/* LA: linear algebra C++ interface library Copyright (C) 2020-2021 Jiri Pittner or This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see . */ //this header defines simple classes for 3-dimensional REAL-valued vectors and matrices to describe rotations etc. //the class is compatible with functions in quaternion.h used for SO(3) parametrization //it should be compilable separately from LA as well as being a part of LA #ifndef _VECMAT3_H_ #define _VECMAT3_H_ #include #ifndef AVOID_STDSTREAM #include #endif #include #include #include namespace LA_Vecmat3 { #ifdef NO_NUMERIC_LIMITS #define DBL_EPSILON 1.19209290e-07f #else #define DBL_EPSILON std::numeric_limits::epsilon() #endif float fast_sqrtinv(float); //forward declaration template class Mat3; template class Vec3 { friend class Mat3; public: //just plain old data T q[3]; T (&elements())[3] {return q;}; const T (&elements()const)[3] {return q;}; // Vec3(void) {}; Vec3(const T x, const T u=0, const T v=0) {q[0]=x; q[1]=u; q[2]=v;}; //Vec3 from real(s) Vec3(const T* x) {memcpy(q,x,3*sizeof(T));} Vec3(const T (&a)[3]) {memcpy(q,a,3*sizeof(T));}; //get pointer to data transparently inline operator const T*() const {return q;}; inline operator T*() {return q;}; //compiler generates default copy constructor and assignment operator //formal indexing inline const T& operator[](const int i) const {return q[i];}; inline T& operator[](const int i) {return q[i];}; //operations of Vec3s with scalars void clear() {memset(q,0,3*sizeof(T));} Vec3& operator*=(const T rhs) {q[0]*=rhs; q[1]*=rhs; q[2]*=rhs; return *this;}; Vec3& operator/=(const T rhs) {return *this *= ((T)1/rhs);}; const Vec3 operator*(const T rhs) const {return Vec3(*this) *= rhs;}; const Vec3 operator/(const T rhs) const {return Vec3(*this) /= rhs;}; T sum() const {return q[0]+q[1]+q[2];}; T asum() const {return abs(q[0])+abs(q[1])+abs(q[2]);}; T sumsqr() const {return q[0]*q[0]+q[1]*q[1]+q[2]*q[2];}; T prod() const {return q[0]*q[1]*q[2];}; //Vec3 algebra const Vec3 operator-() const {Vec3 r(*this); r.q[0]= -r.q[0]; r.q[1]= -r.q[1]; r.q[2]= -r.q[2]; return r;}; //unary minus Vec3& operator+=(const Vec3 &rhs) {q[0]+=rhs.q[0];q[1]+=rhs.q[1];q[2]+=rhs.q[2]; return *this;}; Vec3& operator-=(const Vec3 &rhs) {q[0]-=rhs.q[0];q[1]-=rhs.q[1];q[2]-=rhs.q[2]; return *this;}; const Vec3 operator+(const Vec3 &rhs) const {return Vec3(*this) += rhs;}; const Vec3 operator-(const Vec3 &rhs) const {return Vec3(*this) -= rhs;}; const Vec3 operator*(const Vec3 &rhs) const {Vec3 x; x[0] = q[1]*rhs.q[2]-q[2]*rhs.q[1]; x[1] = q[2]*rhs.q[0]-q[0]*rhs.q[2]; x[2] = q[0]*rhs.q[1]-q[1]*rhs.q[0]; return x;}; //vector product T dot(const Vec3 &rhs) const {return q[0]*rhs.q[0] + q[1]*rhs.q[1] + q[2]*rhs.q[2];}; const Vec3 elementwise_product(const Vec3 &rhs) const {Vec3 x; x[0]=q[0]*rhs.q[0]; x[1]=q[1]*rhs.q[1]; x[2]=q[2]*rhs.q[2]; return x;}; T normsqr(void) const {return dot(*this);}; T norm(void) const {return sqrt(normsqr());}; Vec3& normalize(void) {*this /= norm(); return *this;}; Vec3& fast_normalize(void); const Vec3 operator*(const Mat3 &rhs) const; const Vec3 timesT(const Mat3 &rhs) const; //with transpose Mat3 outer(const Vec3 &rhs) const; //tensor product void addouter(Mat3 &m, const Vec3 &rhs, const T weight) const; //tensor product void inertia(Mat3 &itensor, const T weight) const; //contribution to inertia tensor void randomize(const T x); //C-style IO int fprintf(FILE *f, const char *format) const {return ::fprintf(f,format,q[0],q[1],q[2]);}; int sprintf(char *f, const char *format) const {return ::sprintf(f,format,q[0],q[1],q[2]);}; int fscanf(FILE *f, const char *format) const {return ::fscanf(f,format,q[0],q[1],q[2]);}; int sscanf(char *f, const char *format) const {return ::sscanf(f,format,q[0],q[1],q[2]);}; }; template inline T hypot3(const Vec3 &c, const Vec3 &d) {return((c-d).norm());} template class Mat3 { friend class Vec3; public: //just plain old data T q[3][3]; // T (&elements())[3][3] {return q;}; const T (&elements()const)[3][3] {return q;}; Mat3(void) {}; Mat3(const T (&a)[3][3]) {memcpy(q,a,3*3*sizeof(T));} Mat3(const T x) {memset(q,0,9*sizeof(T)); q[0][0]=q[1][1]=q[2][2]=x;}; //scalar matrix Mat3& operator=(const T &x) {memset(q,0,9*sizeof(T)); q[0][0]=q[1][1]=q[2][2]=x; return *this;}; //scalar matrix void indentity() {*this = (T)1;}; Mat3(const T* x) {memcpy(q,x,9*sizeof(T));} Mat3(const T x00, const T x01,const T x02,const T x10,const T x11,const T x12,const T x20,const T x21,const T x22) {q[0][0]=x00; q[0][1]=x01; q[0][2]=x02; q[1][0]=x10; q[1][1]=x11; q[1][2]=x12; q[2][0]=x20; q[2][1]=x21; q[2][2]=x22;}; //get pointer to data transparently inline operator const T*() const {return &q[0][0];}; inline operator T*() {return &q[0][0];}; //compiler generates default copy constructor and assignment operator //formal indexing inline const T* operator[](const int i) const {return q[i];}; inline T* operator[](const int i) {return q[i];}; inline const T& operator()(const int i, const int j) const {return q[i][j];}; inline T& operator()(const int i, const int j) {return q[i][j];}; //operations of Mat3s with scalars void clear() {memset(&q[0][0],0,9*sizeof(T));} Mat3& operator+=(const T rhs) {q[0][0]+=rhs; q[1][1]+=rhs; q[2][2]+=rhs; return *this;}; Mat3& operator-=(const T rhs) {q[0][0]-=rhs; q[1][1]-=rhs; q[2][2]-=rhs; return *this;}; const Mat3 operator+(const T rhs) const {return Mat3(*this) += rhs;}; const Mat3 operator-(const T rhs) const {return Mat3(*this) -= rhs;}; Mat3& operator*=(const T rhs) {q[0][0]*=rhs; q[0][1]*=rhs; q[0][2]*=rhs; q[1][0]*=rhs; q[1][1]*=rhs; q[1][2]*=rhs; q[2][0]*=rhs; q[2][1]*=rhs; q[2][2]*=rhs; return *this;}; Mat3& operator/=(const T rhs) {return *this *= ((T)1/rhs);}; const Mat3 operator*(const T rhs) const {return Mat3(*this) *= rhs;}; const Mat3 operator/(const T rhs) const {return Mat3(*this) /= rhs;}; void randomize(const T x, const bool symmetric=false); //Mat3 algebra const Mat3 operator-() const {return *this * (T)-1;}; //unary minus Mat3& operator+=(const Mat3 &rhs); Mat3& operator-=(const Mat3 &rhs); const Mat3 operator+(const Mat3 &rhs) const {return Mat3(*this) += rhs;}; const Mat3 operator-(const Mat3 &rhs) const {return Mat3(*this) -= rhs;}; const Mat3 operator*(const Mat3 &rhs) const; //matrix product const Mat3 timesT(const Mat3 &rhs) const; //matrix product with transpose const Mat3 Ttimes(const Mat3 &rhs) const; //matrix product with transpose const Mat3 TtimesT(const Mat3 &rhs) const; //matrix product with transpose const Vec3 operator*(const Vec3 &rhs) const; //matrix times vector const Vec3 Ttimes(const Vec3 &rhs) const; //matrix times vector with transpose T trace() const {return q[0][0]+q[1][1]+q[2][2];}; T determinant() const; void transposeme(); const Mat3 transpose() const {Mat3 r(*this); r.transposeme(); return r;}; const Mat3 inverse(T *det = NULL) const; const Vec3 linear_solve(const Vec3 &rhs, T *det = NULL) const; //alternative to simple_gaussj in simple.h //C-style IO int fprintf(FILE *f, const char *format) const {int n= ::fprintf(f,format,q[0][0],q[0][1],q[0][2]); n+=::fprintf(f,format,q[1][0],q[1][1],q[1][2]); n+=::fprintf(f,format,q[2][0],q[2][1],q[2][2]); return n;}; int fscanf(FILE *f, const char *format) const {return ::fscanf(f,format,q[0][0],q[0][1],q[0][2]) + ::fscanf(f,format,q[1][0],q[1][1],q[1][2]) + ::fscanf(f,format,q[2][0],q[2][1],q[2][2]);}; void symmetrize(); //average offdiagonal elements bool eivec_sym(Vec3 &w, Mat3 &v, const bool sortdown=false) const; //only for real symmetric matrix, symmetry is not checked, returns false on success T norm(const T scalar = 0) const; void qrd(Mat3 &q, Mat3 &r); //not const, destroys the matrix void svd(Mat3 &u, Vec3 &w, Mat3 &v, bool proper_rotations=false) const; //if proper_rotations = true, singular value can be negative but u and v are proper rotations void diagmultl(const Vec3 &rhs); void diagmultr(const Vec3 &rhs); const Mat3 svdinverse(const T thr=1000*DBL_EPSILON) const; }; //stream I/O #ifndef AVOID_STDSTREAM template std::istream& operator>>(std::istream &s, Vec3 &x); template std::ostream& operator<<(std::ostream &s, const Vec3 &x); template std::istream& operator>>(std::istream &s, Mat3 &x); template std::ostream& operator<<(std::ostream &s, const Mat3 &x); #endif //euler angles to rotation matrices cf. https://en.wikipedia.org/wiki/Euler_angles and NASA paper cited therein #define Euler_case(a,b,c) (((a)-'x')*9+((b)-'x')*3+((c)-'x')) template void euler2rotmat(const T *eul, Mat3 &a, const char *type, bool transpose=0, bool direction=0, bool reverse=0); template void rotmat2euler(T *eul, const Mat3 &a, const char *type, bool transpose=0, bool direction=0, bool reverse=0); template void perspective(T *proj_xy, const Vec3 &point, const Mat3 &rot_angle, const Vec3 &camera, const Vec3 &plane_to_camera); }//namespace using namespace LA_Vecmat3; namespace LA { //forward declaration, needed of this file is used separately from the rest of LA template class LA_traits; template class LA_traits > { public: static bool is_plaindata() {return true;}; static void copyonwrite(Vec3& x) {}; typedef T normtype; }; template class LA_traits > { public: static bool is_plaindata() {return true;}; static void copyonwrite(Mat3& x) {}; typedef T normtype; }; } #endif /* _VECMAT3_H_ */