quaternion.h

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// 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"

// Between Irrlicht 1.7 and Irrlicht 1.8 the quaternion-matrix conversions got fixed.
// This define disables all involved functions completely to allow finding all places 
// where the wrong conversions had been in use.
#define IRR_TEST_BROKEN_QUATERNION_USE 0

namespace irr
{
namespace core
{


class quaternion
{
    public:

        quaternion() : X(0.0f), Y(0.0f), Z(0.0f), W(1.0f) {}

        quaternion(f32 x, f32 y, f32 z, f32 w) : X(x), Y(y), Z(z), W(w) { }

        quaternion(f32 x, f32 y, f32 z);

        quaternion(const vector3df& vec);

#if !IRR_TEST_BROKEN_QUATERNION_USE

        quaternion(const matrix4& mat);
#endif

        bool operator==(const quaternion& other) const;

        bool operator!=(const quaternion& other) const;

        inline quaternion& operator=(const quaternion& other);

#if !IRR_TEST_BROKEN_QUATERNION_USE

        inline quaternion& operator=(const matrix4& other);
#endif

        quaternion operator+(const quaternion& other) const;

        quaternion operator*(const quaternion& other) const;

        quaternion operator*(f32 s) const;

        quaternion& operator*=(f32 s);

        vector3df operator*(const vector3df& v) const;

        quaternion& operator*=(const quaternion& other);

        inline f32 dotProduct(const quaternion& other) const;

        inline quaternion& set(f32 x, f32 y, f32 z, f32 w);

        inline quaternion& set(f32 x, f32 y, f32 z);

        inline quaternion& set(const core::vector3df& vec);

        inline quaternion& set(const core::quaternion& quat);

        inline bool equals(const quaternion& other,
                const f32 tolerance = ROUNDING_ERROR_f32 ) const;

        inline quaternion& normalize();

#if !IRR_TEST_BROKEN_QUATERNION_USE

        matrix4 getMatrix() const;
#endif 

        void getMatrix( matrix4 &dest, const core::vector3df &translation=core::vector3df() ) const;

        void getMatrixCenter( matrix4 &dest, const core::vector3df &center, const core::vector3df &translation ) const;

        inline void getMatrix_transposed( matrix4 &dest ) const;

        quaternion& makeInverse();


        quaternion& lerp(quaternion q1, quaternion q2, f32 time);


        quaternion& slerp(quaternion q1, quaternion q2,
                f32 time, f32 threshold=.05f);


        quaternion& fromAngleAxis (f32 angle, const vector3df& axis);

        void toAngleAxis (f32 &angle, core::vector3df& axis) const;

        void toEuler(vector3df& euler) const;

        quaternion& makeIdentity();

        quaternion& rotationFromTo(const vector3df& from, const vector3df& to);

        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);
}

#if !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);
}

// assignment operator
inline quaternion& quaternion::operator=(const quaternion& other)
{
    X = other.X;
    Y = other.Y;
    Z = other.Z;
    W = other.W;
    return *this;
}

#if !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);
}

#if !IRR_TEST_BROKEN_QUATERNION_USE
// Creates a matrix from this quaternion
inline matrix4 quaternion::getMatrix() const
{
    core::matrix4 m;
    getMatrix(m);
    return m;
}
#endif

inline void quaternion::getMatrix(matrix4 &dest,
        const core::vector3df &center) 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] = center.X;
    dest[13] = center.Y;
    dest[14] = center.Z;
    dest[15] = 1.f;

    dest.setDefinitelyIdentityMatrix ( false );
}


inline void quaternion::getMatrixCenter(matrix4 &dest,
                    const core::vector3df &center,
                    const core::vector3df &translation) 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.setRotationCenter ( center, translation );
}

// 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;

    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);
}


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()
{
    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 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);
}


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