irrlicht/include/quaternion.h

549 lines
12 KiB
C++

// Copyright (C) 2002-2008 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"
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);
//! Constructor which converts a matrix to a quaternion
quaternion(const matrix4& mat);
//! Equalilty operator
bool operator==(const quaternion& other) const;
//! Assignment operator
inline quaternion& operator=(const quaternion& other);
//! Matrix assignment operator
inline quaternion& operator=(const matrix4& other);
//! Add operator
quaternion operator+(const quaternion& other) const;
//! Multiplication 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);
//! Normalizes the quaternion
inline quaternion& normalize();
//! Creates a matrix from this quaternion
matrix4 getMatrix() const;
//! Creates a matrix from this quaternion
void getMatrix( matrix4 &dest ) const;
//! Creates a matrix from this quaternion
void getMatrix_transposed( matrix4 &dest ) const;
//! Inverts this quaternion
quaternion& makeInverse();
//! Set this quaternion to the result of the interpolation between two quaternions
quaternion& slerp( quaternion q1, quaternion q2, f32 interpolate );
//! Create quaternion from rotation angle and rotation 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, Y, Z, W;
};
// 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);
}
// Constructor which converts a matrix to a quaternion
inline quaternion::quaternion(const matrix4& mat)
{
(*this) = mat;
}
// equal operator
inline bool quaternion::operator==(const quaternion& other) const
{
return ((X == other.X) &&
(Y == other.Y) &&
(Z == other.Z) &&
(W == other.W));
}
// assignment operator
inline quaternion& quaternion::operator=(const quaternion& other)
{
X = other.X;
Y = other.Y;
Z = other.Z;
W = other.W;
return *this;
}
// matrix assignment operator
inline quaternion& quaternion::operator=(const matrix4& m)
{
const f32 diag = m(0,0) + m(1,1) + m(2,2) + 1;
if( diag > 0.0f )
{
const f32 scale = sqrtf(diag) * 2.0f; // get scale from diagonal
// TODO: speed this up
X = ( m(2,1) - m(1,2)) / scale;
Y = ( m(0,2) - m(2,0)) / scale;
Z = ( m(1,0) - m(0,1)) / scale;
W = 0.25f * scale;
}
else
{
if ( m(0,0) > m(1,1) && m(0,0) > m(2,2))
{
// 1st element of diag is greatest value
// find scale according to 1st element, and double it
const f32 scale = sqrtf( 1.0f + m(0,0) - m(1,1) - m(2,2)) * 2.0f;
// TODO: speed this up
X = 0.25f * scale;
Y = (m(0,1) + m(1,0)) / scale;
Z = (m(2,0) + m(0,2)) / scale;
W = (m(2,1) - m(1,2)) / scale;
}
else if ( m(1,1) > m(2,2))
{
// 2nd element of diag is greatest value
// find scale according to 2nd element, and double it
const f32 scale = sqrtf( 1.0f + m(1,1) - m(0,0) - m(2,2)) * 2.0f;
// TODO: speed this up
X = (m(0,1) + m(1,0) ) / scale;
Y = 0.25f * scale;
Z = (m(1,2) + m(2,1) ) / scale;
W = (m(0,2) - m(2,0) ) / 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(2,2) - m(0,0) - m(1,1)) * 2.0f;
// TODO: speed this up
X = (m(0,2) + m(2,0)) / scale;
Y = (m(1,2) + m(2,1)) / scale;
Z = 0.25f * scale;
W = (m(1,0) - m(0,1)) / scale;
}
}
return normalize();
}
// 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);
}
// Creates a matrix from this quaternion
inline matrix4 quaternion::getMatrix() const
{
core::matrix4 m;
getMatrix_transposed(m);
return m;
}
// Creates a matrix from this quaternion
inline void quaternion::getMatrix( matrix4 &dest ) const
{
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;
}
// Creates a matrix from this quaternion
inline void quaternion::getMatrix_transposed( matrix4 &dest ) const
{
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;
}
// 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);
}
// normalizes the quaternion
inline quaternion& quaternion::normalize()
{
const f32 n = X*X + Y*Y + Z*Z + W*W;
if (n == 1)
return *this;
//n = 1.0f / sqrtf(n);
return (*this *= reciprocal_squareroot ( n ));
}
// set this quaternion to the result of the interpolation between two quaternions
inline quaternion& quaternion::slerp(quaternion q1, quaternion q2, f32 time)
{
f32 angle = q1.dotProduct(q2);
if (angle < 0.0f)
{
q1 *= -1.0f;
angle *= -1.0f;
}
f32 scale;
f32 invscale;
if ((angle + 1.0f) > 0.05f)
{
if ((1.0f - angle) >= 0.05f) // spherical interpolation
{
const f32 theta = acosf(angle);
const f32 invsintheta = reciprocal(sinf(theta));
scale = sinf(theta * (1.0f-time)) * invsintheta;
invscale = sinf(theta * time) * invsintheta;
}
else // linear interploation
{
scale = 1.0f - time;
invscale = time;
}
}
else
{
q2.set(-q1.Y, q1.X, -q1.W, q1.Z);
scale = sinf(PI * (0.5f - time));
invscale = sinf(PI * time);
}
return (*this = (q1*scale) + (q2*invscale));
}
// 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;
// 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 = asinf( clamp(-2.0f * (X*Z - Y*W), -1.0f, 1.0f) );
}
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();
}
const f32 s = sqrtf( (1+d)*2 ); // optimize inv_sqrt
const f32 invs = 1.f / s;
const vector3df c = v0.crossProduct(v1)*invs;
X = c.X;
Y = c.Y;
Z = c.Z;
W = s * 0.5f;
return *this;
}
} // end namespace core
} // end namespace irr
#endif