JUCE/modules/juce_opengl/geometry/juce_Quaternion.h

/*
  ==============================================================================

   This file is part of the JUCE 6 technical preview.
   Copyright (c) 2017 - ROLI Ltd.

   You may use this code under the terms of the GPL v3
   (see www.gnu.org/licenses).

   For this technical preview, this file is not subject to commercial licensing.

   JUCE IS PROVIDED "AS IS" WITHOUT ANY WARRANTY, AND ALL WARRANTIES, WHETHER
   EXPRESSED OR IMPLIED, INCLUDING MERCHANTABILITY AND FITNESS FOR PURPOSE, ARE
   DISCLAIMED.

  ==============================================================================
*/

namespace juce
{

//==============================================================================
/**
    Holds a quaternion (a 3D vector and a scalar value).

    @tags{OpenGL}
*/
template <typename Type>
class Quaternion
{
public:
    Quaternion() noexcept                                               : scalar() {}
    Quaternion (const Quaternion& other) noexcept                       : vector (other.vector), scalar (other.scalar) {}
    Quaternion (Vector3D<Type> vectorPart, Type scalarPart) noexcept    : vector (vectorPart), scalar (scalarPart) {}
    Quaternion (Type x, Type y, Type z, Type w) noexcept                : vector (x, y, z), scalar (w) {}

    /** Creates a quaternion from an angle and an axis. */
    static Quaternion fromAngle (Type angle, Vector3D<Type> axis) noexcept
    {
        return Quaternion (axis.normalised() * std::sin (angle / (Type) 2), std::cos (angle / (Type) 2));
    }

    Quaternion& operator= (Quaternion other) noexcept
    {
        vector = other.vector;
        scalar = other.scalar;
        return *this;
    }

    Quaternion& operator*= (Quaternion other) noexcept
    {
        const Type oldScalar (scalar);
        scalar = (scalar * other.scalar) - (vector * other.vector);
        vector = (other.vector * oldScalar) + (vector * other.scalar) + (vector ^ other.vector);
        return *this;
    }

    Type length() const noexcept        { return std::sqrt (normal()); }
    Type normal() const noexcept        { return scalar * scalar + vector.lengthSquared(); }

    Quaternion normalised() const noexcept
    {
        const Type len (length());
        jassert (len > 0);
        return Quaternion (vector / len, scalar / len);
    }

    /** Returns the matrix that will perform the rotation specified by this quaternion. */
    Matrix3D<Type> getRotationMatrix() const noexcept
    {
        const Type norm (normal());
        const Type s (norm > 0 ? ((Type) 2) / norm : 0);
        const Type xs (s * vector.x),  ys (s * vector.y),  zs (s * vector.z);
        const Type wx (xs * scalar),   wy (ys * scalar),   wz (zs * scalar);
        const Type xx (xs * vector.x), xy (ys * vector.x), xz (zs * vector.x);
        const Type yy (ys * vector.y), yz (zs * vector.y), zz (zs * vector.z);

        return Matrix3D<Type> (((Type) 1) - (yy + zz), xy - wz, xz + wy, 0,
                               xy + wz, ((Type) 1) - (xx+ zz),  yz - wx, 0,
                               xz - wy, yz + wx, ((Type) 1) - (xx + yy), 0,
                               0, 0, 0, (Type) 1);
    }

    /** The vector part of the quaternion. */
    Vector3D<Type> vector;

    /** The scalar part of the quaternion. */
    Type scalar;
};

} // namespace juce