quaternion.h

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/*
 Copyright (C) 2001-2006, William Joseph.
 All Rights Reserved.

 This file is part of GtkRadiant.

 GtkRadiant is free software; you can redistribute it and/or modify
 it under the terms of the GNU General Public License as published by
 the Free Software Foundation; either version 2 of the License, or
 (at your option) any later version.

 GtkRadiant is distributed in the hope that it will be useful,
 but WITHOUT ANY WARRANTY; without even the implied warranty of
 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 GNU General Public License for more details.

 You should have received a copy of the GNU General Public License
 along with GtkRadiant; if not, write to the Free Software
 Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
 */

#if !defined(INCLUDED_MATH_QUATERNION_H)
#define INCLUDED_MATH_QUATERNION_H

#include "math/matrix.h"

typedef Vector4 Quaternion;

const Quaternion c_quaternion_identity(0, 0, 0, 1);

inline Quaternion quaternion_multiplied_by_quaternion (const Quaternion& quaternion, const Quaternion& other)
{
    return Quaternion(quaternion[3] * other[0] + quaternion[0] * other[3] + quaternion[1] * other[2] - quaternion[2]
            * other[1], quaternion[3] * other[1] + quaternion[1] * other[3] + quaternion[2] * other[0] - quaternion[0]
            * other[2], quaternion[3] * other[2] + quaternion[2] * other[3] + quaternion[0] * other[1] - quaternion[1]
            * other[0], quaternion[3] * other[3] - quaternion[0] * other[0] - quaternion[1] * other[1] - quaternion[2]
            * other[2]);
}

inline void quaternion_multiply_by_quaternion (Quaternion& quaternion, const Quaternion& other)
{
    quaternion = quaternion_multiplied_by_quaternion(quaternion, other);
}

inline Quaternion quaternion_for_unit_vectors (const Vector3& from, const Vector3& to)
{
    return Quaternion(from.crossProduct(to), static_cast<float> (from.dot(to)));
}

inline Quaternion quaternion_for_axisangle (const Vector3& axis, double angle)
{
    angle *= 0.5;
    float sa = static_cast<float> (sin(angle));
    return Quaternion(axis[0] * sa, axis[1] * sa, axis[2] * sa, static_cast<float> (cos(angle)));
}

inline Quaternion quaternion_for_x (double angle)
{
    angle *= 0.5;
    return Quaternion(static_cast<float> (sin(angle)), 0, 0, static_cast<float> (cos(angle)));
}

inline Quaternion quaternion_for_y (double angle)
{
    angle *= 0.5;
    return Quaternion(0, static_cast<float> (sin(angle)), 0, static_cast<float> (cos(angle)));
}

inline Quaternion quaternion_for_z (double angle)
{
    angle *= 0.5;
    return Quaternion(0, 0, static_cast<float> (sin(angle)), static_cast<float> (cos(angle)));
}

inline Quaternion quaternion_inverse (const Quaternion& quaternion)
{
    return Quaternion(-quaternion.getVector3(), quaternion[3]);
}

inline void quaternion_conjugate (Quaternion& quaternion)
{
    quaternion = quaternion_inverse(quaternion);
}

inline Quaternion quaternion_normalised (const Quaternion& quaternion)
{
    const double n = (1.0 / (quaternion[0] * quaternion[0] + quaternion[1] * quaternion[1] + quaternion[2]
            * quaternion[2] + quaternion[3] * quaternion[3]));
    return Quaternion(static_cast<float> (quaternion[0] * n), static_cast<float> (quaternion[1] * n),
            static_cast<float> (quaternion[2] * n), static_cast<float> (quaternion[3] * n));
}

inline void quaternion_normalise (Quaternion& quaternion)
{
    quaternion = quaternion_normalised(quaternion);
}

inline Matrix4 matrix4_rotation_for_quaternion (const Quaternion& quaternion)
{
#if 0
    const double xx = quaternion[0] * quaternion[0];
    const double xy = quaternion[0] * quaternion[1];
    const double xz = quaternion[0] * quaternion[2];
    const double xw = quaternion[0] * quaternion[3];

    const double yy = quaternion[1] * quaternion[1];
    const double yz = quaternion[1] * quaternion[2];
    const double yw = quaternion[1] * quaternion[3];

    const double zz = quaternion[2] * quaternion[2];
    const double zw = quaternion[2] * quaternion[3];

    return Matrix4(
            static_cast<float>( 1 - 2 * ( yy + zz ) ),
            static_cast<float>( 2 * ( xy + zw ) ),
            static_cast<float>( 2 * ( xz - yw ) ),
            0,
            static_cast<float>( 2 * ( xy - zw ) ),
            static_cast<float>( 1 - 2 * ( xx + zz ) ),
            static_cast<float>( 2 * ( yz + xw ) ),
            0,
            static_cast<float>( 2 * ( xz + yw ) ),
            static_cast<float>( 2 * ( yz - xw ) ),
            static_cast<float>( 1 - 2 * ( xx + yy ) ),
            0,
            0,
            0,
            0,
            1
    );

#else
    const double x2 = quaternion[0] + quaternion[0];
    const double y2 = quaternion[1] + quaternion[1];
    const double z2 = quaternion[2] + quaternion[2];
    const double xx = quaternion[0] * x2;
    const double xy = quaternion[0] * y2;
    const double xz = quaternion[0] * z2;
    const double yy = quaternion[1] * y2;
    const double yz = quaternion[1] * z2;
    const double zz = quaternion[2] * z2;
    const double wx = quaternion[3] * x2;
    const double wy = quaternion[3] * y2;
    const double wz = quaternion[3] * z2;

    return Matrix4(static_cast<float> (1.0 - (yy + zz)), static_cast<float> (xy + wz), static_cast<float> (xz - wy), 0,
            static_cast<float> (xy - wz), static_cast<float> (1.0 - (xx + zz)), static_cast<float> (yz + wx), 0,
            static_cast<float> (xz + wy), static_cast<float> (yz - wx), static_cast<float> (1.0 - (xx + yy)), 0, 0, 0,
            0, 1);

#endif
}

const double c_half_sqrt2 = 0.70710678118654752440084436210485;
const float c_half_sqrt2f = static_cast<float> (c_half_sqrt2);

inline bool quaternion_component_is_90 (float component)
{
    return (fabs(component) - c_half_sqrt2) < 0.001;
}

inline Matrix4 matrix4_rotation_for_quaternion_quantised (const Quaternion& quaternion)
{
    if (quaternion.y() == 0 && quaternion.z() == 0 && quaternion_component_is_90(quaternion.x())
            && quaternion_component_is_90(quaternion.w())) {
        return matrix4_rotation_for_sincos_x((quaternion.x() > 0) ? 1.f : -1.f, 0);
    }

    if (quaternion.x() == 0 && quaternion.z() == 0 && quaternion_component_is_90(quaternion.y())
            && quaternion_component_is_90(quaternion.w())) {
        return matrix4_rotation_for_sincos_y((quaternion.y() > 0) ? 1.f : -1.f, 0);
    }

    if (quaternion.x() == 0 && quaternion.y() == 0 && quaternion_component_is_90(quaternion.z())
            && quaternion_component_is_90(quaternion.w())) {
        return matrix4_rotation_for_sincos_z((quaternion.z() > 0) ? 1.f : -1.f, 0);
    }

    return matrix4_rotation_for_quaternion(quaternion);
}

inline Quaternion quaternion_for_matrix4_rotation (const Matrix4& matrix4)
{
    Matrix4 transposed = matrix4_transposed(matrix4);

    double trace = transposed[0] + transposed[5] + transposed[10] + 1.0;

    if (trace > 0.0001) {
        double S = 0.5 / sqrt(trace);
        return Quaternion(static_cast<float> ((transposed[9] - transposed[6]) * S), static_cast<float> ((transposed[2]
                - transposed[8]) * S), static_cast<float> ((transposed[4] - transposed[1]) * S),
                static_cast<float> (0.25 / S));
    }

    if (transposed[0] >= transposed[5] && transposed[0] >= transposed[10]) {
        double S = 2.0 * sqrt(1.0 + transposed[0] - transposed[5] - transposed[10]);
        return Quaternion(static_cast<float> (0.25 / S), static_cast<float> ((transposed[1] + transposed[4]) / S),
                static_cast<float> ((transposed[2] + transposed[8]) / S), static_cast<float> ((transposed[6]
                        + transposed[9]) / S));
    }

    if (transposed[5] >= transposed[0] && transposed[5] >= transposed[10]) {
        double S = 2.0 * sqrt(1.0 + transposed[5] - transposed[0] - transposed[10]);
        return Quaternion(static_cast<float> ((transposed[1] + transposed[4]) / S), static_cast<float> (0.25 / S),
                static_cast<float> ((transposed[6] + transposed[9]) / S), static_cast<float> ((transposed[2]
                        + transposed[8]) / S));
    }

    double S = 2.0 * sqrt(1.0 + transposed[10] - transposed[0] - transposed[5]);
    return Quaternion(static_cast<float> ((transposed[2] + transposed[8]) / S), static_cast<float> ((transposed[6]
            + transposed[9]) / S), static_cast<float> (0.25 / S), static_cast<float> ((transposed[1] + transposed[4])
            / S));
}

inline Matrix4 matrix4_rotated_by_quaternion (const Matrix4& self, const Quaternion& rotation)
{
    return matrix4_multiplied_by_matrix4(self, matrix4_rotation_for_quaternion(rotation));
}

inline void matrix4_rotate_by_quaternion (Matrix4& self, const Quaternion& rotation)
{
    self = matrix4_rotated_by_quaternion(self, rotation);
}

inline void matrix4_pivoted_rotate_by_quaternion (Matrix4& self, const Quaternion& rotation, const Vector3& pivotpoint)
{
    matrix4_translate_by_vec3(self, pivotpoint);
    matrix4_rotate_by_quaternion(self, rotation);
    matrix4_translate_by_vec3(self, -pivotpoint);
}

inline Vector3 quaternion_transformed_point (const Quaternion& quaternion, const Vector3& point)
{
    double xx = quaternion.x() * quaternion.x();
    double yy = quaternion.y() * quaternion.y();
    double zz = quaternion.z() * quaternion.z();
    double ww = quaternion.w() * quaternion.w();

    double xy2 = quaternion.x() * quaternion.y() * 2;
    double xz2 = quaternion.x() * quaternion.z() * 2;
    double xw2 = quaternion.x() * quaternion.w() * 2;
    double yz2 = quaternion.y() * quaternion.z() * 2;
    double yw2 = quaternion.y() * quaternion.w() * 2;
    double zw2 = quaternion.z() * quaternion.w() * 2;

    return Vector3(static_cast<float> (ww * point.x() + yw2 * point.z() - zw2 * point.y() + xx * point.x() + xy2
            * point.y() + xz2 * point.z() - zz * point.x() - yy * point.x()), static_cast<float> (xy2 * point.x() + yy
            * point.y() + yz2 * point.z() + zw2 * point.x() - zz * point.y() + ww * point.y() - xw2 * point.z() - xx
            * point.y()), static_cast<float> (xz2 * point.x() + yz2 * point.y() + zz * point.z() - yw2 * point.x() - yy
            * point.z() + xw2 * point.y() - xx * point.z() + ww * point.z()));
}

inline Matrix4 matrix4_rotation_for_axisangle (const Vector3& axis, double angle)
{
    return matrix4_rotation_for_quaternion(quaternion_for_axisangle(axis, angle));
}

inline void matrix4_rotate_by_axisangle (Matrix4& self, const Vector3& axis, double angle)
{
    matrix4_multiply_by_matrix4(self, matrix4_rotation_for_axisangle(axis, angle));
}

inline void matrix4_pivoted_rotate_by_axisangle (Matrix4& self, const Vector3& axis, double angle,
        const Vector3& pivotpoint)
{
    matrix4_translate_by_vec3(self, pivotpoint);
    matrix4_rotate_by_axisangle(self, axis, angle);
    matrix4_translate_by_vec3(self, -pivotpoint);
}

#endif