mirror of
https://github.com/minetest/irrlicht.git
synced 2024-11-04 17:30:38 +01:00
1e7ceac26c
It's identical to the implicit one generated, so we don't need that. And it triggers warnings with -Wdeprecated in newer gcc. It's because the implicit definition of a copy constructor is deprecated if the class has a user-declared copy assignment operator. There's a few more warnings about that in Irrlicht, will have to check them in detail as the other cases are not as trivial to fix as this one. git-svn-id: svn://svn.code.sf.net/p/irrlicht/code/trunk@6279 dfc29bdd-3216-0410-991c-e03cc46cb475
759 lines
20 KiB
C++
759 lines
20 KiB
C++
// Copyright (C) 2002-2012 Nikolaus Gebhardt
|
|
// This file is part of the "Irrlicht Engine".
|
|
// For conditions of distribution and use, see copyright notice in irrlicht.h
|
|
|
|
#ifndef IRR_QUATERNION_H_INCLUDED
|
|
#define IRR_QUATERNION_H_INCLUDED
|
|
|
|
#include "irrTypes.h"
|
|
#include "irrMath.h"
|
|
#include "matrix4.h"
|
|
#include "vector3d.h"
|
|
|
|
// NOTE: You *only* need this when updating an application from Irrlicht before 1.8 to Irrlicht 1.8 or later.
|
|
// Between Irrlicht 1.7 and Irrlicht 1.8 the quaternion-matrix conversions changed.
|
|
// Before the fix they had mixed left- and right-handed rotations.
|
|
// To test if your code was affected by the change enable IRR_TEST_BROKEN_QUATERNION_USE and try to compile your application.
|
|
// This defines removes those functions so you get compile errors anywhere you use them in your code.
|
|
// For every line with a compile-errors you have to change the corresponding lines like that:
|
|
// - When you pass the matrix to the quaternion constructor then replace the matrix by the transposed matrix.
|
|
// - For uses of getMatrix() you have to use quaternion::getMatrix_transposed instead.
|
|
// #define IRR_TEST_BROKEN_QUATERNION_USE
|
|
|
|
namespace irr
|
|
{
|
|
namespace core
|
|
{
|
|
|
|
//! Quaternion class for representing rotations.
|
|
/** It provides cheap combinations and avoids gimbal locks.
|
|
Also useful for interpolations. */
|
|
class quaternion
|
|
{
|
|
public:
|
|
|
|
//! Default Constructor
|
|
quaternion() : X(0.0f), Y(0.0f), Z(0.0f), W(1.0f) {}
|
|
|
|
//! Constructor
|
|
quaternion(f32 x, f32 y, f32 z, f32 w) : X(x), Y(y), Z(z), W(w) { }
|
|
|
|
//! Constructor which converts Euler angles (radians) to a quaternion
|
|
quaternion(f32 x, f32 y, f32 z);
|
|
|
|
//! Constructor which converts Euler angles (radians) to a quaternion
|
|
quaternion(const vector3df& vec);
|
|
|
|
#ifndef IRR_TEST_BROKEN_QUATERNION_USE
|
|
//! Constructor which converts a matrix to a quaternion
|
|
quaternion(const matrix4& mat);
|
|
#endif
|
|
|
|
//! Equality operator
|
|
bool operator==(const quaternion& other) const;
|
|
|
|
//! inequality operator
|
|
bool operator!=(const quaternion& other) const;
|
|
|
|
#ifndef IRR_TEST_BROKEN_QUATERNION_USE
|
|
//! Matrix assignment operator
|
|
inline quaternion& operator=(const matrix4& other);
|
|
#endif
|
|
|
|
//! Add operator
|
|
quaternion operator+(const quaternion& other) const;
|
|
|
|
//! Multiplication operator
|
|
//! Be careful, unfortunately the operator order here is opposite of that in CMatrix4::operator*
|
|
quaternion operator*(const quaternion& other) const;
|
|
|
|
//! Multiplication operator with scalar
|
|
quaternion operator*(f32 s) const;
|
|
|
|
//! Multiplication operator with scalar
|
|
quaternion& operator*=(f32 s);
|
|
|
|
//! Multiplication operator
|
|
vector3df operator*(const vector3df& v) const;
|
|
|
|
//! Multiplication operator
|
|
quaternion& operator*=(const quaternion& other);
|
|
|
|
//! Calculates the dot product
|
|
inline f32 dotProduct(const quaternion& other) const;
|
|
|
|
//! Sets new quaternion
|
|
inline quaternion& set(f32 x, f32 y, f32 z, f32 w);
|
|
|
|
//! Sets new quaternion based on Euler angles (radians)
|
|
inline quaternion& set(f32 x, f32 y, f32 z);
|
|
|
|
//! Sets new quaternion based on Euler angles (radians)
|
|
inline quaternion& set(const core::vector3df& vec);
|
|
|
|
//! Sets new quaternion from other quaternion
|
|
inline quaternion& set(const core::quaternion& quat);
|
|
|
|
//! returns if this quaternion equals the other one, taking floating point rounding errors into account
|
|
inline bool equals(const quaternion& other,
|
|
const f32 tolerance = ROUNDING_ERROR_f32 ) const;
|
|
|
|
//! Normalizes the quaternion
|
|
inline quaternion& normalize();
|
|
|
|
#ifndef IRR_TEST_BROKEN_QUATERNION_USE
|
|
//! Creates a matrix from this quaternion
|
|
matrix4 getMatrix() const;
|
|
#endif
|
|
//! Faster method to create a rotation matrix, you should normalize the quaternion before!
|
|
void getMatrixFast(matrix4 &dest) const;
|
|
|
|
//! Creates a matrix from this quaternion
|
|
void getMatrix( matrix4 &dest, const core::vector3df &translation=core::vector3df() ) const;
|
|
|
|
/*!
|
|
Creates a matrix from this quaternion
|
|
Rotate about a center point
|
|
shortcut for
|
|
core::quaternion q;
|
|
q.rotationFromTo ( vin[i].Normal, forward );
|
|
q.getMatrixCenter ( lookat, center, newPos );
|
|
|
|
core::matrix4 m2;
|
|
m2.setInverseTranslation ( center );
|
|
lookat *= m2;
|
|
|
|
core::matrix4 m3;
|
|
m2.setTranslation ( newPos );
|
|
lookat *= m3;
|
|
|
|
*/
|
|
void getMatrixCenter( matrix4 &dest, const core::vector3df ¢er, const core::vector3df &translation ) const;
|
|
|
|
//! Creates a matrix from this quaternion
|
|
inline void getMatrix_transposed( matrix4 &dest ) const;
|
|
|
|
//! Inverts this quaternion
|
|
quaternion& makeInverse();
|
|
|
|
//! Set this quaternion to the linear interpolation between two quaternions
|
|
/** NOTE: lerp result is *not* a normalized quaternion. In most cases
|
|
you will want to use lerpN instead as most other quaternion functions expect
|
|
to work with a normalized quaternion.
|
|
\param q1 First quaternion to be interpolated.
|
|
\param q2 Second quaternion to be interpolated.
|
|
\param time Progress of interpolation. For time=0 the result is
|
|
q1, for time=1 the result is q2. Otherwise interpolation
|
|
between q1 and q2. Result is not normalized.
|
|
*/
|
|
quaternion& lerp(quaternion q1, quaternion q2, f32 time);
|
|
|
|
//! Set this quaternion to the linear interpolation between two quaternions and normalize the result
|
|
/**
|
|
\param q1 First quaternion to be interpolated.
|
|
\param q2 Second quaternion to be interpolated.
|
|
\param time Progress of interpolation. For time=0 the result is
|
|
q1, for time=1 the result is q2. Otherwise interpolation
|
|
between q1 and q2. Result is normalized.
|
|
*/
|
|
quaternion& lerpN(quaternion q1, quaternion q2, f32 time);
|
|
|
|
//! Set this quaternion to the result of the spherical interpolation between two quaternions
|
|
/** \param q1 First quaternion to be interpolated.
|
|
\param q2 Second quaternion to be interpolated.
|
|
\param time Progress of interpolation. For time=0 the result is
|
|
q1, for time=1 the result is q2. Otherwise interpolation
|
|
between q1 and q2.
|
|
\param threshold To avoid inaccuracies at the end (time=1) the
|
|
interpolation switches to linear interpolation at some point.
|
|
This value defines how much of the remaining interpolation will
|
|
be calculated with lerp. Everything from 1-threshold up will be
|
|
linear interpolation.
|
|
*/
|
|
quaternion& slerp(quaternion q1, quaternion q2,
|
|
f32 time, f32 threshold=.05f);
|
|
|
|
//! Set this quaternion to represent a rotation from angle and axis.
|
|
/** Axis must be unit length.
|
|
The quaternion representing the rotation is
|
|
q = cos(A/2)+sin(A/2)*(x*i+y*j+z*k).
|
|
\param angle Rotation Angle in radians.
|
|
\param axis Rotation axis. */
|
|
quaternion& fromAngleAxis (f32 angle, const vector3df& axis);
|
|
|
|
//! Fills an angle (radians) around an axis (unit vector)
|
|
void toAngleAxis (f32 &angle, core::vector3df& axis) const;
|
|
|
|
//! Output this quaternion to an Euler angle (radians)
|
|
void toEuler(vector3df& euler) const;
|
|
|
|
//! Set quaternion to identity
|
|
quaternion& makeIdentity();
|
|
|
|
//! Set quaternion to represent a rotation from one vector to another.
|
|
quaternion& rotationFromTo(const vector3df& from, const vector3df& to);
|
|
|
|
//! Quaternion elements.
|
|
f32 X; // vectorial (imaginary) part
|
|
f32 Y;
|
|
f32 Z;
|
|
f32 W; // real part
|
|
};
|
|
|
|
|
|
// Constructor which converts Euler angles to a quaternion
|
|
inline quaternion::quaternion(f32 x, f32 y, f32 z)
|
|
{
|
|
set(x,y,z);
|
|
}
|
|
|
|
|
|
// Constructor which converts Euler angles to a quaternion
|
|
inline quaternion::quaternion(const vector3df& vec)
|
|
{
|
|
set(vec.X,vec.Y,vec.Z);
|
|
}
|
|
|
|
#ifndef IRR_TEST_BROKEN_QUATERNION_USE
|
|
// Constructor which converts a matrix to a quaternion
|
|
inline quaternion::quaternion(const matrix4& mat)
|
|
{
|
|
(*this) = mat;
|
|
}
|
|
#endif
|
|
|
|
// equal operator
|
|
inline bool quaternion::operator==(const quaternion& other) const
|
|
{
|
|
return ((X == other.X) &&
|
|
(Y == other.Y) &&
|
|
(Z == other.Z) &&
|
|
(W == other.W));
|
|
}
|
|
|
|
// inequality operator
|
|
inline bool quaternion::operator!=(const quaternion& other) const
|
|
{
|
|
return !(*this == other);
|
|
}
|
|
|
|
|
|
#ifndef IRR_TEST_BROKEN_QUATERNION_USE
|
|
// matrix assignment operator
|
|
inline quaternion& quaternion::operator=(const matrix4& m)
|
|
{
|
|
const f32 diag = m[0] + m[5] + m[10] + 1;
|
|
|
|
if( diag > 0.0f )
|
|
{
|
|
const f32 scale = sqrtf(diag) * 2.0f; // get scale from diagonal
|
|
|
|
// TODO: speed this up
|
|
X = (m[6] - m[9]) / scale;
|
|
Y = (m[8] - m[2]) / scale;
|
|
Z = (m[1] - m[4]) / scale;
|
|
W = 0.25f * scale;
|
|
}
|
|
else
|
|
{
|
|
if (m[0]>m[5] && m[0]>m[10])
|
|
{
|
|
// 1st element of diag is greatest value
|
|
// find scale according to 1st element, and double it
|
|
const f32 scale = sqrtf(1.0f + m[0] - m[5] - m[10]) * 2.0f;
|
|
|
|
// TODO: speed this up
|
|
X = 0.25f * scale;
|
|
Y = (m[4] + m[1]) / scale;
|
|
Z = (m[2] + m[8]) / scale;
|
|
W = (m[6] - m[9]) / scale;
|
|
}
|
|
else if (m[5]>m[10])
|
|
{
|
|
// 2nd element of diag is greatest value
|
|
// find scale according to 2nd element, and double it
|
|
const f32 scale = sqrtf(1.0f + m[5] - m[0] - m[10]) * 2.0f;
|
|
|
|
// TODO: speed this up
|
|
X = (m[4] + m[1]) / scale;
|
|
Y = 0.25f * scale;
|
|
Z = (m[9] + m[6]) / scale;
|
|
W = (m[8] - m[2]) / scale;
|
|
}
|
|
else
|
|
{
|
|
// 3rd element of diag is greatest value
|
|
// find scale according to 3rd element, and double it
|
|
const f32 scale = sqrtf(1.0f + m[10] - m[0] - m[5]) * 2.0f;
|
|
|
|
// TODO: speed this up
|
|
X = (m[8] + m[2]) / scale;
|
|
Y = (m[9] + m[6]) / scale;
|
|
Z = 0.25f * scale;
|
|
W = (m[1] - m[4]) / scale;
|
|
}
|
|
}
|
|
|
|
return normalize();
|
|
}
|
|
#endif
|
|
|
|
|
|
// multiplication operator
|
|
inline quaternion quaternion::operator*(const quaternion& other) const
|
|
{
|
|
quaternion tmp;
|
|
|
|
tmp.W = (other.W * W) - (other.X * X) - (other.Y * Y) - (other.Z * Z);
|
|
tmp.X = (other.W * X) + (other.X * W) + (other.Y * Z) - (other.Z * Y);
|
|
tmp.Y = (other.W * Y) + (other.Y * W) + (other.Z * X) - (other.X * Z);
|
|
tmp.Z = (other.W * Z) + (other.Z * W) + (other.X * Y) - (other.Y * X);
|
|
|
|
return tmp;
|
|
}
|
|
|
|
|
|
// multiplication operator
|
|
inline quaternion quaternion::operator*(f32 s) const
|
|
{
|
|
return quaternion(s*X, s*Y, s*Z, s*W);
|
|
}
|
|
|
|
|
|
// multiplication operator
|
|
inline quaternion& quaternion::operator*=(f32 s)
|
|
{
|
|
X*=s;
|
|
Y*=s;
|
|
Z*=s;
|
|
W*=s;
|
|
return *this;
|
|
}
|
|
|
|
// multiplication operator
|
|
inline quaternion& quaternion::operator*=(const quaternion& other)
|
|
{
|
|
return (*this = other * (*this));
|
|
}
|
|
|
|
// add operator
|
|
inline quaternion quaternion::operator+(const quaternion& b) const
|
|
{
|
|
return quaternion(X+b.X, Y+b.Y, Z+b.Z, W+b.W);
|
|
}
|
|
|
|
#ifndef IRR_TEST_BROKEN_QUATERNION_USE
|
|
// Creates a matrix from this quaternion
|
|
inline matrix4 quaternion::getMatrix() const
|
|
{
|
|
core::matrix4 m;
|
|
getMatrix(m);
|
|
return m;
|
|
}
|
|
#endif
|
|
|
|
//! Faster method to create a rotation matrix, you should normalize the quaternion before!
|
|
inline void quaternion::getMatrixFast( matrix4 &dest) const
|
|
{
|
|
// TODO:
|
|
// gpu quaternion skinning => fast Bones transform chain O_O YEAH!
|
|
// http://www.mrelusive.com/publications/papers/SIMD-From-Quaternion-to-Matrix-and-Back.pdf
|
|
dest[0] = 1.0f - 2.0f*Y*Y - 2.0f*Z*Z;
|
|
dest[1] = 2.0f*X*Y + 2.0f*Z*W;
|
|
dest[2] = 2.0f*X*Z - 2.0f*Y*W;
|
|
dest[3] = 0.0f;
|
|
|
|
dest[4] = 2.0f*X*Y - 2.0f*Z*W;
|
|
dest[5] = 1.0f - 2.0f*X*X - 2.0f*Z*Z;
|
|
dest[6] = 2.0f*Z*Y + 2.0f*X*W;
|
|
dest[7] = 0.0f;
|
|
|
|
dest[8] = 2.0f*X*Z + 2.0f*Y*W;
|
|
dest[9] = 2.0f*Z*Y - 2.0f*X*W;
|
|
dest[10] = 1.0f - 2.0f*X*X - 2.0f*Y*Y;
|
|
dest[11] = 0.0f;
|
|
|
|
dest[12] = 0.f;
|
|
dest[13] = 0.f;
|
|
dest[14] = 0.f;
|
|
dest[15] = 1.f;
|
|
|
|
dest.setDefinitelyIdentityMatrix(false);
|
|
}
|
|
|
|
/*!
|
|
Creates a matrix from this quaternion
|
|
*/
|
|
inline void quaternion::getMatrix(matrix4 &dest,
|
|
const core::vector3df ¢er) const
|
|
{
|
|
// ok creating a copy may be slower, but at least avoid internal
|
|
// state chance (also because otherwise we cannot keep this method "const").
|
|
|
|
quaternion q( *this);
|
|
q.normalize();
|
|
f32 X = q.X;
|
|
f32 Y = q.Y;
|
|
f32 Z = q.Z;
|
|
f32 W = q.W;
|
|
|
|
dest[0] = 1.0f - 2.0f*Y*Y - 2.0f*Z*Z;
|
|
dest[1] = 2.0f*X*Y + 2.0f*Z*W;
|
|
dest[2] = 2.0f*X*Z - 2.0f*Y*W;
|
|
dest[3] = 0.0f;
|
|
|
|
dest[4] = 2.0f*X*Y - 2.0f*Z*W;
|
|
dest[5] = 1.0f - 2.0f*X*X - 2.0f*Z*Z;
|
|
dest[6] = 2.0f*Z*Y + 2.0f*X*W;
|
|
dest[7] = 0.0f;
|
|
|
|
dest[8] = 2.0f*X*Z + 2.0f*Y*W;
|
|
dest[9] = 2.0f*Z*Y - 2.0f*X*W;
|
|
dest[10] = 1.0f - 2.0f*X*X - 2.0f*Y*Y;
|
|
dest[11] = 0.0f;
|
|
|
|
dest[12] = center.X;
|
|
dest[13] = center.Y;
|
|
dest[14] = center.Z;
|
|
dest[15] = 1.f;
|
|
|
|
dest.setDefinitelyIdentityMatrix ( false );
|
|
}
|
|
|
|
|
|
/*!
|
|
Creates a matrix from this quaternion
|
|
Rotate about a center point
|
|
shortcut for
|
|
core::quaternion q;
|
|
q.rotationFromTo(vin[i].Normal, forward);
|
|
q.getMatrix(lookat, center);
|
|
|
|
core::matrix4 m2;
|
|
m2.setInverseTranslation(center);
|
|
lookat *= m2;
|
|
*/
|
|
inline void quaternion::getMatrixCenter(matrix4 &dest,
|
|
const core::vector3df ¢er,
|
|
const core::vector3df &translation) const
|
|
{
|
|
quaternion q(*this);
|
|
q.normalize();
|
|
f32 X = q.X;
|
|
f32 Y = q.Y;
|
|
f32 Z = q.Z;
|
|
f32 W = q.W;
|
|
|
|
dest[0] = 1.0f - 2.0f*Y*Y - 2.0f*Z*Z;
|
|
dest[1] = 2.0f*X*Y + 2.0f*Z*W;
|
|
dest[2] = 2.0f*X*Z - 2.0f*Y*W;
|
|
dest[3] = 0.0f;
|
|
|
|
dest[4] = 2.0f*X*Y - 2.0f*Z*W;
|
|
dest[5] = 1.0f - 2.0f*X*X - 2.0f*Z*Z;
|
|
dest[6] = 2.0f*Z*Y + 2.0f*X*W;
|
|
dest[7] = 0.0f;
|
|
|
|
dest[8] = 2.0f*X*Z + 2.0f*Y*W;
|
|
dest[9] = 2.0f*Z*Y - 2.0f*X*W;
|
|
dest[10] = 1.0f - 2.0f*X*X - 2.0f*Y*Y;
|
|
dest[11] = 0.0f;
|
|
|
|
dest.setRotationCenter ( center, translation );
|
|
}
|
|
|
|
// Creates a matrix from this quaternion
|
|
inline void quaternion::getMatrix_transposed(matrix4 &dest) const
|
|
{
|
|
quaternion q(*this);
|
|
q.normalize();
|
|
f32 X = q.X;
|
|
f32 Y = q.Y;
|
|
f32 Z = q.Z;
|
|
f32 W = q.W;
|
|
|
|
dest[0] = 1.0f - 2.0f*Y*Y - 2.0f*Z*Z;
|
|
dest[4] = 2.0f*X*Y + 2.0f*Z*W;
|
|
dest[8] = 2.0f*X*Z - 2.0f*Y*W;
|
|
dest[12] = 0.0f;
|
|
|
|
dest[1] = 2.0f*X*Y - 2.0f*Z*W;
|
|
dest[5] = 1.0f - 2.0f*X*X - 2.0f*Z*Z;
|
|
dest[9] = 2.0f*Z*Y + 2.0f*X*W;
|
|
dest[13] = 0.0f;
|
|
|
|
dest[2] = 2.0f*X*Z + 2.0f*Y*W;
|
|
dest[6] = 2.0f*Z*Y - 2.0f*X*W;
|
|
dest[10] = 1.0f - 2.0f*X*X - 2.0f*Y*Y;
|
|
dest[14] = 0.0f;
|
|
|
|
dest[3] = 0.f;
|
|
dest[7] = 0.f;
|
|
dest[11] = 0.f;
|
|
dest[15] = 1.f;
|
|
|
|
dest.setDefinitelyIdentityMatrix(false);
|
|
}
|
|
|
|
|
|
// Inverts this quaternion
|
|
inline quaternion& quaternion::makeInverse()
|
|
{
|
|
X = -X; Y = -Y; Z = -Z;
|
|
return *this;
|
|
}
|
|
|
|
|
|
// sets new quaternion
|
|
inline quaternion& quaternion::set(f32 x, f32 y, f32 z, f32 w)
|
|
{
|
|
X = x;
|
|
Y = y;
|
|
Z = z;
|
|
W = w;
|
|
return *this;
|
|
}
|
|
|
|
|
|
// sets new quaternion based on Euler angles
|
|
inline quaternion& quaternion::set(f32 x, f32 y, f32 z)
|
|
{
|
|
f64 angle;
|
|
|
|
angle = x * 0.5;
|
|
const f64 sr = sin(angle);
|
|
const f64 cr = cos(angle);
|
|
|
|
angle = y * 0.5;
|
|
const f64 sp = sin(angle);
|
|
const f64 cp = cos(angle);
|
|
|
|
angle = z * 0.5;
|
|
const f64 sy = sin(angle);
|
|
const f64 cy = cos(angle);
|
|
|
|
const f64 cpcy = cp * cy;
|
|
const f64 spcy = sp * cy;
|
|
const f64 cpsy = cp * sy;
|
|
const f64 spsy = sp * sy;
|
|
|
|
X = (f32)(sr * cpcy - cr * spsy);
|
|
Y = (f32)(cr * spcy + sr * cpsy);
|
|
Z = (f32)(cr * cpsy - sr * spcy);
|
|
W = (f32)(cr * cpcy + sr * spsy);
|
|
|
|
return normalize();
|
|
}
|
|
|
|
// sets new quaternion based on Euler angles
|
|
inline quaternion& quaternion::set(const core::vector3df& vec)
|
|
{
|
|
return set( vec.X, vec.Y, vec.Z);
|
|
}
|
|
|
|
// sets new quaternion based on other quaternion
|
|
inline quaternion& quaternion::set(const core::quaternion& quat)
|
|
{
|
|
return (*this=quat);
|
|
}
|
|
|
|
|
|
//! returns if this quaternion equals the other one, taking floating point rounding errors into account
|
|
inline bool quaternion::equals(const quaternion& other, const f32 tolerance) const
|
|
{
|
|
return core::equals( X, other.X, tolerance) &&
|
|
core::equals( Y, other.Y, tolerance) &&
|
|
core::equals( Z, other.Z, tolerance) &&
|
|
core::equals( W, other.W, tolerance);
|
|
}
|
|
|
|
|
|
// normalizes the quaternion
|
|
inline quaternion& quaternion::normalize()
|
|
{
|
|
// removed conditional branch since it may slow down and anyway the condition was
|
|
// false even after normalization in some cases.
|
|
return (*this *= (f32)reciprocal_squareroot ( (f64)(X*X + Y*Y + Z*Z + W*W) ));
|
|
}
|
|
|
|
// 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 linear interpolation between two quaternions and normalize the result
|
|
inline quaternion& quaternion::lerpN( quaternion q1, quaternion q2, f32 time)
|
|
{
|
|
const f32 scale = 1.0f - time;
|
|
return (*this = ((q1*scale) + (q2*time)).normalize() );
|
|
}
|
|
|
|
// 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 interpolation
|
|
return lerpN(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;
|
|
const 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
|