260 lines
10 KiB
C++
260 lines
10 KiB
C++
/*
|
|
LA: linear algebra C++ interface library
|
|
Copyright (C) 2020-2021 Jiri Pittner <jiri.pittner@jh-inst.cas.cz> or <jiri@pittnerovi.com>
|
|
|
|
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 <http://www.gnu.org/licenses/>.
|
|
*/
|
|
|
|
//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 <stdlib.h>
|
|
#ifndef AVOID_STDSTREAM
|
|
#include <iostream>
|
|
#endif
|
|
#include <string.h>
|
|
#include <math.h>
|
|
#include <stdio.h>
|
|
|
|
namespace LA_Vecmat3 {
|
|
|
|
#ifndef DBL_EPSILON
|
|
|
|
#ifdef NO_NUMERIC_LIMITS
|
|
#define DBL_EPSILON 1.19209290e-07f
|
|
#else
|
|
#define DBL_EPSILON std::numeric_limits<T>::epsilon()
|
|
#endif
|
|
|
|
#endif
|
|
|
|
|
|
|
|
float fast_sqrtinv(float);
|
|
|
|
//forward declaration
|
|
template <typename T> class Mat3;
|
|
|
|
|
|
template <typename T>
|
|
class Vec3
|
|
{
|
|
friend class Mat3<T>;
|
|
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<T> &rhs) const;
|
|
const Vec3 timesT(const Mat3<T> &rhs) const; //with transpose
|
|
Mat3<T> outer(const Vec3 &rhs) const; //tensor product
|
|
void addouter(Mat3<T> &m, const Vec3 &rhs, const T weight) const; //tensor product
|
|
void inertia(Mat3<T> &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 <typename T>
|
|
inline T hypot3(const Vec3<T> &c, const Vec3<T> &d) {return((c-d).norm());}
|
|
|
|
|
|
template <typename T>
|
|
class Mat3
|
|
{
|
|
friend class Vec3<T>;
|
|
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<T> operator*(const Vec3<T> &rhs) const; //matrix times vector
|
|
const Vec3<T> Ttimes(const Vec3<T> &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<T> linear_solve(const Vec3<T> &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<T> &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<T> &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<T> &rhs);
|
|
void diagmultr(const Vec3<T> &rhs);
|
|
const Mat3 svdinverse(const T thr=1000*DBL_EPSILON) const;
|
|
};
|
|
|
|
|
|
|
|
//stream I/O
|
|
#ifndef AVOID_STDSTREAM
|
|
template <typename T>
|
|
std::istream& operator>>(std::istream &s, Vec3<T> &x);
|
|
|
|
template <typename T>
|
|
std::ostream& operator<<(std::ostream &s, const Vec3<T> &x);
|
|
|
|
template <typename T>
|
|
std::istream& operator>>(std::istream &s, Mat3<T> &x);
|
|
|
|
template <typename T>
|
|
std::ostream& operator<<(std::ostream &s, const Mat3<T> &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<typename T>
|
|
void euler2rotmat(const T *eul, Mat3<T> &a, const char *type, bool transpose=0, bool direction=0, bool reverse=0);
|
|
|
|
template<typename T>
|
|
void rotmat2euler(T *eul, const Mat3<T> &a, const char *type, bool transpose=0, bool direction=0, bool reverse=0);
|
|
|
|
template<typename T>
|
|
void perspective(T *proj_xy, const Vec3<T> &point, const Mat3<T> &rot_angle, const Vec3<T> &camera, const Vec3<T> &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<typename T>
|
|
class LA_traits;
|
|
|
|
template<typename T>
|
|
class LA_traits<Vec3<T> >
|
|
{
|
|
public:
|
|
static bool is_plaindata() {return true;};
|
|
static void copyonwrite(Vec3<T>& x) {};
|
|
typedef T normtype;
|
|
};
|
|
|
|
template<typename T>
|
|
class LA_traits<Mat3<T> >
|
|
{
|
|
public:
|
|
static bool is_plaindata() {return true;};
|
|
static void copyonwrite(Mat3<T>& x) {};
|
|
typedef T normtype;
|
|
};
|
|
|
|
|
|
}
|
|
#endif /* _VECMAT3_H_ */
|
|
|