mirror of
https://github.com/ptitSeb/Serious-Engine
synced 2024-10-05 23:44:51 +02:00
467 lines
12 KiB
C++
Executable File
467 lines
12 KiB
C++
Executable File
/* Copyright (c) 2002-2012 Croteam Ltd.
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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 version 2 of the GNU General Public License as published by
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the Free Software Foundation
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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 along
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with this program; if not, write to the Free Software Foundation, Inc.,
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51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. */
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#ifndef SE_INCL_QUATERNION_H
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#define SE_INCL_QUATERNION_H
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#ifdef PRAGMA_ONCE
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#pragma once
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#endif
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#include <Engine/Base/Assert.h>
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#include <Engine/Math/Functions.h>
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/*
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* Template class for quaternion of arbitrary precision.
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*/
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template<class Type>
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class Quaternion {
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public:
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Type q_w, q_x, q_y, q_z;
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public:
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// default constructor
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inline Quaternion(void);
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// constructor from four scalar values
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inline Quaternion(Type w, Type x, Type y, Type z);
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// conversion from euler angles
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void FromEuler(const Vector<Type, 3> &a);
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inline Type EPS(Type orig) const;
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// conversion to matrix
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void ToMatrix(Matrix<Type, 3, 3> &m) const;
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// conversion from matrix
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void FromMatrix(Matrix<Type, 3, 3> &m);
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// conversion to/from axis-angle
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void FromAxisAngle(const Vector<Type, 3> &n, Type a);
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void ToAxisAngle(Vector<Type, 3> &n, Type &a);
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// unary minus (fliping of the quaternion)
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inline Quaternion<Type> operator-(void) const;
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// conjugation
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inline Quaternion<Type> operator~(void) const;
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// inversion
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inline Quaternion<Type> Inv(void) const;
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// multiplication/division by a scalar
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inline Quaternion<Type> operator*(Type t) const;
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inline Quaternion<Type> &operator*=(Type t);
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friend Quaternion<Type> operator*(Type t, Quaternion<Type> q)
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{
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return Quaternion<Type>(q.q_w*t, q.q_x*t, q.q_y*t, q.q_z*t);
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}
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inline Quaternion<Type> operator/(Type t) const;
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inline Quaternion<Type> &operator/=(Type t);
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// addition/substraction
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inline Quaternion<Type> operator+(const Quaternion<Type> &q2) const;
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inline Quaternion<Type> &operator+=(const Quaternion<Type> &q2);
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inline Quaternion<Type> operator-(const Quaternion<Type> &q2) const;
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inline Quaternion<Type> &operator-=(const Quaternion<Type> &q2);
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// multiplication
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inline Quaternion<Type> operator*(const Quaternion<Type> &q2) const;
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inline Quaternion<Type> &operator*=(const Quaternion<Type> &q2);
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// dot product
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inline Type operator%(const Quaternion<Type> &q2) const;
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// quaternion norm (euclidian length of a 4d vector)
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inline Type Norm(void) const;
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friend __forceinline CTStream &operator>>(CTStream &strm, Quaternion<Type> &q) {
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strm>>q.q_w;
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strm>>q.q_x;
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strm>>q.q_y;
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strm>>q.q_z;
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return strm;
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}
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friend __forceinline CTStream &operator<<(CTStream &strm, const Quaternion<Type> &q) {
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strm<<q.q_w;
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strm<<q.q_x;
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strm<<q.q_y;
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strm<<q.q_z;
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return strm;
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}
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// transcendental functions
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friend Quaternion<Type> Exp(const Quaternion<Type> &q)
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{
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Type tAngle = (Type)sqrt(q.q_x*q.q_x + q.q_y*q.q_y + q.q_z*q.q_z);
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Type tSin = sin(tAngle);
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Type tCos = cos(tAngle);
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if (fabs(tSin)<0.001) {
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return Quaternion<Type>(tCos, q.q_x, q.q_y, q.q_z);
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} else {
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Type tRatio = tSin/tAngle;
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return Quaternion<Type>(tCos, q.q_x*tRatio, q.q_y*tRatio, q.q_z*tRatio);
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}
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}
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friend Quaternion<Type> Log(const Quaternion<Type> &q)
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{
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if (fabs(q.q_w)<1.0) {
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Type tAngle = acos(q.q_w);
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Type tSin = sin(tAngle);
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if (fabs(tSin)>=0.001) {
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Type tRatio = tAngle/tSin;
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return Quaternion<Type>(Type(0), q.q_x*tRatio, q.q_y*tRatio, q.q_z*tRatio);
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}
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}
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return Quaternion<Type>(Type(0), q.q_x, q.q_y, q.q_z);
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}
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// spherical linear interpolation
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friend Quaternion<Type> Slerp(Type tT,
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const Quaternion<Type> &q1, const Quaternion<Type> &q2)
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{
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Type tCos = q1%q2;
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Quaternion<Type> qTemp;
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if (tCos<Type(0)) {
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tCos = -tCos;
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qTemp = -q2;
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} else {
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qTemp = q2;
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}
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Type tF1, tF2;
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if ((Type(1)-tCos) > Type(0.001)) {
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// standard case (slerp)
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Type tAngle = acos(tCos);
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Type tSin = sin(tAngle);
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tF1 = sin((Type(1)-tT)*tAngle)/tSin;
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tF2 = sin(tT*tAngle)/tSin;
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} else {
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// linear interpolation
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tF1 = Type(1)-tT;
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tF2 = tT;
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}
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return q1*tF1 + qTemp*tF2;
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}
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// spherical quadratic interpolation
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friend Quaternion<Type> Squad(Type tT,
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const Quaternion<Type> &q1, const Quaternion<Type> &q2,
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const Quaternion<Type> &qa, const Quaternion<Type> &qb)
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{
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return Slerp(2*tT*(1-tT),Slerp(tT,q1,q2),Slerp(tT,qa,qb));
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}
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};
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// inline functions implementation
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/*
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* Default constructor.
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*/
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template<class Type>
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inline Quaternion<Type>::Quaternion(void) {};
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/* Constructor from three values. */
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template<class Type>
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inline Quaternion<Type>::Quaternion(Type w, Type x, Type y, Type z)
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: q_w(w), q_x(x), q_y(y), q_z(z) {};
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// unary minus (additive inversion)
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template<class Type>
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inline Quaternion<Type> Quaternion<Type>::operator-(void) const {
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return Quaternion<Type>(-q_w, -q_x, -q_y, -q_z);
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}
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// conjugation
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template<class Type>
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inline Quaternion<Type> Quaternion<Type>::operator~(void) const {
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return Quaternion<Type>(q_w, -q_x, -q_y, -q_z);
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}
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// multiplicative inversion
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template<class Type>
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inline Quaternion<Type> Quaternion<Type>::Inv(void) const {
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return (~(*this))/Norm();
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}
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// multiplication/division by a scalar
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template<class Type>
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inline Quaternion<Type> Quaternion<Type>::operator*(Type t) const {
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return Quaternion<Type>(q_w*t, q_x*t, q_y*t, q_z*t);
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}
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template<class Type>
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inline Quaternion<Type> &Quaternion<Type>::operator*=(Type t) {
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q_w*=t; q_x*=t; q_y*=t; q_z*=t;
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return *this;
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}
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#if 0
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template<class Type>
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inline Quaternion<Type> operator*(Type t, Quaternion<Type> q) {
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return Quaternion<Type>(q.q_w*t, q.q_x*t, q.q_y*t, q.q_z*t);
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}
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#endif
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template<class Type>
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inline Quaternion<Type> Quaternion<Type>::operator/(Type t) const {
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return Quaternion<Type>(q_w/t, q_x/t, q_y/t, q_z/t);
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}
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template<class Type>
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inline Quaternion<Type> &Quaternion<Type>::operator/=(Type t) {
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q_w/=t; q_x/=t; q_y/=t; q_z/=t;
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return *this;
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}
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// addition/substraction
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template<class Type>
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inline Quaternion<Type> Quaternion<Type>::operator+(const Quaternion<Type> &q2) const {
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return Quaternion<Type>(q_w+q2.q_w, q_x+q2.q_x, q_y+q2.q_y, q_z+q2.q_z);
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}
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template<class Type>
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inline Quaternion<Type> &Quaternion<Type>::operator+=(const Quaternion<Type> &q2) {
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q_w+=q2.q_w; q_x+=q2.q_x; q_y+=q2.q_y; q_z+=q2.q_z;
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return *this;
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}
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template<class Type>
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inline Quaternion<Type> Quaternion<Type>::operator-(const Quaternion<Type> &q2) const {
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return Quaternion<Type>(q_w-q2.q_w, q_x-q2.q_x, q_y-q2.q_y, q_z-q2.q_z);
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}
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template<class Type>
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inline Quaternion<Type> &Quaternion<Type>::operator-=(const Quaternion<Type> &q2) {
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q_w-=q2.q_w; q_x-=q2.q_x; q_y-=q2.q_y; q_z-=q2.q_z;
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return *this;
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}
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// multiplication
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template<class Type>
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inline Quaternion<Type> Quaternion<Type>::operator*(const Quaternion<Type> &q2) const {
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return Quaternion<Type>(
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q_w*q2.q_w - q_x*q2.q_x - q_y*q2.q_y - q_z*q2.q_z,
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q_w*q2.q_x + q_x*q2.q_w + q_y*q2.q_z - q_z*q2.q_y,
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q_w*q2.q_y - q_x*q2.q_z + q_y*q2.q_w + q_z*q2.q_x,
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q_w*q2.q_z + q_x*q2.q_y - q_y*q2.q_x + q_z*q2.q_w);
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}
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template<class Type>
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inline Quaternion<Type> &Quaternion<Type>::operator*=(const Quaternion<Type> &q2) {
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*this = (*this)*q2;
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return *this;
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}
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// dot product
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template<class Type>
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inline Type Quaternion<Type>::operator%(const Quaternion<Type> &q2) const {
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return q_w*q2.q_w + q_x*q2.q_x + q_y*q2.q_y + q_z*q2.q_z;
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}
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// quaternion norm (euclidian length of a 4d vector)
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template<class Type>
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inline Type Quaternion<Type>::Norm(void) const {
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return (Type)sqrt(q_w*q_w + q_x*q_x + q_y*q_y + q_z*q_z);
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}
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#if 0
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// transcendental functions
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template<class Type>
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inline Quaternion<Type> Exp(const Quaternion<Type> &q)
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{
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Type tAngle = (Type)sqrt(q.q_x*q.q_x + q.q_y*q.q_y + q.q_z*q.q_z);
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Type tSin = sin(tAngle);
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Type tCos = cos(tAngle);
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if (fabs(tSin)<0.001) {
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return Quaternion<Type>(tCos, q.q_x, q.q_y, q.q_z);
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} else {
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Type tRatio = tSin/tAngle;
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return Quaternion<Type>(tCos, q.q_x*tRatio, q.q_y*tRatio, q.q_z*tRatio);
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}
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}
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// transcendental functions
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template<class Type>
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inline Quaternion<Type> Log(const Quaternion<Type> &q)
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{
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if (fabs(q.q_w)<1.0) {
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Type tAngle = acos(q.q_w);
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Type tSin = sin(tAngle);
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if (fabs(tSin)>=0.001) {
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Type tRatio = tAngle/tSin;
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return Quaternion<Type>(Type(0), q.q_x*tRatio, q.q_y*tRatio, q.q_z*tRatio);
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}
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}
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return Quaternion<Type>(Type(0), q.q_x, q.q_y, q.q_z);
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}
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// spherical linear interpolation
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template<class Type>
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inline Quaternion<Type> Slerp(Type tT,
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const Quaternion<Type> &q1, const Quaternion<Type> &q2)
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{
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Type tCos = q1%q2;
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Quaternion<Type> qTemp;
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if (tCos<Type(0)) {
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tCos = -tCos;
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qTemp = -q2;
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} else {
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qTemp = q2;
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}
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Type tF1, tF2;
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if ((Type(1)-tCos) > Type(0.001)) {
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// standard case (slerp)
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Type tAngle = acos(tCos);
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Type tSin = sin(tAngle);
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tF1 = sin((Type(1)-tT)*tAngle)/tSin;
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tF2 = sin(tT*tAngle)/tSin;
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} else {
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// linear interpolation
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tF1 = Type(1)-tT;
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tF2 = tT;
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}
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return q1*tF1 + qTemp*tF2;
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}
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// spherical quadratic interpolation
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template<class Type>
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inline Quaternion<Type> Squad(Type tT,
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const Quaternion<Type> &q1, const Quaternion<Type> &q2,
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const Quaternion<Type> &qa, const Quaternion<Type> &qb)
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{
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return Slerp(2*tT*(1-tT),Slerp(tT,q1,q2),Slerp(tT,qa,qb));
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}
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#endif
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// conversion from euler angles
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template<class Type>
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void Quaternion<Type>::FromEuler(const Vector<Type, 3> &a)
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{
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Quaternion<Type> qH;
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Quaternion<Type> qP;
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Quaternion<Type> qB;
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qH.q_w = Cos(a(1)/2);
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qH.q_x = 0;
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qH.q_y = Sin(a(1)/2);
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qH.q_z = 0;
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qP.q_w = Cos(a(2)/2);
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qP.q_x = Sin(a(2)/2);
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qP.q_y = 0;
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qP.q_z = 0;
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qB.q_w = Cos(a(3)/2);
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qB.q_x = 0;
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qB.q_y = 0;
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qB.q_z = Sin(a(3)/2);
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(*this) = qH*qP*qB;
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}
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// Check for almost, not really, but should be 0.0 values...
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template<class Type>
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Type Quaternion<Type>::EPS(Type orig) const
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{
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if ((orig <= 10e-6f) && (orig >= -10e-6f))
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return(0.0f);
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return(orig);
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}
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// conversion to matrix
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template<class Type>
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void Quaternion<Type>::ToMatrix(Matrix<Type, 3, 3> &m) const
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{
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Type xx = 2*q_x*q_x; Type xy = 2*q_x*q_y; Type xz = 2*q_x*q_z;
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Type yy = 2*q_y*q_y; Type yz = 2*q_y*q_z; Type zz = 2*q_z*q_z;
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Type wx = 2*q_w*q_x; Type wy = 2*q_w*q_y; Type wz = 2*q_w*q_z;
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m(1,1) = EPS(1.0f-(yy+zz));m(1,2) = EPS(xy-wz); m(1,3) = EPS(xz+wy);
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m(2,1) = EPS(xy+wz); m(2,2) = EPS(1.0f-(xx+zz));m(2,3) = EPS(yz-wx);
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m(3,1) = EPS(xz-wy); m(3,2) = EPS(yz+wx); m(3,3) = EPS(1.0f-(xx+yy));
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}
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// conversion from matrix
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template<class Type>
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void Quaternion<Type>::FromMatrix(Matrix<Type, 3, 3> &m)
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{
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Type trace = m(1,1)+m(2,2)+m(3,3);
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Type root;
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if ( trace > 0.0f )
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{
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// |w| > 1/2, may as well choose w > 1/2
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root = sqrt(trace+1.0f); // 2w
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q_w = 0.5f*root;
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root = 0.5f/root; // 1/(4w)
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q_x = (m(3,2)-m(2,3))*root;
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q_y = (m(1,3)-m(3,1))*root;
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q_z = (m(2,1)-m(1,2))*root;
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}
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else
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{
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// |w| <= 1/2
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static int next[3] = { 1, 2, 0 };
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int i = 0;
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if ( m(2,2) > m(1,1) )
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i = 1;
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if ( m(3,3) > m(i+1,i+1) )
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i = 2;
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int j = next[i];
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int k = next[j];
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root = sqrt(m(i+1,i+1)-m(j+1,j+1)-m(k+1,k+1)+1.0f);
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Type* quat[3] = { &q_x, &q_y, &q_z };
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*quat[i] = 0.5f*root;
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root = 0.5f/root;
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q_w = (m(k+1,j+1)-m(j+1,k+1))*root;
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*quat[j] = (m(j+1,i+1)+m(i+1,j+1))*root;
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*quat[k] = (m(k+1,i+1)+m(i+1,k+1))*root;
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}
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}
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// conversion to/from axis-angle
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template<class Type>
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void Quaternion<Type>::FromAxisAngle(const Vector<Type, 3> &n, Type a)
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{
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Type tSin = sin(a/2);
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Type tCos = cos(a/2);
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q_x = n(1)*tSin;
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q_y = n(2)*tSin;
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q_z = n(3)*tSin;
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q_w = tCos;
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}
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template<class Type>
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void Quaternion<Type>::ToAxisAngle(Vector<Type, 3> &n, Type &a)
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{
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Type tCos = q_w;
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Type tSin = sqrt(Type(1)-tCos*tCos);
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a = 2*acos(tCos);
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// if angle is not zero
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if (Abs(tSin)>=0.001) {
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n(1) = q_x / tSin;
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n(2) = q_y / tSin;
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n(3) = q_z / tSin;
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// if angle is zero
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} else {
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n(1) = Type(1);
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n(2) = Type(0);
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n(3) = Type(0);
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}
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}
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#endif /* include-once check. */
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