697 lines
17 KiB
C++
697 lines
17 KiB
C++
// Copyright (C) 2002-2012 Nikolaus Gebhardt
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// This file is part of the "Irrlicht Engine".
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// For conditions of distribution and use, see copyright notice in irrlicht.h
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#ifndef __IRR_QUATERNION_H_INCLUDED__
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#define __IRR_QUATERNION_H_INCLUDED__
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#include "irrTypes.h"
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#include "irrMath.h"
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#include "matrix4.h"
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#include "vector3d.h"
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// Between Irrlicht 1.7 and Irrlicht 1.8 the quaternion-matrix conversions got fixed.
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// This define disables all involved functions completely to allow finding all places
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// where the wrong conversions had been in use.
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#define IRR_TEST_BROKEN_QUATERNION_USE 0
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namespace irr
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{
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namespace core
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{
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//! Quaternion class for representing rotations.
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/** It provides cheap combinations and avoids gimbal locks.
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Also useful for interpolations. */
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class quaternion
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{
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public:
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//! Default Constructor
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quaternion() : X(0.0f), Y(0.0f), Z(0.0f), W(1.0f) {}
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//! Constructor
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quaternion(f32 x, f32 y, f32 z, f32 w) : X(x), Y(y), Z(z), W(w) { }
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//! Constructor which converts euler angles (radians) to a quaternion
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quaternion(f32 x, f32 y, f32 z);
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//! Constructor which converts euler angles (radians) to a quaternion
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quaternion(const vector3df& vec);
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#if !IRR_TEST_BROKEN_QUATERNION_USE
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//! Constructor which converts a matrix to a quaternion
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quaternion(const matrix4& mat);
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#endif
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//! Equalilty operator
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bool operator==(const quaternion& other) const;
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//! inequality operator
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bool operator!=(const quaternion& other) const;
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//! Assignment operator
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inline quaternion& operator=(const quaternion& other);
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#if !IRR_TEST_BROKEN_QUATERNION_USE
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//! Matrix assignment operator
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inline quaternion& operator=(const matrix4& other);
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#endif
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//! Add operator
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quaternion operator+(const quaternion& other) const;
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//! Multiplication operator
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quaternion operator*(const quaternion& other) const;
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//! Multiplication operator with scalar
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quaternion operator*(f32 s) const;
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//! Multiplication operator with scalar
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quaternion& operator*=(f32 s);
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//! Multiplication operator
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vector3df operator*(const vector3df& v) const;
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//! Multiplication operator
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quaternion& operator*=(const quaternion& other);
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//! Calculates the dot product
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inline f32 dotProduct(const quaternion& other) const;
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//! Sets new quaternion
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inline quaternion& set(f32 x, f32 y, f32 z, f32 w);
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//! Sets new quaternion based on euler angles (radians)
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inline quaternion& set(f32 x, f32 y, f32 z);
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//! Sets new quaternion based on euler angles (radians)
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inline quaternion& set(const core::vector3df& vec);
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//! Sets new quaternion from other quaternion
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inline quaternion& set(const core::quaternion& quat);
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//! returns if this quaternion equals the other one, taking floating point rounding errors into account
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inline bool equals(const quaternion& other,
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const f32 tolerance = ROUNDING_ERROR_f32 ) const;
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//! Normalizes the quaternion
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inline quaternion& normalize();
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#if !IRR_TEST_BROKEN_QUATERNION_USE
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//! Creates a matrix from this quaternion
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matrix4 getMatrix() const;
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#endif
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//! Creates a matrix from this quaternion
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void getMatrix( matrix4 &dest, const core::vector3df &translation=core::vector3df() ) const;
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/*!
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Creates a matrix from this quaternion
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Rotate about a center point
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shortcut for
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core::quaternion q;
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q.rotationFromTo ( vin[i].Normal, forward );
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q.getMatrixCenter ( lookat, center, newPos );
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core::matrix4 m2;
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m2.setInverseTranslation ( center );
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lookat *= m2;
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core::matrix4 m3;
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m2.setTranslation ( newPos );
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lookat *= m3;
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*/
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void getMatrixCenter( matrix4 &dest, const core::vector3df ¢er, const core::vector3df &translation ) const;
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//! Creates a matrix from this quaternion
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inline void getMatrix_transposed( matrix4 &dest ) const;
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//! Inverts this quaternion
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quaternion& makeInverse();
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//! Set this quaternion to the linear interpolation between two quaternions
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/** \param q1 First quaternion to be interpolated.
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\param q2 Second quaternion to be interpolated.
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\param time Progress of interpolation. For time=0 the result is
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q1, for time=1 the result is q2. Otherwise interpolation
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between q1 and q2.
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*/
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quaternion& lerp(quaternion q1, quaternion q2, f32 time);
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//! Set this quaternion to the result of the spherical interpolation between two quaternions
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/** \param q1 First quaternion to be interpolated.
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\param q2 Second quaternion to be interpolated.
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\param time Progress of interpolation. For time=0 the result is
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q1, for time=1 the result is q2. Otherwise interpolation
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between q1 and q2.
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\param threshold To avoid inaccuracies at the end (time=1) the
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interpolation switches to linear interpolation at some point.
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This value defines how much of the remaining interpolation will
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be calculated with lerp. Everything from 1-threshold up will be
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linear interpolation.
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*/
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quaternion& slerp(quaternion q1, quaternion q2,
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f32 time, f32 threshold=.05f);
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//! Create quaternion from rotation angle and rotation axis.
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/** Axis must be unit length.
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The quaternion representing the rotation is
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q = cos(A/2)+sin(A/2)*(x*i+y*j+z*k).
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\param angle Rotation Angle in radians.
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\param axis Rotation axis. */
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quaternion& fromAngleAxis (f32 angle, const vector3df& axis);
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//! Fills an angle (radians) around an axis (unit vector)
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void toAngleAxis (f32 &angle, core::vector3df& axis) const;
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//! Output this quaternion to an euler angle (radians)
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void toEuler(vector3df& euler) const;
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//! Set quaternion to identity
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quaternion& makeIdentity();
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//! Set quaternion to represent a rotation from one vector to another.
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quaternion& rotationFromTo(const vector3df& from, const vector3df& to);
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//! Quaternion elements.
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f32 X; // vectorial (imaginary) part
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f32 Y;
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f32 Z;
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f32 W; // real part
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};
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// Constructor which converts euler angles to a quaternion
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inline quaternion::quaternion(f32 x, f32 y, f32 z)
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{
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set(x,y,z);
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}
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// Constructor which converts euler angles to a quaternion
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inline quaternion::quaternion(const vector3df& vec)
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{
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set(vec.X,vec.Y,vec.Z);
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}
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#if !IRR_TEST_BROKEN_QUATERNION_USE
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// Constructor which converts a matrix to a quaternion
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inline quaternion::quaternion(const matrix4& mat)
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{
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(*this) = mat;
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}
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#endif
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// equal operator
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inline bool quaternion::operator==(const quaternion& other) const
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{
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return ((X == other.X) &&
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(Y == other.Y) &&
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(Z == other.Z) &&
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(W == other.W));
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}
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// inequality operator
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inline bool quaternion::operator!=(const quaternion& other) const
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{
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return !(*this == other);
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}
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// assignment operator
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inline quaternion& quaternion::operator=(const quaternion& other)
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{
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X = other.X;
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Y = other.Y;
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Z = other.Z;
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W = other.W;
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return *this;
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}
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#if !IRR_TEST_BROKEN_QUATERNION_USE
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// matrix assignment operator
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inline quaternion& quaternion::operator=(const matrix4& m)
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{
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const f32 diag = m[0] + m[5] + m[10] + 1;
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if( diag > 0.0f )
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{
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const f32 scale = sqrtf(diag) * 2.0f; // get scale from diagonal
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// TODO: speed this up
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X = (m[6] - m[9]) / scale;
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Y = (m[8] - m[2]) / scale;
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Z = (m[1] - m[4]) / scale;
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W = 0.25f * scale;
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}
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else
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{
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if (m[0]>m[5] && m[0]>m[10])
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{
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// 1st element of diag is greatest value
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// find scale according to 1st element, and double it
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const f32 scale = sqrtf(1.0f + m[0] - m[5] - m[10]) * 2.0f;
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// TODO: speed this up
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X = 0.25f * scale;
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Y = (m[4] + m[1]) / scale;
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Z = (m[2] + m[8]) / scale;
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W = (m[6] - m[9]) / scale;
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}
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else if (m[5]>m[10])
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{
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// 2nd element of diag is greatest value
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// find scale according to 2nd element, and double it
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const f32 scale = sqrtf(1.0f + m[5] - m[0] - m[10]) * 2.0f;
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// TODO: speed this up
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X = (m[4] + m[1]) / scale;
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Y = 0.25f * scale;
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Z = (m[9] + m[6]) / scale;
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W = (m[8] - m[2]) / scale;
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}
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else
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{
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// 3rd element of diag is greatest value
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// find scale according to 3rd element, and double it
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const f32 scale = sqrtf(1.0f + m[10] - m[0] - m[5]) * 2.0f;
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// TODO: speed this up
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X = (m[8] + m[2]) / scale;
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Y = (m[9] + m[6]) / scale;
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Z = 0.25f * scale;
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W = (m[1] - m[4]) / scale;
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}
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}
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return normalize();
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}
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#endif
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// multiplication operator
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inline quaternion quaternion::operator*(const quaternion& other) const
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{
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quaternion tmp;
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tmp.W = (other.W * W) - (other.X * X) - (other.Y * Y) - (other.Z * Z);
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tmp.X = (other.W * X) + (other.X * W) + (other.Y * Z) - (other.Z * Y);
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tmp.Y = (other.W * Y) + (other.Y * W) + (other.Z * X) - (other.X * Z);
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tmp.Z = (other.W * Z) + (other.Z * W) + (other.X * Y) - (other.Y * X);
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return tmp;
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}
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// multiplication operator
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inline quaternion quaternion::operator*(f32 s) const
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{
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return quaternion(s*X, s*Y, s*Z, s*W);
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}
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// multiplication operator
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inline quaternion& quaternion::operator*=(f32 s)
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{
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X*=s;
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Y*=s;
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Z*=s;
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W*=s;
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return *this;
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}
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// multiplication operator
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inline quaternion& quaternion::operator*=(const quaternion& other)
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{
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return (*this = other * (*this));
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}
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// add operator
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inline quaternion quaternion::operator+(const quaternion& b) const
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{
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return quaternion(X+b.X, Y+b.Y, Z+b.Z, W+b.W);
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}
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#if !IRR_TEST_BROKEN_QUATERNION_USE
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// Creates a matrix from this quaternion
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inline matrix4 quaternion::getMatrix() const
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{
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core::matrix4 m;
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getMatrix(m);
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return m;
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}
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#endif
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/*!
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Creates a matrix from this quaternion
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*/
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inline void quaternion::getMatrix(matrix4 &dest,
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const core::vector3df ¢er) const
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{
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dest[0] = 1.0f - 2.0f*Y*Y - 2.0f*Z*Z;
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dest[1] = 2.0f*X*Y + 2.0f*Z*W;
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dest[2] = 2.0f*X*Z - 2.0f*Y*W;
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dest[3] = 0.0f;
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dest[4] = 2.0f*X*Y - 2.0f*Z*W;
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dest[5] = 1.0f - 2.0f*X*X - 2.0f*Z*Z;
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dest[6] = 2.0f*Z*Y + 2.0f*X*W;
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dest[7] = 0.0f;
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dest[8] = 2.0f*X*Z + 2.0f*Y*W;
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dest[9] = 2.0f*Z*Y - 2.0f*X*W;
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dest[10] = 1.0f - 2.0f*X*X - 2.0f*Y*Y;
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dest[11] = 0.0f;
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dest[12] = center.X;
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dest[13] = center.Y;
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dest[14] = center.Z;
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dest[15] = 1.f;
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dest.setDefinitelyIdentityMatrix ( false );
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}
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/*!
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Creates a matrix from this quaternion
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Rotate about a center point
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shortcut for
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core::quaternion q;
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q.rotationFromTo(vin[i].Normal, forward);
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q.getMatrix(lookat, center);
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core::matrix4 m2;
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m2.setInverseTranslation(center);
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lookat *= m2;
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*/
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inline void quaternion::getMatrixCenter(matrix4 &dest,
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const core::vector3df ¢er,
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const core::vector3df &translation) const
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{
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dest[0] = 1.0f - 2.0f*Y*Y - 2.0f*Z*Z;
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dest[1] = 2.0f*X*Y + 2.0f*Z*W;
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dest[2] = 2.0f*X*Z - 2.0f*Y*W;
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dest[3] = 0.0f;
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dest[4] = 2.0f*X*Y - 2.0f*Z*W;
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dest[5] = 1.0f - 2.0f*X*X - 2.0f*Z*Z;
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dest[6] = 2.0f*Z*Y + 2.0f*X*W;
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dest[7] = 0.0f;
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dest[8] = 2.0f*X*Z + 2.0f*Y*W;
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dest[9] = 2.0f*Z*Y - 2.0f*X*W;
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dest[10] = 1.0f - 2.0f*X*X - 2.0f*Y*Y;
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dest[11] = 0.0f;
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dest.setRotationCenter ( center, translation );
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}
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// Creates a matrix from this quaternion
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inline void quaternion::getMatrix_transposed(matrix4 &dest) const
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{
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dest[0] = 1.0f - 2.0f*Y*Y - 2.0f*Z*Z;
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dest[4] = 2.0f*X*Y + 2.0f*Z*W;
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dest[8] = 2.0f*X*Z - 2.0f*Y*W;
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dest[12] = 0.0f;
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dest[1] = 2.0f*X*Y - 2.0f*Z*W;
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dest[5] = 1.0f - 2.0f*X*X - 2.0f*Z*Z;
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dest[9] = 2.0f*Z*Y + 2.0f*X*W;
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dest[13] = 0.0f;
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dest[2] = 2.0f*X*Z + 2.0f*Y*W;
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dest[6] = 2.0f*Z*Y - 2.0f*X*W;
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dest[10] = 1.0f - 2.0f*X*X - 2.0f*Y*Y;
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dest[14] = 0.0f;
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dest[3] = 0.f;
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dest[7] = 0.f;
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dest[11] = 0.f;
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dest[15] = 1.f;
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dest.setDefinitelyIdentityMatrix(false);
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}
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// Inverts this quaternion
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inline quaternion& quaternion::makeInverse()
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{
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X = -X; Y = -Y; Z = -Z;
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return *this;
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}
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// sets new quaternion
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inline quaternion& quaternion::set(f32 x, f32 y, f32 z, f32 w)
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{
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X = x;
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Y = y;
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Z = z;
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W = w;
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return *this;
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}
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// sets new quaternion based on euler angles
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inline quaternion& quaternion::set(f32 x, f32 y, f32 z)
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{
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f64 angle;
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angle = x * 0.5;
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const f64 sr = sin(angle);
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const f64 cr = cos(angle);
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angle = y * 0.5;
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const f64 sp = sin(angle);
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const f64 cp = cos(angle);
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angle = z * 0.5;
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const f64 sy = sin(angle);
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const f64 cy = cos(angle);
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const f64 cpcy = cp * cy;
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const f64 spcy = sp * cy;
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const f64 cpsy = cp * sy;
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const f64 spsy = sp * sy;
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X = (f32)(sr * cpcy - cr * spsy);
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Y = (f32)(cr * spcy + sr * cpsy);
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Z = (f32)(cr * cpsy - sr * spcy);
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W = (f32)(cr * cpcy + sr * spsy);
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return normalize();
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}
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// sets new quaternion based on euler angles
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inline quaternion& quaternion::set(const core::vector3df& vec)
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{
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return set(vec.X, vec.Y, vec.Z);
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}
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// sets new quaternion based on other quaternion
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inline quaternion& quaternion::set(const core::quaternion& quat)
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{
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return (*this=quat);
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}
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//! returns if this quaternion equals the other one, taking floating point rounding errors into account
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inline bool quaternion::equals(const quaternion& other, const f32 tolerance) const
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{
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return core::equals(X, other.X, tolerance) &&
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core::equals(Y, other.Y, tolerance) &&
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core::equals(Z, other.Z, tolerance) &&
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core::equals(W, other.W, tolerance);
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}
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// normalizes the quaternion
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inline quaternion& quaternion::normalize()
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{
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const f32 n = X*X + Y*Y + Z*Z + W*W;
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if (n == 1)
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return *this;
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|
|
|
//n = 1.0f / sqrtf(n);
|
|
return (*this *= reciprocal_squareroot ( n ));
|
|
}
|
|
|
|
|
|
// set this quaternion to the result of the linear interpolation between two quaternions
|
|
inline quaternion& quaternion::lerp(quaternion q1, quaternion q2, f32 time)
|
|
{
|
|
const f32 scale = 1.0f - time;
|
|
return (*this = (q1*scale) + (q2*time));
|
|
}
|
|
|
|
|
|
// set this quaternion to the result of the interpolation between two quaternions
|
|
inline quaternion& quaternion::slerp(quaternion q1, quaternion q2, f32 time, f32 threshold)
|
|
{
|
|
f32 angle = q1.dotProduct(q2);
|
|
|
|
// make sure we use the short rotation
|
|
if (angle < 0.0f)
|
|
{
|
|
q1 *= -1.0f;
|
|
angle *= -1.0f;
|
|
}
|
|
|
|
if (angle <= (1-threshold)) // spherical interpolation
|
|
{
|
|
const f32 theta = acosf(angle);
|
|
const f32 invsintheta = reciprocal(sinf(theta));
|
|
const f32 scale = sinf(theta * (1.0f-time)) * invsintheta;
|
|
const f32 invscale = sinf(theta * time) * invsintheta;
|
|
return (*this = (q1*scale) + (q2*invscale));
|
|
}
|
|
else // linear interploation
|
|
return lerp(q1,q2,time);
|
|
}
|
|
|
|
|
|
// calculates the dot product
|
|
inline f32 quaternion::dotProduct(const quaternion& q2) const
|
|
{
|
|
return (X * q2.X) + (Y * q2.Y) + (Z * q2.Z) + (W * q2.W);
|
|
}
|
|
|
|
|
|
//! axis must be unit length, angle in radians
|
|
inline quaternion& quaternion::fromAngleAxis(f32 angle, const vector3df& axis)
|
|
{
|
|
const f32 fHalfAngle = 0.5f*angle;
|
|
const f32 fSin = sinf(fHalfAngle);
|
|
W = cosf(fHalfAngle);
|
|
X = fSin*axis.X;
|
|
Y = fSin*axis.Y;
|
|
Z = fSin*axis.Z;
|
|
return *this;
|
|
}
|
|
|
|
|
|
inline void quaternion::toAngleAxis(f32 &angle, core::vector3df &axis) const
|
|
{
|
|
const f32 scale = sqrtf(X*X + Y*Y + Z*Z);
|
|
|
|
if (core::iszero(scale) || W > 1.0f || W < -1.0f)
|
|
{
|
|
angle = 0.0f;
|
|
axis.X = 0.0f;
|
|
axis.Y = 1.0f;
|
|
axis.Z = 0.0f;
|
|
}
|
|
else
|
|
{
|
|
const f32 invscale = reciprocal(scale);
|
|
angle = 2.0f * acosf(W);
|
|
axis.X = X * invscale;
|
|
axis.Y = Y * invscale;
|
|
axis.Z = Z * invscale;
|
|
}
|
|
}
|
|
|
|
inline void quaternion::toEuler(vector3df& euler) const
|
|
{
|
|
const f64 sqw = W*W;
|
|
const f64 sqx = X*X;
|
|
const f64 sqy = Y*Y;
|
|
const f64 sqz = Z*Z;
|
|
const f64 test = 2.0 * (Y*W - X*Z);
|
|
|
|
if (core::equals(test, 1.0, 0.000001))
|
|
{
|
|
// heading = rotation about z-axis
|
|
euler.Z = (f32) (-2.0*atan2(X, W));
|
|
// bank = rotation about x-axis
|
|
euler.X = 0;
|
|
// attitude = rotation about y-axis
|
|
euler.Y = (f32) (core::PI64/2.0);
|
|
}
|
|
else if (core::equals(test, -1.0, 0.000001))
|
|
{
|
|
// heading = rotation about z-axis
|
|
euler.Z = (f32) (2.0*atan2(X, W));
|
|
// bank = rotation about x-axis
|
|
euler.X = 0;
|
|
// attitude = rotation about y-axis
|
|
euler.Y = (f32) (core::PI64/-2.0);
|
|
}
|
|
else
|
|
{
|
|
// heading = rotation about z-axis
|
|
euler.Z = (f32) atan2(2.0 * (X*Y +Z*W),(sqx - sqy - sqz + sqw));
|
|
// bank = rotation about x-axis
|
|
euler.X = (f32) atan2(2.0 * (Y*Z +X*W),(-sqx - sqy + sqz + sqw));
|
|
// attitude = rotation about y-axis
|
|
euler.Y = (f32) asin( clamp(test, -1.0, 1.0) );
|
|
}
|
|
}
|
|
|
|
|
|
inline vector3df quaternion::operator* (const vector3df& v) const
|
|
{
|
|
// nVidia SDK implementation
|
|
|
|
vector3df uv, uuv;
|
|
vector3df qvec(X, Y, Z);
|
|
uv = qvec.crossProduct(v);
|
|
uuv = qvec.crossProduct(uv);
|
|
uv *= (2.0f * W);
|
|
uuv *= 2.0f;
|
|
|
|
return v + uv + uuv;
|
|
}
|
|
|
|
// set quaternion to identity
|
|
inline core::quaternion& quaternion::makeIdentity()
|
|
{
|
|
W = 1.f;
|
|
X = 0.f;
|
|
Y = 0.f;
|
|
Z = 0.f;
|
|
return *this;
|
|
}
|
|
|
|
inline core::quaternion& quaternion::rotationFromTo(const vector3df& from, const vector3df& to)
|
|
{
|
|
// Based on Stan Melax's article in Game Programming Gems
|
|
// Copy, since cannot modify local
|
|
vector3df v0 = from;
|
|
vector3df v1 = to;
|
|
v0.normalize();
|
|
v1.normalize();
|
|
|
|
const f32 d = v0.dotProduct(v1);
|
|
if (d >= 1.0f) // If dot == 1, vectors are the same
|
|
{
|
|
return makeIdentity();
|
|
}
|
|
else if (d <= -1.0f) // exactly opposite
|
|
{
|
|
core::vector3df axis(1.0f, 0.f, 0.f);
|
|
axis = axis.crossProduct(v0);
|
|
if (axis.getLength()==0)
|
|
{
|
|
axis.set(0.f,1.f,0.f);
|
|
axis = axis.crossProduct(v0);
|
|
}
|
|
// same as fromAngleAxis(core::PI, axis).normalize();
|
|
return set(axis.X, axis.Y, axis.Z, 0).normalize();
|
|
}
|
|
|
|
const f32 s = sqrtf( (1+d)*2 ); // optimize inv_sqrt
|
|
const f32 invs = 1.f / s;
|
|
const vector3df c = v0.crossProduct(v1)*invs;
|
|
return set(c.X, c.Y, c.Z, s * 0.5f).normalize();
|
|
}
|
|
|
|
|
|
} // end namespace core
|
|
} // end namespace irr
|
|
|
|
#endif
|
|
|