q.x) || ((p.x == q.x) && (p.z < q.z)))); +} + +void b3ConvexHullInternal::compute(const void* coords, bool doubleCoords, int stride, int count) +{ + b3Vector3 min = b3MakeVector3(b3Scalar(1e30), b3Scalar(1e30), b3Scalar(1e30)), max = b3MakeVector3(b3Scalar(-1e30), b3Scalar(-1e30), b3Scalar(-1e30)); + const char* ptr = (const char*) coords; + if (doubleCoords) + { + for (int i = 0; i < count; i++) + { + const double* v = (const double*) ptr; + b3Vector3 p = b3MakeVector3((b3Scalar) v[0], (b3Scalar) v[1], (b3Scalar) v[2]); + ptr += stride; + min.setMin(p); + max.setMax(p); + } + } + else + { + for (int i = 0; i < count; i++) + { + const float* v = (const float*) ptr; + b3Vector3 p = b3MakeVector3(v[0], v[1], v[2]); + ptr += stride; + min.setMin(p); + max.setMax(p); + } + } + + b3Vector3 s = max - min; + maxAxis = s.maxAxis(); + minAxis = s.minAxis(); + if (minAxis == maxAxis) + { + minAxis = (maxAxis + 1) % 3; + } + medAxis = 3 - maxAxis - minAxis; + + s /= b3Scalar(10216); + if (((medAxis + 1) % 3) != maxAxis) + { + s *= -1; + } + scaling = s; + + if (s[0] != 0) + { + s[0] = b3Scalar(1) / s[0]; + } + if (s[1] != 0) + { + s[1] = b3Scalar(1) / s[1]; + } + if (s[2] != 0) + { + s[2] = b3Scalar(1) / s[2]; + } + + center = (min + max) * b3Scalar(0.5); + + b3AlignedObjectArray<Point32> points; + points.resize(count); + ptr = (const char*) coords; + if (doubleCoords) + { + for (int i = 0; i < count; i++) + { + const double* v = (const double*) ptr; + b3Vector3 p = b3MakeVector3((b3Scalar) v[0], (b3Scalar) v[1], (b3Scalar) v[2]); + ptr += stride; + p = (p - center) * s; + points[i].x = (btInt32_t) p[medAxis]; + points[i].y = (btInt32_t) p[maxAxis]; + points[i].z = (btInt32_t) p[minAxis]; + points[i].index = i; + } + } + else + { + for (int i = 0; i < count; i++) + { + const float* v = (const float*) ptr; + b3Vector3 p = b3MakeVector3(v[0], v[1], v[2]); + ptr += stride; + p = (p - center) * s; + points[i].x = (btInt32_t) p[medAxis]; + points[i].y = (btInt32_t) p[maxAxis]; + points[i].z = (btInt32_t) p[minAxis]; + points[i].index = i; + } + } + points.quickSort(b3PointCmp); + + vertexPool.reset(); + vertexPool.setArraySize(count); + originalVertices.resize(count); + for (int i = 0; i < count; i++) + { + Vertex* v = vertexPool.newObject(); + v->edges = NULL; + v->point = points[i]; + v->copy = -1; + originalVertices[i] = v; + } + + points.clear(); + + edgePool.reset(); + edgePool.setArraySize(6 * count); + + usedEdgePairs = 0; + maxUsedEdgePairs = 0; + + mergeStamp = -3; + + IntermediateHull hull; + computeInternal(0, count, hull); + vertexList = hull.minXy; +#ifdef DEBUG_CONVEX_HULL + b3Printf("max. edges %d (3v = %d)", maxUsedEdgePairs, 3 * count); +#endif +} + +b3Vector3 b3ConvexHullInternal::toBtVector(const Point32& v) +{ + b3Vector3 p; + p[medAxis] = b3Scalar(v.x); + p[maxAxis] = b3Scalar(v.y); + p[minAxis] = b3Scalar(v.z); + return p * scaling; +} + +b3Vector3 b3ConvexHullInternal::getBtNormal(Face* face) +{ + return toBtVector(face->dir0).cross(toBtVector(face->dir1)).normalized(); +} + +b3Vector3 b3ConvexHullInternal::getCoordinates(const Vertex* v) +{ + b3Vector3 p; + p[medAxis] = v->xvalue(); + p[maxAxis] = v->yvalue(); + p[minAxis] = v->zvalue(); + return p * scaling + center; +} + +b3Scalar b3ConvexHullInternal::shrink(b3Scalar amount, b3Scalar clampAmount) +{ + if (!vertexList) + { + return 0; + } + int stamp = --mergeStamp; + b3AlignedObjectArray<Vertex*> stack; + vertexList->copy = stamp; + stack.push_back(vertexList); + b3AlignedObjectArray<Face*> faces; + + Point32 ref = vertexList->point; + Int128 hullCenterX(0, 0); + Int128 hullCenterY(0, 0); + Int128 hullCenterZ(0, 0); + Int128 volume(0, 0); + + while (stack.size() > 0) + { + Vertex* v = stack[stack.size() - 1]; + stack.pop_back(); + Edge* e = v->edges; + if (e) + { + do + { + if (e->target->copy != stamp) + { + e->target->copy = stamp; + stack.push_back(e->target); + } + if (e->copy != stamp) + { + Face* face = facePool.newObject(); + face->init(e->target, e->reverse->prev->target, v); + faces.push_back(face); + Edge* f = e; + + Vertex* a = NULL; + Vertex* b = NULL; + do + { + if (a && b) + { + btInt64_t vol = (v->point - ref).dot((a->point - ref).cross(b->point - ref)); + b3Assert(vol >= 0); + Point32 c = v->point + a->point + b->point + ref; + hullCenterX += vol * c.x; + hullCenterY += vol * c.y; + hullCenterZ += vol * c.z; + volume += vol; + } + + b3Assert(f->copy != stamp); + f->copy = stamp; + f->face = face; + + a = b; + b = f->target; + + f = f->reverse->prev; + } while (f != e); + } + e = e->next; + } while (e != v->edges); + } + } + + if (volume.getSign() <= 0) + { + return 0; + } + + b3Vector3 hullCenter; + hullCenter[medAxis] = hullCenterX.toScalar(); + hullCenter[maxAxis] = hullCenterY.toScalar(); + hullCenter[minAxis] = hullCenterZ.toScalar(); + hullCenter /= 4 * volume.toScalar(); + hullCenter *= scaling; + + int faceCount = faces.size(); + + if (clampAmount > 0) + { + b3Scalar minDist = B3_INFINITY; + for (int i = 0; i < faceCount; i++) + { + b3Vector3 normal = getBtNormal(faces[i]); + b3Scalar dist = normal.dot(toBtVector(faces[i]->origin) - hullCenter); + if (dist < minDist) + { + minDist = dist; + } + } + + if (minDist <= 0) + { + return 0; + } + + amount = b3Min(amount, minDist * clampAmount); + } + + unsigned int seed = 243703; + for (int i = 0; i < faceCount; i++, seed = 1664525 * seed + 1013904223) + { + b3Swap(faces[i], faces[seed % faceCount]); + } + + for (int i = 0; i < faceCount; i++) + { + if (!shiftFace(faces[i], amount, stack)) + { + return -amount; + } + } + + return amount; +} + +bool b3ConvexHullInternal::shiftFace(Face* face, b3Scalar amount, b3AlignedObjectArray<Vertex*> stack) +{ + b3Vector3 origShift = getBtNormal(face) * -amount; + if (scaling[0] != 0) + { + origShift[0] /= scaling[0]; + } + if (scaling[1] != 0) + { + origShift[1] /= scaling[1]; + } + if (scaling[2] != 0) + { + origShift[2] /= scaling[2]; + } + Point32 shift((btInt32_t) origShift[medAxis], (btInt32_t) origShift[maxAxis], (btInt32_t) origShift[minAxis]); + if (shift.isZero()) + { + return true; + } + Point64 normal = face->getNormal(); +#ifdef DEBUG_CONVEX_HULL + b3Printf("\nShrinking face (%d %d %d) (%d %d %d) (%d %d %d) by (%d %d %d)\n", + face->origin.x, face->origin.y, face->origin.z, face->dir0.x, face->dir0.y, face->dir0.z, face->dir1.x, face->dir1.y, face->dir1.z, shift.x, shift.y, shift.z); +#endif + btInt64_t origDot = face->origin.dot(normal); + Point32 shiftedOrigin = face->origin + shift; + btInt64_t shiftedDot = shiftedOrigin.dot(normal); + b3Assert(shiftedDot <= origDot); + if (shiftedDot >= origDot) + { + return false; + } + + Edge* intersection = NULL; + + Edge* startEdge = face->nearbyVertex->edges; +#ifdef DEBUG_CONVEX_HULL + b3Printf("Start edge is "); + startEdge->print(); + b3Printf(", normal is (%lld %lld %lld), shifted dot is %lld\n", normal.x, normal.y, normal.z, shiftedDot); +#endif + Rational128 optDot = face->nearbyVertex->dot(normal); + int cmp = optDot.compare(shiftedDot); +#ifdef SHOW_ITERATIONS + int n = 0; +#endif + if (cmp >= 0) + { + Edge* e = startEdge; + do + { +#ifdef SHOW_ITERATIONS + n++; +#endif + Rational128 dot = e->target->dot(normal); + b3Assert(dot.compare(origDot) <= 0); +#ifdef DEBUG_CONVEX_HULL + b3Printf("Moving downwards, edge is "); + e->print(); + b3Printf(", dot is %f (%f %lld)\n", (float) dot.toScalar(), (float) optDot.toScalar(), shiftedDot); +#endif + if (dot.compare(optDot) < 0) + { + int c = dot.compare(shiftedDot); + optDot = dot; + e = e->reverse; + startEdge = e; + if (c < 0) + { + intersection = e; + break; + } + cmp = c; + } + e = e->prev; + } while (e != startEdge); + + if (!intersection) + { + return false; + } + } + else + { + Edge* e = startEdge; + do + { +#ifdef SHOW_ITERATIONS + n++; +#endif + Rational128 dot = e->target->dot(normal); + b3Assert(dot.compare(origDot) <= 0); +#ifdef DEBUG_CONVEX_HULL + b3Printf("Moving upwards, edge is "); + e->print(); + b3Printf(", dot is %f (%f %lld)\n", (float) dot.toScalar(), (float) optDot.toScalar(), shiftedDot); +#endif + if (dot.compare(optDot) > 0) + { + cmp = dot.compare(shiftedDot); + if (cmp >= 0) + { + intersection = e; + break; + } + optDot = dot; + e = e->reverse; + startEdge = e; + } + e = e->prev; + } while (e != startEdge); + + if (!intersection) + { + return true; + } + } + +#ifdef SHOW_ITERATIONS + b3Printf("Needed %d iterations to find initial intersection\n", n); +#endif + + if (cmp == 0) + { + Edge* e = intersection->reverse->next; +#ifdef SHOW_ITERATIONS + n = 0; +#endif + while (e->target->dot(normal).compare(shiftedDot) <= 0) + { +#ifdef SHOW_ITERATIONS + n++; +#endif + e = e->next; + if (e == intersection->reverse) + { + return true; + } +#ifdef DEBUG_CONVEX_HULL + b3Printf("Checking for outwards edge, current edge is "); + e->print(); + b3Printf("\n"); +#endif + } +#ifdef SHOW_ITERATIONS + b3Printf("Needed %d iterations to check for complete containment\n", n); +#endif + } + + Edge* firstIntersection = NULL; + Edge* faceEdge = NULL; + Edge* firstFaceEdge = NULL; + +#ifdef SHOW_ITERATIONS + int m = 0; +#endif + while (true) + { +#ifdef SHOW_ITERATIONS + m++; +#endif +#ifdef DEBUG_CONVEX_HULL + b3Printf("Intersecting edge is "); + intersection->print(); + b3Printf("\n"); +#endif + if (cmp == 0) + { + Edge* e = intersection->reverse->next; + startEdge = e; +#ifdef SHOW_ITERATIONS + n = 0; +#endif + while (true) + { +#ifdef SHOW_ITERATIONS + n++; +#endif + if (e->target->dot(normal).compare(shiftedDot) >= 0) + { + break; + } + intersection = e->reverse; + e = e->next; + if (e == startEdge) + { + return true; + } + } +#ifdef SHOW_ITERATIONS + b3Printf("Needed %d iterations to advance intersection\n", n); +#endif + } + +#ifdef DEBUG_CONVEX_HULL + b3Printf("Advanced intersecting edge to "); + intersection->print(); + b3Printf(", cmp = %d\n", cmp); +#endif + + if (!firstIntersection) + { + firstIntersection = intersection; + } + else if (intersection == firstIntersection) + { + break; + } + + int prevCmp = cmp; + Edge* prevIntersection = intersection; + Edge* prevFaceEdge = faceEdge; + + Edge* e = intersection->reverse; +#ifdef SHOW_ITERATIONS + n = 0; +#endif + while (true) + { +#ifdef SHOW_ITERATIONS + n++; +#endif + e = e->reverse->prev; + b3Assert(e != intersection->reverse); + cmp = e->target->dot(normal).compare(shiftedDot); +#ifdef DEBUG_CONVEX_HULL + b3Printf("Testing edge "); + e->print(); + b3Printf(" -> cmp = %d\n", cmp); +#endif + if (cmp >= 0) + { + intersection = e; + break; + } + } +#ifdef SHOW_ITERATIONS + b3Printf("Needed %d iterations to find other intersection of face\n", n); +#endif + + if (cmp > 0) + { + Vertex* removed = intersection->target; + e = intersection->reverse; + if (e->prev == e) + { + removed->edges = NULL; + } + else + { + removed->edges = e->prev; + e->prev->link(e->next); + e->link(e); + } +#ifdef DEBUG_CONVEX_HULL + b3Printf("1: Removed part contains (%d %d %d)\n", removed->point.x, removed->point.y, removed->point.z); +#endif + + Point64 n0 = intersection->face->getNormal(); + Point64 n1 = intersection->reverse->face->getNormal(); + btInt64_t m00 = face->dir0.dot(n0); + btInt64_t m01 = face->dir1.dot(n0); + btInt64_t m10 = face->dir0.dot(n1); + btInt64_t m11 = face->dir1.dot(n1); + btInt64_t r0 = (intersection->face->origin - shiftedOrigin).dot(n0); + btInt64_t r1 = (intersection->reverse->face->origin - shiftedOrigin).dot(n1); + Int128 det = Int128::mul(m00, m11) - Int128::mul(m01, m10); + b3Assert(det.getSign() != 0); + Vertex* v = vertexPool.newObject(); + v->point.index = -1; + v->copy = -1; + v->point128 = PointR128(Int128::mul(face->dir0.x * r0, m11) - Int128::mul(face->dir0.x * r1, m01) + + Int128::mul(face->dir1.x * r1, m00) - Int128::mul(face->dir1.x * r0, m10) + det * shiftedOrigin.x, + Int128::mul(face->dir0.y * r0, m11) - Int128::mul(face->dir0.y * r1, m01) + + Int128::mul(face->dir1.y * r1, m00) - Int128::mul(face->dir1.y * r0, m10) + det * shiftedOrigin.y, + Int128::mul(face->dir0.z * r0, m11) - Int128::mul(face->dir0.z * r1, m01) + + Int128::mul(face->dir1.z * r1, m00) - Int128::mul(face->dir1.z * r0, m10) + det * shiftedOrigin.z, + det); + v->point.x = (btInt32_t) v->point128.xvalue(); + v->point.y = (btInt32_t) v->point128.yvalue(); + v->point.z = (btInt32_t) v->point128.zvalue(); + intersection->target = v; + v->edges = e; + + stack.push_back(v); + stack.push_back(removed); + stack.push_back(NULL); + } + + if (cmp || prevCmp || (prevIntersection->reverse->next->target != intersection->target)) + { + faceEdge = newEdgePair(prevIntersection->target, intersection->target); + if (prevCmp == 0) + { + faceEdge->link(prevIntersection->reverse->next); + } + if ((prevCmp == 0) || prevFaceEdge) + { + prevIntersection->reverse->link(faceEdge); + } + if (cmp == 0) + { + intersection->reverse->prev->link(faceEdge->reverse); + } + faceEdge->reverse->link(intersection->reverse); + } + else + { + faceEdge = prevIntersection->reverse->next; + } + + if (prevFaceEdge) + { + if (prevCmp > 0) + { + faceEdge->link(prevFaceEdge->reverse); + } + else if (faceEdge != prevFaceEdge->reverse) + { + stack.push_back(prevFaceEdge->target); + while (faceEdge->next != prevFaceEdge->reverse) + { + Vertex* removed = faceEdge->next->target; + removeEdgePair(faceEdge->next); + stack.push_back(removed); +#ifdef DEBUG_CONVEX_HULL + b3Printf("2: Removed part contains (%d %d %d)\n", removed->point.x, removed->point.y, removed->point.z); +#endif + } + stack.push_back(NULL); + } + } + faceEdge->face = face; + faceEdge->reverse->face = intersection->face; + + if (!firstFaceEdge) + { + firstFaceEdge = faceEdge; + } + } +#ifdef SHOW_ITERATIONS + b3Printf("Needed %d iterations to process all intersections\n", m); +#endif + + if (cmp > 0) + { + firstFaceEdge->reverse->target = faceEdge->target; + firstIntersection->reverse->link(firstFaceEdge); + firstFaceEdge->link(faceEdge->reverse); + } + else if (firstFaceEdge != faceEdge->reverse) + { + stack.push_back(faceEdge->target); + while (firstFaceEdge->next != faceEdge->reverse) + { + Vertex* removed = firstFaceEdge->next->target; + removeEdgePair(firstFaceEdge->next); + stack.push_back(removed); +#ifdef DEBUG_CONVEX_HULL + b3Printf("3: Removed part contains (%d %d %d)\n", removed->point.x, removed->point.y, removed->point.z); +#endif + } + stack.push_back(NULL); + } + + b3Assert(stack.size() > 0); + vertexList = stack[0]; + +#ifdef DEBUG_CONVEX_HULL + b3Printf("Removing part\n"); +#endif +#ifdef SHOW_ITERATIONS + n = 0; +#endif + int pos = 0; + while (pos < stack.size()) + { + int end = stack.size(); + while (pos < end) + { + Vertex* kept = stack[pos++]; +#ifdef DEBUG_CONVEX_HULL + kept->print(); +#endif + bool deeper = false; + Vertex* removed; + while ((removed = stack[pos++]) != NULL) + { +#ifdef SHOW_ITERATIONS + n++; +#endif + kept->receiveNearbyFaces(removed); + while (removed->edges) + { + if (!deeper) + { + deeper = true; + stack.push_back(kept); + } + stack.push_back(removed->edges->target); + removeEdgePair(removed->edges); + } + } + if (deeper) + { + stack.push_back(NULL); + } + } + } +#ifdef SHOW_ITERATIONS + b3Printf("Needed %d iterations to remove part\n", n); +#endif + + stack.resize(0); + face->origin = shiftedOrigin; + + return true; +} + + +static int getVertexCopy(b3ConvexHullInternal::Vertex* vertex, b3AlignedObjectArray<b3ConvexHullInternal::Vertex*>& vertices) +{ + int index = vertex->copy; + if (index < 0) + { + index = vertices.size(); + vertex->copy = index; + vertices.push_back(vertex); +#ifdef DEBUG_CONVEX_HULL + b3Printf("Vertex %d gets index *%d\n", vertex->point.index, index); +#endif + } + return index; +} + +b3Scalar b3ConvexHullComputer::compute(const void* coords, bool doubleCoords, int stride, int count, b3Scalar shrink, b3Scalar shrinkClamp) +{ + if (count <= 0) + { + vertices.clear(); + edges.clear(); + faces.clear(); + return 0; + } + + b3ConvexHullInternal hull; + hull.compute(coords, doubleCoords, stride, count); + + b3Scalar shift = 0; + if ((shrink > 0) && ((shift = hull.shrink(shrink, shrinkClamp)) < 0)) + { + vertices.clear(); + edges.clear(); + faces.clear(); + return shift; + } + + vertices.resize(0); + edges.resize(0); + faces.resize(0); + + b3AlignedObjectArray<b3ConvexHullInternal::Vertex*> oldVertices; + getVertexCopy(hull.vertexList, oldVertices); + int copied = 0; + while (copied < oldVertices.size()) + { + b3ConvexHullInternal::Vertex* v = oldVertices[copied]; + vertices.push_back(hull.getCoordinates(v)); + b3ConvexHullInternal::Edge* firstEdge = v->edges; + if (firstEdge) + { + int firstCopy = -1; + int prevCopy = -1; + b3ConvexHullInternal::Edge* e = firstEdge; + do + { + if (e->copy < 0) + { + int s = edges.size(); + edges.push_back(Edge()); + edges.push_back(Edge()); + Edge* c = &edges[s]; + Edge* r = &edges[s + 1]; + e->copy = s; + e->reverse->copy = s + 1; + c->reverse = 1; + r->reverse = -1; + c->targetVertex = getVertexCopy(e->target, oldVertices); + r->targetVertex = copied; +#ifdef DEBUG_CONVEX_HULL + b3Printf(" CREATE: Vertex *%d has edge to *%d\n", copied, c->getTargetVertex()); +#endif + } + if (prevCopy >= 0) + { + edges[e->copy].next = prevCopy - e->copy; + } + else + { + firstCopy = e->copy; + } + prevCopy = e->copy; + e = e->next; + } while (e != firstEdge); + edges[firstCopy].next = prevCopy - firstCopy; + } + copied++; + } + + for (int i = 0; i < copied; i++) + { + b3ConvexHullInternal::Vertex* v = oldVertices[i]; + b3ConvexHullInternal::Edge* firstEdge = v->edges; + if (firstEdge) + { + b3ConvexHullInternal::Edge* e = firstEdge; + do + { + if (e->copy >= 0) + { +#ifdef DEBUG_CONVEX_HULL + b3Printf("Vertex *%d has edge to *%d\n", i, edges[e->copy].getTargetVertex()); +#endif + faces.push_back(e->copy); + b3ConvexHullInternal::Edge* f = e; + do + { +#ifdef DEBUG_CONVEX_HULL + b3Printf(" Face *%d\n", edges[f->copy].getTargetVertex()); +#endif + f->copy = -1; + f = f->reverse->prev; + } while (f != e); + } + e = e->next; + } while (e != firstEdge); + } + } + + return shift; +} + + + + + |