mirror of https://github.com/PCSX2/pcsx2.git
910 lines
27 KiB
C++
910 lines
27 KiB
C++
#ifndef ZEROGS_MATH_H
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#define ZEROGS_MATH_H
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#ifndef _WIN32
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#include <alloca.h>
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#endif
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#include <string.h>
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#include <math.h>
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#ifndef PI
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#define PI ((dReal)3.141592654)
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#endif
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#define rswap(x, y) *(int*)&(x) ^= *(int*)&(y) ^= *(int*)&(x) ^= *(int*)&(y);
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template <class T> inline T RAD_2_DEG(T radians) { return (radians * (T)57.29577951); }
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class Transform;
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class TransformMatrix;
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typedef float dReal;
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typedef dReal dMatrix3[3*4];
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inline dReal* normalize3(dReal* pfout, const dReal* pf);
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inline dReal* normalize4(dReal* pfout, const dReal* pf);
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inline dReal* cross3(dReal* pfout, const dReal* pf1, const dReal* pf2);
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// multiplies 3x3 matrices
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inline dReal* mult3(dReal* pfres, const dReal* pf1, const dReal* pf2);
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inline double* mult3(double* pfres, const double* pf1, const double* pf2);
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inline dReal* inv3(const dReal* pf, dReal* pfres, int stride);
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inline dReal* inv4(const dReal* pf, dReal* pfres);
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// class used for 3 and 4 dim vectors and quaternions
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// It is better to use this for a 3 dim vector because it is 16byte aligned and SIMD instructions can be used
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class Vector
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{
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public:
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dReal x, y, z, w;
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Vector() : x(0), y(0), z(0), w(0) {}
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Vector(dReal x, dReal y, dReal z) : x(x), y(y), z(z), w(0) {}
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Vector(dReal x, dReal y, dReal z, dReal w) : x(x), y(y), z(z), w(w) {}
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Vector(const Vector &vec) : x(vec.x), y(vec.y), z(vec.z), w(vec.w) {}
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Vector(const dReal* pf) { assert(pf != NULL); x = pf[0]; y = pf[1]; z = pf[2]; w = 0; }
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dReal operator[](int i) const { return (&x)[i]; }
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dReal& operator[](int i) { return (&x)[i]; }
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// casting operators
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operator dReal* () { return &x; }
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operator const dReal* () const { return (const dReal*)&x; }
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// SCALAR FUNCTIONS
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inline dReal dot(const Vector &v) const { return x*v.x + y*v.y + z*v.z + w*v.w; }
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inline void normalize() { normalize4(&x, &x); }
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inline void Set3(const float* pvals) { x = pvals[0]; y = pvals[1]; z = pvals[2]; }
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inline void Set4(const float* pvals) { x = pvals[0]; y = pvals[1]; z = pvals[2]; w = pvals[3]; }
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inline void SetColor(u32 color)
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{
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x = (color & 0xff) / 255.0f;
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y = ((color >> 8) & 0xff) / 255.0f;
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z = ((color >> 16) & 0xff) / 255.0f;
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}
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// 3 dim cross product, w is not touched
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/// this = this x v
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inline void Cross(const Vector &v) { cross3(&x, &x, v); }
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/// this = u x v
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inline void Cross(const Vector &u, const Vector &v) { cross3(&x, u, v); }
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inline Vector operator-() const { Vector v; v.x = -x; v.y = -y; v.z = -z; v.w = -w; return v; }
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inline Vector operator+(const Vector &r) const { Vector v; v.x = x+r.x; v.y = y+r.y; v.z = z+r.z; v.w = w+r.w; return v; }
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inline Vector operator-(const Vector &r) const { Vector v; v.x = x-r.x; v.y = y-r.y; v.z = z-r.z; v.w = w-r.w; return v; }
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inline Vector operator*(const Vector &r) const { Vector v; v.x = r.x*x; v.y = r.y*y; v.z = r.z*z; v.w = r.w*w; return v; }
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inline Vector operator*(dReal k) const { Vector v; v.x = k*x; v.y = k*y; v.z = k*z; v.w = k*w; return v; }
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inline Vector& operator += (const Vector& r) { x += r.x; y += r.y; z += r.z; w += r.w; return *this; }
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inline Vector& operator -= (const Vector& r) { x -= r.x; y -= r.y; z -= r.z; w -= r.w; return *this; }
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inline Vector& operator *= (const Vector& r) { x *= r.x; y *= r.y; z *= r.z; w *= r.w; return *this; }
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inline Vector& operator *= (const dReal k) { x *= k; y *= k; z *= k; w *= k; return *this; }
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inline Vector& operator /= (const dReal _k) { dReal k=1/_k; x *= k; y *= k; z *= k; w *= k; return *this; }
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friend Vector operator* (float f, const Vector& v);
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//friend ostream& operator<<(ostream& O, const Vector& v);
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//friend istream& operator>>(istream& I, Vector& v);
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};
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inline Vector operator* (float f, const Vector& left)
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{
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Vector v;
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v.x = f * left.x;
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v.y = f * left.y;
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v.z = f * left.z;
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return v;
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}
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struct AABB
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{
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Vector pos, extents;
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};
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struct OBB
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{
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Vector right, up, dir, pos, extents;
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};
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struct TRIANGLE
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{
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TRIANGLE() {}
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TRIANGLE(const Vector& v1, const Vector& v2, const Vector& v3) : v1(v1), v2(v2), v3(v3) {}
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~TRIANGLE() {}
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Vector v1, v2, v3; //!< the vertices of the triangle
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const Vector& operator[](int i) const { return (&v1)[i]; }
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Vector& operator[](int i) { return (&v1)[i]; }
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/// assumes CCW ordering of vertices
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inline Vector ComputeNormal() {
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Vector normal;
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cross3(normal, v2-v1, v3-v1);
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return normal;
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}
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};
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// Routines made for 3D graphics that deal with 3 or 4 dim algebra structures
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// Functions with postfix 3 are for 3x3 operations, etc
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// all fns return pfout on success or NULL on failure
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// results and arguments can share pointers
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// multiplies 4x4 matrices
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inline dReal* mult4(dReal* pfres, const dReal* pf1, const dReal* pf2);
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inline double* mult4(double* pfres, const double* pf1, const double* pf2);
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// pf1^T * pf2
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inline dReal* multtrans3(dReal* pfres, const dReal* pf1, const dReal* pf2);
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inline double* multtrans3(double* pfres, const double* pf1, const double* pf2);
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inline dReal* multtrans4(dReal* pfres, const dReal* pf1, const dReal* pf2);
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inline double* multtrans4(double* pfres, const double* pf1, const double* pf2);
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inline dReal* transpose3(const dReal* pf, dReal* pfres);
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inline double* transpose3(const double* pf, double* pfres);
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inline dReal* transpose4(const dReal* pf, dReal* pfres);
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inline double* transpose4(const double* pf, double* pfres);
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inline dReal dot2(const dReal* pf1, const dReal* pf2);
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inline dReal dot3(const dReal* pf1, const dReal* pf2);
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inline dReal dot4(const dReal* pf1, const dReal* pf2);
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inline dReal lengthsqr2(const dReal* pf);
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inline dReal lengthsqr3(const dReal* pf);
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inline dReal lengthsqr4(const dReal* pf);
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inline dReal* normalize2(dReal* pfout, const dReal* pf);
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inline dReal* normalize3(dReal* pfout, const dReal* pf);
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inline dReal* normalize4(dReal* pfout, const dReal* pf);
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////
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// More complex ops that deal with arbitrary matrices //
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////
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// extract eigen values and vectors from a 2x2 matrix and returns true if all values are real
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// returned eigen vectors are normalized
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inline bool eig2(const dReal* pfmat, dReal* peigs, dReal& fv1x, dReal& fv1y, dReal& fv2x, dReal& fv2y);
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// Simple routines for linear algebra algorithms //
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int CubicRoots (double c0, double c1, double c2, double *r0, double *r1, double *r2);
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bool QLAlgorithm3 (dReal* m_aafEntry, dReal* afDiag, dReal* afSubDiag);
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void EigenSymmetric3(dReal* fCovariance, dReal* eval, dReal* fAxes);
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void GetCovarBasisVectors(dReal fCovariance[3][3], Vector* vRight, Vector* vUp, Vector* vDir);
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// first root returned is always >= second, roots are defined if the quadratic doesn't have real solutions
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void QuadraticSolver(dReal* pfQuadratic, dReal* pfRoots);
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int insideQuadrilateral(const Vector* p0,const Vector* p1, const Vector* p2,const Vector* p3);
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int insideTriangle(const Vector* p0, const Vector* p1, const Vector* p2);
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// multiplies a matrix by a scalar
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template <class T> inline void mult(T* pf, T fa, int r);
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// multiplies a r1xc1 by c1xc2 matrix into pfres, if badd is true adds the result to pfres
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// does not handle cases where pfres is equal to pf1 or pf2, use multtox for those cases
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template <class T, class S, class R>
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inline T* mult(T* pf1, R* pf2, int r1, int c1, int c2, S* pfres, bool badd = false);
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// pf1 is transposed before mult
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// rows of pf2 must equal rows of pf1
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// pfres will be c1xc2 matrix
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template <class T, class S, class R>
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inline T* multtrans(T* pf1, R* pf2, int r1, int c1, int c2, S* pfres, bool badd = false);
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// pf2 is transposed before mult
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// the columns of both matrices must be the same and equal to c1
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// r2 is the number of rows in pf2
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// pfres must be an r1xr2 matrix
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template <class T, class S, class R>
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inline T* multtrans_to2(T* pf1, R* pf2, int r1, int c1, int r2, S* pfres, bool badd = false);
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// multiplies rxc matrix pf1 and cxc matrix pf2 and stores the result in pf1,
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// the function needs a temporary buffer the size of c doubles, if pftemp == NULL,
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// the function will allocate the necessary memory, otherwise pftemp should be big
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// enough to store all the entries
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template <class T> inline T* multto1(T* pf1, T* pf2, int r1, int c1, T* pftemp = NULL);
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// same as multto1 except stores the result in pf2, pf1 has to be an r2xr2 matrix
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// pftemp must be of size r2 if not NULL
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template <class T, class S> inline T* multto2(T* pf1, S* pf2, int r2, int c2, S* pftemp = NULL);
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// add pf1 + pf2 and store in pf1
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template <class T> inline void sub(T* pf1, T* pf2, int r);
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template <class T> inline T normsqr(T* pf1, int r);
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template <class T> inline T lengthsqr(T* pf1, T* pf2, int length);
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template <class T> inline T dot(T* pf1, T* pf2, int length);
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template <class T> inline T sum(T* pf, int length);
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// takes the inverse of the 3x3 matrix pf and stores it into pfres, returns true if matrix is invertible
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template <class T> inline bool inv2(T* pf, T* pfres);
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///////////////////////
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// Function Definitions
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///////////////////////
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bool eig2(const dReal* pfmat, dReal* peigs, dReal& fv1x, dReal& fv1y, dReal& fv2x, dReal& fv2y)
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{
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// x^2 + bx + c
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dReal a, b, c, d;
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b = -(pfmat[0] + pfmat[3]);
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c = pfmat[0] * pfmat[3] - pfmat[1] * pfmat[2];
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d = b * b - 4.0f * c + 1e-16f;
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if( d < 0 ) return false;
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if( d < 1e-16f ) {
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a = -0.5f * b;
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peigs[0] = a; peigs[1] = a;
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fv1x = pfmat[1]; fv1y = a - pfmat[0];
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c = 1 / sqrtf(fv1x*fv1x + fv1y*fv1y);
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fv1x *= c; fv1y *= c;
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fv2x = -fv1y; fv2y = fv1x;
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return true;
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}
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// two roots
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d = sqrtf(d);
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a = -0.5f * (b + d);
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peigs[0] = a;
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fv1x = pfmat[1]; fv1y = a-pfmat[0];
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c = 1 / sqrtf(fv1x*fv1x + fv1y*fv1y);
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fv1x *= c; fv1y *= c;
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a += d;
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peigs[1] = a;
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fv2x = pfmat[1]; fv2y = a-pfmat[0];
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c = 1 / sqrtf(fv2x*fv2x + fv2y*fv2y);
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fv2x *= c; fv2y *= c;
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return true;
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}
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//#ifndef TI_USING_IPP
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// Functions that are replacable by ipp library funcs
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template <class T> inline T* _mult3(T* pfres, const T* pf1, const T* pf2)
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{
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assert( pf1 != NULL && pf2 != NULL && pfres != NULL );
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T* pfres2;
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if( pfres == pf1 || pfres == pf2 ) pfres2 = (T*)alloca(9 * sizeof(T));
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else pfres2 = pfres;
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pfres2[0*4+0] = pf1[0*4+0]*pf2[0*4+0]+pf1[0*4+1]*pf2[1*4+0]+pf1[0*4+2]*pf2[2*4+0];
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pfres2[0*4+1] = pf1[0*4+0]*pf2[0*4+1]+pf1[0*4+1]*pf2[1*4+1]+pf1[0*4+2]*pf2[2*4+1];
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pfres2[0*4+2] = pf1[0*4+0]*pf2[0*4+2]+pf1[0*4+1]*pf2[1*4+2]+pf1[0*4+2]*pf2[2*4+2];
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pfres2[1*4+0] = pf1[1*4+0]*pf2[0*4+0]+pf1[1*4+1]*pf2[1*4+0]+pf1[1*4+2]*pf2[2*4+0];
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pfres2[1*4+1] = pf1[1*4+0]*pf2[0*4+1]+pf1[1*4+1]*pf2[1*4+1]+pf1[1*4+2]*pf2[2*4+1];
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pfres2[1*4+2] = pf1[1*4+0]*pf2[0*4+2]+pf1[1*4+1]*pf2[1*4+2]+pf1[1*4+2]*pf2[2*4+2];
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pfres2[2*4+0] = pf1[2*4+0]*pf2[0*4+0]+pf1[2*4+1]*pf2[1*4+0]+pf1[2*4+2]*pf2[2*4+0];
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pfres2[2*4+1] = pf1[2*4+0]*pf2[0*4+1]+pf1[2*4+1]*pf2[1*4+1]+pf1[2*4+2]*pf2[2*4+1];
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pfres2[2*4+2] = pf1[2*4+0]*pf2[0*4+2]+pf1[2*4+1]*pf2[1*4+2]+pf1[2*4+2]*pf2[2*4+2];
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if( pfres2 != pfres ) memcpy(pfres, pfres2, 9*sizeof(T));
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return pfres;
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}
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inline dReal* mult3(dReal* pfres, const dReal* pf1, const dReal* pf2) { return _mult3<dReal>(pfres, pf1, pf2); }
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inline double* mult3(double* pfres, const double* pf1, const double* pf2) { return _mult3<double>(pfres, pf1, pf2); }
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template <class T>
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inline T* _mult4(T* pfres, const T* p1, const T* p2)
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{
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assert( pfres != NULL && p1 != NULL && p2 != NULL );
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T* pfres2;
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if( pfres == p1 || pfres == p2 ) pfres2 = (T*)alloca(16 * sizeof(T));
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else pfres2 = pfres;
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pfres2[0*4+0] = p1[0*4+0]*p2[0*4+0] + p1[0*4+1]*p2[1*4+0] + p1[0*4+2]*p2[2*4+0] + p1[0*4+3]*p2[3*4+0];
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pfres2[0*4+1] = p1[0*4+0]*p2[0*4+1] + p1[0*4+1]*p2[1*4+1] + p1[0*4+2]*p2[2*4+1] + p1[0*4+3]*p2[3*4+1];
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pfres2[0*4+2] = p1[0*4+0]*p2[0*4+2] + p1[0*4+1]*p2[1*4+2] + p1[0*4+2]*p2[2*4+2] + p1[0*4+3]*p2[3*4+2];
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pfres2[0*4+3] = p1[0*4+0]*p2[0*4+3] + p1[0*4+1]*p2[1*4+3] + p1[0*4+2]*p2[2*4+3] + p1[0*4+3]*p2[3*4+3];
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pfres2[1*4+0] = p1[1*4+0]*p2[0*4+0] + p1[1*4+1]*p2[1*4+0] + p1[1*4+2]*p2[2*4+0] + p1[1*4+3]*p2[3*4+0];
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pfres2[1*4+1] = p1[1*4+0]*p2[0*4+1] + p1[1*4+1]*p2[1*4+1] + p1[1*4+2]*p2[2*4+1] + p1[1*4+3]*p2[3*4+1];
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pfres2[1*4+2] = p1[1*4+0]*p2[0*4+2] + p1[1*4+1]*p2[1*4+2] + p1[1*4+2]*p2[2*4+2] + p1[1*4+3]*p2[3*4+2];
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pfres2[1*4+3] = p1[1*4+0]*p2[0*4+3] + p1[1*4+1]*p2[1*4+3] + p1[1*4+2]*p2[2*4+3] + p1[1*4+3]*p2[3*4+3];
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pfres2[2*4+0] = p1[2*4+0]*p2[0*4+0] + p1[2*4+1]*p2[1*4+0] + p1[2*4+2]*p2[2*4+0] + p1[2*4+3]*p2[3*4+0];
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pfres2[2*4+1] = p1[2*4+0]*p2[0*4+1] + p1[2*4+1]*p2[1*4+1] + p1[2*4+2]*p2[2*4+1] + p1[2*4+3]*p2[3*4+1];
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pfres2[2*4+2] = p1[2*4+0]*p2[0*4+2] + p1[2*4+1]*p2[1*4+2] + p1[2*4+2]*p2[2*4+2] + p1[2*4+3]*p2[3*4+2];
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pfres2[2*4+3] = p1[2*4+0]*p2[0*4+3] + p1[2*4+1]*p2[1*4+3] + p1[2*4+2]*p2[2*4+3] + p1[2*4+3]*p2[3*4+3];
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pfres2[3*4+0] = p1[3*4+0]*p2[0*4+0] + p1[3*4+1]*p2[1*4+0] + p1[3*4+2]*p2[2*4+0] + p1[3*4+3]*p2[3*4+0];
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pfres2[3*4+1] = p1[3*4+0]*p2[0*4+1] + p1[3*4+1]*p2[1*4+1] + p1[3*4+2]*p2[2*4+1] + p1[3*4+3]*p2[3*4+1];
|
|
pfres2[3*4+2] = p1[3*4+0]*p2[0*4+2] + p1[3*4+1]*p2[1*4+2] + p1[3*4+2]*p2[2*4+2] + p1[3*4+3]*p2[3*4+2];
|
|
pfres2[3*4+3] = p1[3*4+0]*p2[0*4+3] + p1[3*4+1]*p2[1*4+3] + p1[3*4+2]*p2[2*4+3] + p1[3*4+3]*p2[3*4+3];
|
|
|
|
if( pfres != pfres2 ) memcpy(pfres, pfres2, sizeof(T)*16);
|
|
return pfres;
|
|
}
|
|
|
|
inline dReal* mult4(dReal* pfres, const dReal* pf1, const dReal* pf2) { return _mult4<dReal>(pfres, pf1, pf2); }
|
|
inline double* mult4(double* pfres, const double* pf1, const double* pf2) { return _mult4<double>(pfres, pf1, pf2); }
|
|
|
|
template <class T>
|
|
inline T* _multtrans3(T* pfres, const T* pf1, const T* pf2)
|
|
{
|
|
T* pfres2;
|
|
if( pfres == pf1 ) pfres2 = (T*)alloca(9 * sizeof(T));
|
|
else pfres2 = pfres;
|
|
|
|
pfres2[0] = pf1[0]*pf2[0]+pf1[3]*pf2[3]+pf1[6]*pf2[6];
|
|
pfres2[1] = pf1[0]*pf2[1]+pf1[3]*pf2[4]+pf1[6]*pf2[7];
|
|
pfres2[2] = pf1[0]*pf2[2]+pf1[3]*pf2[5]+pf1[6]*pf2[8];
|
|
|
|
pfres2[3] = pf1[1]*pf2[0]+pf1[4]*pf2[3]+pf1[7]*pf2[6];
|
|
pfres2[4] = pf1[1]*pf2[1]+pf1[4]*pf2[4]+pf1[7]*pf2[7];
|
|
pfres2[5] = pf1[1]*pf2[2]+pf1[4]*pf2[5]+pf1[7]*pf2[8];
|
|
|
|
pfres2[6] = pf1[2]*pf2[0]+pf1[5]*pf2[3]+pf1[8]*pf2[6];
|
|
pfres2[7] = pf1[2]*pf2[1]+pf1[5]*pf2[4]+pf1[8]*pf2[7];
|
|
pfres2[8] = pf1[2]*pf2[2]+pf1[5]*pf2[5]+pf1[8]*pf2[8];
|
|
|
|
if( pfres2 != pfres ) memcpy(pfres, pfres2, 9*sizeof(T));
|
|
|
|
return pfres;
|
|
}
|
|
|
|
template <class T>
|
|
inline T* _multtrans4(T* pfres, const T* pf1, const T* pf2)
|
|
{
|
|
T* pfres2;
|
|
if( pfres == pf1 ) pfres2 = (T*)alloca(16 * sizeof(T));
|
|
else pfres2 = pfres;
|
|
|
|
for(int i = 0; i < 4; ++i) {
|
|
for(int j = 0; j < 4; ++j) {
|
|
pfres[4*i+j] = pf1[i] * pf2[j] + pf1[i+4] * pf2[j+4] + pf1[i+8] * pf2[j+8] + pf1[i+12] * pf2[j+12];
|
|
}
|
|
}
|
|
|
|
return pfres;
|
|
}
|
|
|
|
inline dReal* multtrans3(dReal* pfres, const dReal* pf1, const dReal* pf2) { return _multtrans3<dReal>(pfres, pf1, pf2); }
|
|
inline double* multtrans3(double* pfres, const double* pf1, const double* pf2) { return _multtrans3<double>(pfres, pf1, pf2); }
|
|
inline dReal* multtrans4(dReal* pfres, const dReal* pf1, const dReal* pf2) { return _multtrans4<dReal>(pfres, pf1, pf2); }
|
|
inline double* multtrans4(double* pfres, const double* pf1, const double* pf2) { return _multtrans4<double>(pfres, pf1, pf2); }
|
|
|
|
// stride is in T
|
|
template <class T> inline T* _inv3(const T* pf, T* pfres, int stride)
|
|
{
|
|
T* pfres2;
|
|
if( pfres == pf ) pfres2 = (T*)alloca(3 * stride * sizeof(T));
|
|
else pfres2 = pfres;
|
|
|
|
// inverse = C^t / det(pf) where C is the matrix of coefficients
|
|
|
|
// calc C^t
|
|
pfres2[0*stride + 0] = pf[1*stride + 1] * pf[2*stride + 2] - pf[1*stride + 2] * pf[2*stride + 1];
|
|
pfres2[0*stride + 1] = pf[0*stride + 2] * pf[2*stride + 1] - pf[0*stride + 1] * pf[2*stride + 2];
|
|
pfres2[0*stride + 2] = pf[0*stride + 1] * pf[1*stride + 2] - pf[0*stride + 2] * pf[1*stride + 1];
|
|
pfres2[1*stride + 0] = pf[1*stride + 2] * pf[2*stride + 0] - pf[1*stride + 0] * pf[2*stride + 2];
|
|
pfres2[1*stride + 1] = pf[0*stride + 0] * pf[2*stride + 2] - pf[0*stride + 2] * pf[2*stride + 0];
|
|
pfres2[1*stride + 2] = pf[0*stride + 2] * pf[1*stride + 0] - pf[0*stride + 0] * pf[1*stride + 2];
|
|
pfres2[2*stride + 0] = pf[1*stride + 0] * pf[2*stride + 1] - pf[1*stride + 1] * pf[2*stride + 0];
|
|
pfres2[2*stride + 1] = pf[0*stride + 1] * pf[2*stride + 0] - pf[0*stride + 0] * pf[2*stride + 1];
|
|
pfres2[2*stride + 2] = pf[0*stride + 0] * pf[1*stride + 1] - pf[0*stride + 1] * pf[1*stride + 0];
|
|
|
|
T fdet = pf[0*stride + 2] * pfres2[2*stride + 0] + pf[1*stride + 2] * pfres2[2*stride + 1] +
|
|
pf[2*stride + 2] * pfres2[2*stride + 2];
|
|
|
|
if( fabs(fdet) < 1e-6 ) return NULL;
|
|
|
|
fdet = 1 / fdet;
|
|
//if( pfdet != NULL ) *pfdet = fdet;
|
|
|
|
if( pfres != pf ) {
|
|
pfres[0*stride+0] *= fdet; pfres[0*stride+1] *= fdet; pfres[0*stride+2] *= fdet;
|
|
pfres[1*stride+0] *= fdet; pfres[1*stride+1] *= fdet; pfres[1*stride+2] *= fdet;
|
|
pfres[2*stride+0] *= fdet; pfres[2*stride+1] *= fdet; pfres[2*stride+2] *= fdet;
|
|
return pfres;
|
|
}
|
|
|
|
pfres[0*stride+0] = pfres2[0*stride+0] * fdet;
|
|
pfres[0*stride+1] = pfres2[0*stride+1] * fdet;
|
|
pfres[0*stride+2] = pfres2[0*stride+2] * fdet;
|
|
pfres[1*stride+0] = pfres2[1*stride+0] * fdet;
|
|
pfres[1*stride+1] = pfres2[1*stride+1] * fdet;
|
|
pfres[1*stride+2] = pfres2[1*stride+2] * fdet;
|
|
pfres[2*stride+0] = pfres2[2*stride+0] * fdet;
|
|
pfres[2*stride+1] = pfres2[2*stride+1] * fdet;
|
|
pfres[2*stride+2] = pfres2[2*stride+2] * fdet;
|
|
return pfres;
|
|
}
|
|
|
|
inline dReal* inv3(const dReal* pf, dReal* pfres, int stride) { return _inv3<dReal>(pf, pfres, stride); }
|
|
|
|
// inverse if 92 mults and 39 adds
|
|
template <class T> inline T* _inv4(const T* pf, T* pfres)
|
|
{
|
|
T* pfres2;
|
|
if( pfres == pf ) pfres2 = (T*)alloca(16 * sizeof(T));
|
|
else pfres2 = pfres;
|
|
|
|
// inverse = C^t / det(pf) where C is the matrix of coefficients
|
|
|
|
// calc C^t
|
|
|
|
// determinants of all possibel 2x2 submatrices formed by last two rows
|
|
T fd0, fd1, fd2;
|
|
T f1, f2, f3;
|
|
fd0 = pf[2*4 + 0] * pf[3*4 + 1] - pf[2*4 + 1] * pf[3*4 + 0];
|
|
fd1 = pf[2*4 + 1] * pf[3*4 + 2] - pf[2*4 + 2] * pf[3*4 + 1];
|
|
fd2 = pf[2*4 + 2] * pf[3*4 + 3] - pf[2*4 + 3] * pf[3*4 + 2];
|
|
|
|
f1 = pf[2*4 + 1] * pf[3*4 + 3] - pf[2*4 + 3] * pf[3*4 + 1];
|
|
f2 = pf[2*4 + 0] * pf[3*4 + 3] - pf[2*4 + 3] * pf[3*4 + 0];
|
|
f3 = pf[2*4 + 0] * pf[3*4 + 2] - pf[2*4 + 2] * pf[3*4 + 0];
|
|
|
|
pfres2[0*4 + 0] = pf[1*4 + 1] * fd2 - pf[1*4 + 2] * f1 + pf[1*4 + 3] * fd1;
|
|
pfres2[0*4 + 1] = -(pf[0*4 + 1] * fd2 - pf[0*4 + 2] * f1 + pf[0*4 + 3] * fd1);
|
|
|
|
pfres2[1*4 + 0] = -(pf[1*4 + 0] * fd2 - pf[1*4 + 2] * f2 + pf[1*4 + 3] * f3);
|
|
pfres2[1*4 + 1] = pf[0*4 + 0] * fd2 - pf[0*4 + 2] * f2 + pf[0*4 + 3] * f3;
|
|
|
|
pfres2[2*4 + 0] = pf[1*4 + 0] * f1 - pf[1*4 + 1] * f2 + pf[1*4 + 3] * fd0;
|
|
pfres2[2*4 + 1] = -(pf[0*4 + 0] * f1 - pf[0*4 + 1] * f2 + pf[0*4 + 3] * fd0);
|
|
|
|
pfres2[3*4 + 0] = -(pf[1*4 + 0] * fd1 - pf[1*4 + 1] * f3 + pf[1*4 + 2] * fd0);
|
|
pfres2[3*4 + 1] = pf[0*4 + 0] * fd1 - pf[0*4 + 1] * f3 + pf[0*4 + 2] * fd0;
|
|
|
|
// determinants of first 2 rows of 4x4 matrix
|
|
fd0 = pf[0*4 + 0] * pf[1*4 + 1] - pf[0*4 + 1] * pf[1*4 + 0];
|
|
fd1 = pf[0*4 + 1] * pf[1*4 + 2] - pf[0*4 + 2] * pf[1*4 + 1];
|
|
fd2 = pf[0*4 + 2] * pf[1*4 + 3] - pf[0*4 + 3] * pf[1*4 + 2];
|
|
|
|
f1 = pf[0*4 + 1] * pf[1*4 + 3] - pf[0*4 + 3] * pf[1*4 + 1];
|
|
f2 = pf[0*4 + 0] * pf[1*4 + 3] - pf[0*4 + 3] * pf[1*4 + 0];
|
|
f3 = pf[0*4 + 0] * pf[1*4 + 2] - pf[0*4 + 2] * pf[1*4 + 0];
|
|
|
|
pfres2[0*4 + 2] = pf[3*4 + 1] * fd2 - pf[3*4 + 2] * f1 + pf[3*4 + 3] * fd1;
|
|
pfres2[0*4 + 3] = -(pf[2*4 + 1] * fd2 - pf[2*4 + 2] * f1 + pf[2*4 + 3] * fd1);
|
|
|
|
pfres2[1*4 + 2] = -(pf[3*4 + 0] * fd2 - pf[3*4 + 2] * f2 + pf[3*4 + 3] * f3);
|
|
pfres2[1*4 + 3] = pf[2*4 + 0] * fd2 - pf[2*4 + 2] * f2 + pf[2*4 + 3] * f3;
|
|
|
|
pfres2[2*4 + 2] = pf[3*4 + 0] * f1 - pf[3*4 + 1] * f2 + pf[3*4 + 3] * fd0;
|
|
pfres2[2*4 + 3] = -(pf[2*4 + 0] * f1 - pf[2*4 + 1] * f2 + pf[2*4 + 3] * fd0);
|
|
|
|
pfres2[3*4 + 2] = -(pf[3*4 + 0] * fd1 - pf[3*4 + 1] * f3 + pf[3*4 + 2] * fd0);
|
|
pfres2[3*4 + 3] = pf[2*4 + 0] * fd1 - pf[2*4 + 1] * f3 + pf[2*4 + 2] * fd0;
|
|
|
|
T fdet = pf[0*4 + 3] * pfres2[3*4 + 0] + pf[1*4 + 3] * pfres2[3*4 + 1] +
|
|
pf[2*4 + 3] * pfres2[3*4 + 2] + pf[3*4 + 3] * pfres2[3*4 + 3];
|
|
|
|
if( fabs(fdet) < 1e-6) return NULL;
|
|
|
|
fdet = 1 / fdet;
|
|
//if( pfdet != NULL ) *pfdet = fdet;
|
|
|
|
if( pfres2 == pfres ) {
|
|
mult(pfres, fdet, 16);
|
|
return pfres;
|
|
}
|
|
|
|
int i = 0;
|
|
while(i < 16) {
|
|
pfres[i] = pfres2[i] * fdet;
|
|
++i;
|
|
}
|
|
|
|
return pfres;
|
|
}
|
|
|
|
inline dReal* inv4(const dReal* pf, dReal* pfres) { return _inv4<dReal>(pf, pfres); }
|
|
|
|
template <class T> inline T* _transpose3(const T* pf, T* pfres)
|
|
{
|
|
assert( pf != NULL && pfres != NULL );
|
|
|
|
if( pf == pfres ) {
|
|
rswap(pfres[1], pfres[3]);
|
|
rswap(pfres[2], pfres[6]);
|
|
rswap(pfres[5], pfres[7]);
|
|
return pfres;
|
|
}
|
|
|
|
pfres[0] = pf[0]; pfres[1] = pf[3]; pfres[2] = pf[6];
|
|
pfres[3] = pf[1]; pfres[4] = pf[4]; pfres[5] = pf[7];
|
|
pfres[6] = pf[2]; pfres[7] = pf[5]; pfres[8] = pf[8];
|
|
|
|
return pfres;
|
|
}
|
|
|
|
inline dReal* transpose3(const dReal* pf, dReal* pfres) { return _transpose3(pf, pfres); }
|
|
inline double* transpose3(const double* pf, double* pfres) { return _transpose3(pf, pfres); }
|
|
|
|
template <class T> inline T* _transpose4(const T* pf, T* pfres)
|
|
{
|
|
assert( pf != NULL && pfres != NULL );
|
|
|
|
if( pf == pfres ) {
|
|
rswap(pfres[1], pfres[4]);
|
|
rswap(pfres[2], pfres[8]);
|
|
rswap(pfres[3], pfres[12]);
|
|
rswap(pfres[6], pfres[9]);
|
|
rswap(pfres[7], pfres[13]);
|
|
rswap(pfres[11], pfres[15]);
|
|
return pfres;
|
|
}
|
|
|
|
pfres[0] = pf[0]; pfres[1] = pf[4]; pfres[2] = pf[8]; pfres[3] = pf[12];
|
|
pfres[4] = pf[1]; pfres[5] = pf[5]; pfres[6] = pf[9]; pfres[7] = pf[13];
|
|
pfres[8] = pf[2]; pfres[9] = pf[6]; pfres[10] = pf[10]; pfres[11] = pf[14];
|
|
pfres[12] = pf[3]; pfres[13] = pf[7]; pfres[14] = pf[11]; pfres[15] = pf[15];
|
|
return pfres;
|
|
}
|
|
|
|
inline dReal* transpose4(const dReal* pf, dReal* pfres) { return _transpose4(pf, pfres); }
|
|
inline double* transpose4(const double* pf, double* pfres) { return _transpose4(pf, pfres); }
|
|
|
|
inline dReal dot2(const dReal* pf1, const dReal* pf2)
|
|
{
|
|
assert( pf1 != NULL && pf2 != NULL );
|
|
return pf1[0]*pf2[0] + pf1[1]*pf2[1];
|
|
}
|
|
|
|
inline dReal dot3(const dReal* pf1, const dReal* pf2)
|
|
{
|
|
assert( pf1 != NULL && pf2 != NULL );
|
|
return pf1[0]*pf2[0] + pf1[1]*pf2[1] + pf1[2]*pf2[2];
|
|
}
|
|
|
|
inline dReal dot4(const dReal* pf1, const dReal* pf2)
|
|
{
|
|
assert( pf1 != NULL && pf2 != NULL );
|
|
return pf1[0]*pf2[0] + pf1[1]*pf2[1] + pf1[2]*pf2[2] + pf1[3] * pf2[3];
|
|
}
|
|
|
|
inline dReal lengthsqr2(const dReal* pf)
|
|
{
|
|
assert( pf != NULL );
|
|
return pf[0] * pf[0] + pf[1] * pf[1];
|
|
}
|
|
|
|
inline dReal lengthsqr3(const dReal* pf)
|
|
{
|
|
assert( pf != NULL );
|
|
return pf[0] * pf[0] + pf[1] * pf[1] + pf[2] * pf[2];
|
|
}
|
|
|
|
inline dReal lengthsqr4(const dReal* pf)
|
|
{
|
|
assert( pf != NULL );
|
|
return pf[0] * pf[0] + pf[1] * pf[1] + pf[2] * pf[2] + pf[3] * pf[3];
|
|
}
|
|
|
|
inline dReal* normalize2(dReal* pfout, const dReal* pf)
|
|
{
|
|
assert(pf != NULL);
|
|
|
|
dReal f = pf[0]*pf[0] + pf[1]*pf[1];
|
|
f = 1.0f / sqrtf(f);
|
|
pfout[0] = pf[0] * f;
|
|
pfout[1] = pf[1] * f;
|
|
|
|
return pfout;
|
|
}
|
|
|
|
inline dReal* normalize3(dReal* pfout, const dReal* pf)
|
|
{
|
|
assert(pf != NULL);
|
|
|
|
dReal f = pf[0]*pf[0] + pf[1]*pf[1] + pf[2]*pf[2];
|
|
|
|
f = 1.0f / sqrtf(f);
|
|
pfout[0] = pf[0] * f;
|
|
pfout[1] = pf[1] * f;
|
|
pfout[2] = pf[2] * f;
|
|
|
|
return pfout;
|
|
}
|
|
|
|
inline dReal* normalize4(dReal* pfout, const dReal* pf)
|
|
{
|
|
assert(pf != NULL);
|
|
|
|
dReal f = pf[0]*pf[0] + pf[1]*pf[1] + pf[2]*pf[2] + pf[3]*pf[3];
|
|
|
|
f = 1.0f / sqrtf(f);
|
|
pfout[0] = pf[0] * f;
|
|
pfout[1] = pf[1] * f;
|
|
pfout[2] = pf[2] * f;
|
|
pfout[3] = pf[3] * f;
|
|
|
|
return pfout;
|
|
}
|
|
|
|
inline dReal* cross3(dReal* pfout, const dReal* pf1, const dReal* pf2)
|
|
{
|
|
assert( pfout != NULL && pf1 != NULL && pf2 != NULL );
|
|
|
|
dReal temp[3];
|
|
temp[0] = pf1[1] * pf2[2] - pf1[2] * pf2[1];
|
|
temp[1] = pf1[2] * pf2[0] - pf1[0] * pf2[2];
|
|
temp[2] = pf1[0] * pf2[1] - pf1[1] * pf2[0];
|
|
|
|
pfout[0] = temp[0]; pfout[1] = temp[1]; pfout[2] = temp[2];
|
|
return pfout;
|
|
}
|
|
|
|
template <class T> inline void mult(T* pf, T fa, int r)
|
|
{
|
|
assert( pf != NULL );
|
|
|
|
while(r > 0) {
|
|
--r;
|
|
pf[r] *= fa;
|
|
}
|
|
}
|
|
|
|
template <class T, class S, class R>
|
|
inline T* mult(T* pf1, R* pf2, int r1, int c1, int c2, S* pfres, bool badd)
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{
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assert( pf1 != NULL && pf2 != NULL && pfres != NULL);
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int j, k;
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|
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if( !badd ) memset(pfres, 0, sizeof(S) * r1 * c2);
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|
|
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while(r1 > 0) {
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--r1;
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|
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j = 0;
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while(j < c2) {
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k = 0;
|
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while(k < c1) {
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pfres[j] += pf1[k] * pf2[k*c2 + j];
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++k;
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}
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++j;
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}
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|
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pf1 += c1;
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pfres += c2;
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}
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|
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return pfres;
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|
}
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|
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template <class T, class S, class R>
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inline T* multtrans(T* pf1, R* pf2, int r1, int c1, int c2, S* pfres, bool badd)
|
|
{
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|
assert( pf1 != NULL && pf2 != NULL && pfres != NULL);
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|
int i, j, k;
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|
|
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if( !badd ) memset(pfres, 0, sizeof(S) * c1 * c2);
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|
|
|
i = 0;
|
|
while(i < c1) {
|
|
|
|
j = 0;
|
|
while(j < c2) {
|
|
|
|
k = 0;
|
|
while(k < r1) {
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|
pfres[j] += pf1[k*c1] * pf2[k*c2 + j];
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|
++k;
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|
}
|
|
++j;
|
|
}
|
|
|
|
pfres += c2;
|
|
++pf1;
|
|
|
|
++i;
|
|
}
|
|
|
|
return pfres;
|
|
}
|
|
|
|
template <class T, class S, class R>
|
|
inline T* multtrans_to2(T* pf1, R* pf2, int r1, int c1, int r2, S* pfres, bool badd)
|
|
{
|
|
assert( pf1 != NULL && pf2 != NULL && pfres != NULL);
|
|
int j, k;
|
|
|
|
if( !badd ) memset(pfres, 0, sizeof(S) * r1 * r2);
|
|
|
|
while(r1 > 0) {
|
|
--r1;
|
|
|
|
j = 0;
|
|
while(j < r2) {
|
|
k = 0;
|
|
while(k < c1) {
|
|
pfres[j] += pf1[k] * pf2[j*c1 + k];
|
|
++k;
|
|
}
|
|
++j;
|
|
}
|
|
|
|
pf1 += c1;
|
|
pfres += r2;
|
|
}
|
|
|
|
return pfres;
|
|
}
|
|
|
|
template <class T> inline T* multto1(T* pf1, T* pf2, int r, int c, T* pftemp)
|
|
{
|
|
assert( pf1 != NULL && pf2 != NULL );
|
|
|
|
int j, k;
|
|
bool bdel = false;
|
|
|
|
if( pftemp == NULL ) {
|
|
pftemp = new T[c];
|
|
bdel = true;
|
|
}
|
|
|
|
while(r > 0) {
|
|
--r;
|
|
|
|
j = 0;
|
|
while(j < c) {
|
|
|
|
pftemp[j] = 0.0;
|
|
|
|
k = 0;
|
|
while(k < c) {
|
|
pftemp[j] += pf1[k] * pf2[k*c + j];
|
|
++k;
|
|
}
|
|
++j;
|
|
}
|
|
|
|
memcpy(pf1, pftemp, c * sizeof(T));
|
|
pf1 += c;
|
|
}
|
|
|
|
if( bdel ) delete[] pftemp;
|
|
|
|
return pf1;
|
|
}
|
|
|
|
template <class T, class S> inline T* multto2(T* pf1, S* pf2, int r2, int c2, S* pftemp)
|
|
{
|
|
assert( pf1 != NULL && pf2 != NULL );
|
|
|
|
int i, j, k;
|
|
bool bdel = false;
|
|
|
|
if( pftemp == NULL ) {
|
|
pftemp = new S[r2];
|
|
bdel = true;
|
|
}
|
|
|
|
// do columns first
|
|
j = 0;
|
|
while(j < c2) {
|
|
i = 0;
|
|
while(i < r2) {
|
|
|
|
pftemp[i] = 0.0;
|
|
|
|
k = 0;
|
|
while(k < r2) {
|
|
pftemp[i] += pf1[i*r2 + k] * pf2[k*c2 + j];
|
|
++k;
|
|
}
|
|
++i;
|
|
}
|
|
|
|
i = 0;
|
|
while(i < r2) {
|
|
*(pf2+i*c2+j) = pftemp[i];
|
|
++i;
|
|
}
|
|
|
|
++j;
|
|
}
|
|
|
|
if( bdel ) delete[] pftemp;
|
|
|
|
return pf1;
|
|
}
|
|
|
|
template <class T> inline void add(T* pf1, T* pf2, int r)
|
|
{
|
|
assert( pf1 != NULL && pf2 != NULL);
|
|
|
|
while(r > 0) {
|
|
--r;
|
|
pf1[r] += pf2[r];
|
|
}
|
|
}
|
|
|
|
template <class T> inline void sub(T* pf1, T* pf2, int r)
|
|
{
|
|
assert( pf1 != NULL && pf2 != NULL);
|
|
|
|
while(r > 0) {
|
|
--r;
|
|
pf1[r] -= pf2[r];
|
|
}
|
|
}
|
|
|
|
template <class T> inline T normsqr(T* pf1, int r)
|
|
{
|
|
assert( pf1 != NULL );
|
|
|
|
T d = 0.0;
|
|
while(r > 0) {
|
|
--r;
|
|
d += pf1[r] * pf1[r];
|
|
}
|
|
|
|
return d;
|
|
}
|
|
|
|
template <class T> inline T lengthsqr(T* pf1, T* pf2, int length)
|
|
{
|
|
T d = 0;
|
|
while(length > 0) {
|
|
--length;
|
|
d += sqr(pf1[length] - pf2[length]);
|
|
}
|
|
|
|
return d;
|
|
}
|
|
|
|
template <class T> inline T dot(T* pf1, T* pf2, int length)
|
|
{
|
|
T d = 0;
|
|
while(length > 0) {
|
|
--length;
|
|
d += pf1[length] * pf2[length];
|
|
}
|
|
|
|
return d;
|
|
}
|
|
|
|
template <class T> inline T sum(T* pf, int length)
|
|
{
|
|
T d = 0;
|
|
while(length > 0) {
|
|
--length;
|
|
d += pf[length];
|
|
}
|
|
|
|
return d;
|
|
}
|
|
|
|
template <class T> inline bool inv2(T* pf, T* pfres)
|
|
{
|
|
T fdet = pf[0] * pf[3] - pf[1] * pf[2];
|
|
|
|
if( fabs(fdet) < 1e-16 ) return false;
|
|
|
|
fdet = 1 / fdet;
|
|
//if( pfdet != NULL ) *pfdet = fdet;
|
|
|
|
if( pfres != pf ) {
|
|
pfres[0] = fdet * pf[3]; pfres[1] = -fdet * pf[1];
|
|
pfres[2] = -fdet * pf[2]; pfres[3] = fdet * pf[0];
|
|
return true;
|
|
}
|
|
|
|
dReal ftemp = pf[0];
|
|
pfres[0] = pf[3] * fdet;
|
|
pfres[1] *= -fdet;
|
|
pfres[2] *= -fdet;
|
|
pfres[3] = ftemp * pf[0];
|
|
|
|
return true;
|
|
}
|
|
|
|
#endif
|