200 lines
8.3 KiB
C++
200 lines
8.3 KiB
C++
/*
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LA: linear algebra C++ interface library
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Copyright (C) 2020-2021 Jiri Pittner <jiri.pittner@jh-inst.cas.cz> or <jiri@pittnerovi.com>
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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//this header defines simple classes for 3-dimensional vectors and matrices to describe rotations etc.
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//the class is compatible with functions in quaternion.h used for SO(3) parametrization
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//it should be compilable separately from LA as well as being a part of LA
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#ifndef _VECMAT3_H_
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#define _VECMAT3_H_
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#include <stdlib.h>
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#ifndef AVOID_STDSTREAM
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#include <iostream>
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#endif
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#include <string.h>
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#include <math.h>
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#include <stdio.h>
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namespace LA_Vecmat3 {
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float fast_sqrtinv(float);
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//forward declaration
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template <typename T> class Mat3;
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template <typename T>
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class Vec3
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{
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friend class Mat3<T>;
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public:
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//just plain old data
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T q[3];
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T (&elements())[3] {return q;};
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const T (&elements()const)[3] {return q;};
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//
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Vec3(void) {};
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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)
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Vec3(const T* x) {memcpy(q,x,3*sizeof(T));}
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Vec3(const T (&a)[3]) {memcpy(q,a,3*sizeof(T));};
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//get pointer to data transparently
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inline operator const T*() const {return q;};
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inline operator T*() {return q;};
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//compiler generates default copy constructor and assignment operator
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//formal indexing
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inline const T operator[](const int i) const {return q[i];};
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inline T& operator[](const int i) {return q[i];};
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//operations of Vec3s with scalars
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void clear() {memset(q,0,3*sizeof(T));}
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Vec3& operator*=(const T rhs) {q[0]*=rhs; q[1]*=rhs; q[2]*=rhs; return *this;};
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Vec3& operator/=(const T rhs) {return *this *= ((T)1/rhs);};
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const Vec3 operator*(const T rhs) const {return Vec3(*this) *= rhs;};
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const Vec3 operator/(const T rhs) const {return Vec3(*this) /= rhs;};
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//Vec3 algebra
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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
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Vec3& operator+=(const Vec3 &rhs) {q[0]+=rhs.q[0];q[1]+=rhs.q[1];q[2]+=rhs.q[2]; return *this;};
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Vec3& operator-=(const Vec3 &rhs) {q[0]-=rhs.q[0];q[1]-=rhs.q[1];q[2]-=rhs.q[2]; return *this;};
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const Vec3 operator+(const Vec3 &rhs) const {return Vec3(*this) += rhs;};
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const Vec3 operator-(const Vec3 &rhs) const {return Vec3(*this) -= rhs;};
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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
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T dot(const Vec3 &rhs) const {return q[0]*rhs.q[0] + q[1]*rhs.q[1] + q[2]*rhs.q[2];};
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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;};
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T normsqr(void) const {return dot(*this);};
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T norm(void) const {return sqrt(normsqr());};
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Vec3& normalize(void) {*this /= norm(); return *this;};
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Vec3& fast_normalize(void);
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const Vec3 operator*(const Mat3<T> &rhs) const;
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Mat3<T> outer(const Vec3 &rhs) const; //tensor product
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void inertia(Mat3<T> &itensor, const T weight) const; //contribution to inertia tensor
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//C-style IO
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int fprintf(FILE *f, const char *format) const {return ::fprintf(f,format,q[0],q[1],q[2]);};
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int sprintf(char *f, const char *format) const {return ::sprintf(f,format,q[0],q[1],q[2]);};
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int fscanf(FILE *f, const char *format) const {return ::fscanf(f,format,q[0],q[1],q[2]);};
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int sscanf(char *f, const char *format) const {return ::sscanf(f,format,q[0],q[1],q[2]);};
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};
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template <typename T>
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inline T hypot3(const Vec3<T> &c, const Vec3<T> &d) {return((c-d).norm());}
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template <typename T>
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class Mat3
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{
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friend class Vec3<T>;
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public:
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//just plain old data
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T q[3][3];
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//
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T (&elements())[3][3] {return q;};
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const T (&elements()const)[3][3] {return q;};
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Mat3(void) {};
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Mat3(const T (&a)[3][3]) {memcpy(q,a,3*3*sizeof(T));}
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Mat3(const T x) {memset(q,0,9*sizeof(T)); q[0][0]=q[1][1]=q[2][2]=x;}; //scalar matrix
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Mat3(const T* x) {memcpy(q,x,9*sizeof(T));}
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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)
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{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;};
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//get pointer to data transparently
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inline operator const T*() const {return &q[0][0];};
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inline operator T*() {return &q[0][0];};
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//compiler generates default copy constructor and assignment operator
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//formal indexing
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inline const T* operator[](const int i) const {return q[i];};
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inline T* operator[](const int i) {return q[i];};
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inline const T operator()(const int i, const int j) const {return q[i][j];};
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inline T& operator()(const int i, const int j) {return q[i][j];};
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//operations of Mat3s with scalars
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void clear() {memset(&q[0][0],0,9*sizeof(T));}
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Mat3& operator+=(const T rhs) {q[0][0]+=rhs; q[1][1]+=rhs; q[2][2]+=rhs; return *this;};
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Mat3& operator-=(const T rhs) {q[0][0]-=rhs; q[1][1]-=rhs; q[2][2]-=rhs; return *this;};
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const Mat3 operator+(const T rhs) const {return Mat3(*this) += rhs;};
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const Mat3 operator-(const T rhs) const {return Mat3(*this) -= rhs;};
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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;};
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Mat3& operator/=(const T rhs) {return *this *= ((T)1/rhs);};
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const Mat3 operator*(const T rhs) const {return Mat3(*this) *= rhs;};
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const Mat3 operator/(const T rhs) const {return Mat3(*this) /= rhs;};
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//Mat3 algebra
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const Mat3 operator-() const {return *this * (T)-1;}; //unary minus
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Mat3& operator+=(const Mat3 &rhs);
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Mat3& operator-=(const Mat3 &rhs);
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const Mat3 operator+(const Mat3 &rhs) const {return Mat3(*this) += rhs;};
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const Mat3 operator-(const Mat3 &rhs) const {return Mat3(*this) -= rhs;};
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const Mat3 operator*(const Mat3 &rhs) const; //matrix product
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const Vec3<T> operator*(const Vec3<T> &rhs) const; //matrix times vector
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T trace() const {return q[0][0]+q[1][1]+q[2][2];};
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T determinant() const;
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void transposeme();
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const Mat3 transpose() const {Mat3 r(*this); r.transposeme(); return r;};
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const Mat3 inverse() const;
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//C-style IO
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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;};
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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]);};
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void symmetrize(); //average offdiagonal elements
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void eival_sym(Vec3<T> &w) const; //only for real symmetric matrix, symmetry is not checked
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void eivec_sym(Vec3<T> &w, Mat3 &v) const; //only for real symmetric matrix, symmetry is not checked
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T norm(const T scalar = 0) const;
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};
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//stream I/O
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#ifndef AVOID_STDSTREAM
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template <typename T>
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std::istream& operator>>(std::istream &s, Vec3<T> &x);
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template <typename T>
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std::ostream& operator<<(std::ostream &s, const Vec3<T> &x);
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template <typename T>
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std::istream& operator>>(std::istream &s, Mat3<T> &x);
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template <typename T>
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std::ostream& operator<<(std::ostream &s, const Mat3<T> &x);
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#endif
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//euler angles to rotation matrices cf. https://en.wikipedia.org/wiki/Euler_angles and NASA paper cited therein
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#define Euler_case(a,b,c) (((a)-'x')*9+((b)-'x')*3+((c)-'x'))
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template<typename T>
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void euler2rotmat(const T *eul, Mat3<T> &a, const char *type, bool transpose=0, bool direction=0, bool reverse=0);
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template<typename T>
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void rotmat2euler(T *eul, const Mat3<T> &a, const char *type, bool transpose=0, bool direction=0, bool reverse=0);
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template<typename T>
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void perspective(T *proj_xy, const Vec3<T> &point, const Mat3<T> &rot_angle, const Vec3<T> &camera, const Vec3<T> &plane_to_camera);
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}//namespace
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#endif /* _VECMAT3_H_ */
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