219 lines
8.5 KiB
C++
219 lines
8.5 KiB
C++
/*
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LA: linear algebra C++ interface library
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Copyright (C) 2008-2020 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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//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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//
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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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//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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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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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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const Vec3 operator*(const Mat3<T> &rhs) const
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{
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Vec3 r;
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r[0] = q[0]*rhs.q[0][0] + q[1]*rhs.q[1][0] + q[2]*rhs.q[2][0];
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r[1] = q[0]*rhs.q[0][1] + q[1]*rhs.q[1][1] + q[2]*rhs.q[2][1];
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r[2] = q[0]*rhs.q[0][2] + q[1]*rhs.q[1][2] + q[2]*rhs.q[2][2];
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return r;
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}; //matrix times vector
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};
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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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Mat3(void) {};
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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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//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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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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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) {q[0][0]+=rhs.q[0][0];q[0][1]+=rhs.q[0][1];q[0][2]+=rhs.q[0][2]; q[1][0]+=rhs.q[1][0];q[1][1]+=rhs.q[1][1];q[1][2]+=rhs.q[1][2]; q[2][0]+=rhs.q[2][0];q[2][1]+=rhs.q[2][1];q[2][2]+=rhs.q[2][2]; return *this;};
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Mat3& operator-=(const Mat3 &rhs) {q[0][0]-=rhs.q[0][0];q[0][1]-=rhs.q[0][1];q[0][2]-=rhs.q[0][2]; q[1][0]-=rhs.q[1][0];q[1][1]-=rhs.q[1][1];q[1][2]-=rhs.q[1][2]; q[2][0]-=rhs.q[2][0];q[2][1]-=rhs.q[2][1];q[2][2]-=rhs.q[2][2]; return *this;};
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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
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{
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Mat3 r;
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r[0][0]= q[0][0]*rhs.q[0][0] + q[0][1]*rhs.q[1][0] + q[0][2]*rhs.q[2][0];
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r[0][1]= q[0][0]*rhs.q[0][1] + q[0][1]*rhs.q[1][1] + q[0][2]*rhs.q[2][1];
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r[0][2]= q[0][0]*rhs.q[0][2] + q[0][1]*rhs.q[1][2] + q[0][2]*rhs.q[2][2];
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r[1][0]= q[1][0]*rhs.q[0][0] + q[1][1]*rhs.q[1][0] + q[1][2]*rhs.q[2][0];
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r[1][1]= q[1][0]*rhs.q[0][1] + q[1][1]*rhs.q[1][1] + q[1][2]*rhs.q[2][1];
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r[1][2]= q[1][0]*rhs.q[0][2] + q[1][1]*rhs.q[1][2] + q[1][2]*rhs.q[2][2];
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r[2][0]= q[2][0]*rhs.q[0][0] + q[2][1]*rhs.q[1][0] + q[2][2]*rhs.q[2][0];
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r[2][1]= q[2][0]*rhs.q[0][1] + q[2][1]*rhs.q[1][1] + q[2][2]*rhs.q[2][1];
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r[2][2]= q[2][0]*rhs.q[0][2] + q[2][1]*rhs.q[1][2] + q[2][2]*rhs.q[2][2];
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return r;
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}; //matrix product
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const Vec3<T> operator*(const Vec3<T> &rhs) const
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{
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Vec3<T> r;
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r[0] = q[0][0]*rhs.q[0] + q[0][1]*rhs.q[1] + q[0][2]*rhs.q[2];
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r[1] = q[1][0]*rhs.q[0] + q[1][1]*rhs.q[1] + q[1][2]*rhs.q[2];
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r[2] = q[2][0]*rhs.q[0] + q[2][1]*rhs.q[1] + q[2][2]*rhs.q[2];
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return r;
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}; //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 {return q[0][0]*(q[2][2]*q[1][1]-q[2][1]*q[1][2])-q[1][0]*(q[2][2]*q[0][1]-q[2][1]*q[0][2])+q[2][0]*(q[1][2]*q[0][1]-q[1][1]*q[0][2]); };//determinant
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void transposeme() {T t; t=q[0][1]; q[0][1]=q[1][0]; q[1][0]=t; t=q[0][2]; q[0][2]=q[2][0]; q[2][0]=t; t=q[1][2]; q[1][2]=q[2][1]; q[2][1]=t;};
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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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{
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Mat3 r;
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r[0][0]= q[2][2]*q[1][1]-q[2][1]*q[1][2];
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r[0][1]= -q[2][2]*q[0][1]+q[2][1]*q[0][2];
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r[0][2]= q[1][2]*q[0][1]-q[1][1]*q[0][2];
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r[1][0]= -q[2][2]*q[1][0]+q[2][0]*q[1][1];
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r[1][1]= q[2][2]*q[0][0]-q[2][0]*q[0][2];
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r[1][2]= -q[1][2]*q[0][0]+q[1][0]*q[0][2];
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r[2][0]= q[2][1]*q[1][0]-q[2][0]*q[1][1];
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r[2][1]= -q[2][1]*q[0][0]+q[2][0]*q[0][1];
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r[2][2]= q[1][1]*q[0][0]-q[1][0]*q[0][1];
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return r/determinant();
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};
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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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{
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s >> x.q[0];
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s >> x.q[1];
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s >> x.q[2];
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return s;
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}
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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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s << x.q[0]<<" ";
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s << x.q[1]<<" ";
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s << x.q[2];
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return s;
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}
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template <typename T>
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std::istream& operator>>(std::istream &s, Mat3<T> &x)
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{
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s >> x.q[0][0];
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s >> x.q[0][1];
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s >> x.q[0][2];
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s >> x.q[1][0];
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s >> x.q[1][1];
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s >> x.q[1][2];
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s >> x.q[2][0];
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s >> x.q[2][1];
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s >> x.q[2][2];
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return s;
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}
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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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s << x.q[0][0]<<" "<< x.q[0][1]<<" " << x.q[0][2]<<std::endl;
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s << x.q[1][0]<<" "<< x.q[1][1]<<" " << x.q[1][2]<<std::endl;
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s << x.q[2][0]<<" "<< x.q[2][1]<<" " << x.q[2][2]<<std::endl;
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return s;
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}
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#endif
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#endif /* _VECMAT3_H_ */
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