urho3d/Extras/LuaScript/pkgs/Math/Quaternion.pkg

$#include "Quaternion.h"

/// Rotation represented as a four-dimensional normalized vector.
class Quaternion
{
public:
    /// Construct identity quaternion.
    Quaternion() :
        w_(1.0f),
        x_(0.0f),
        y_(0.0f),
        z_(0.0f)
    {
    }
    
    /// Copy-construct from another quaternion.
    Quaternion(const Quaternion& quat) :
        w_(quat.w_),
        x_(quat.x_),
        y_(quat.y_),
        z_(quat.z_)
    {
    }
    
    /// Construct from values.
    Quaternion(float w, float x, float y, float z) :
        w_(w),
        x_(x),
        y_(y),
        z_(z)
    {
    }
    
    /// Construct from an angle (in degrees) and axis.
    Quaternion(float angle, const Vector3& axis)
    {
        FromAngleAxis(angle, axis);
    }
    
    /// Construct from Euler angles (in degrees.)
    Quaternion(float x, float y, float z)
    {
        FromEulerAngles(x, y, z);
    }
    
    /// Construct from the rotation difference between two vectors.
    Quaternion(const Vector3& start, const Vector3& end)
    {
        FromRotationTo(start, end);
    }
    
    /// Construct from orthonormal axes.
    Quaternion(const Vector3& xAxis, const Vector3& yAxis, const Vector3& zAxis)
    {
        FromAxes(xAxis, yAxis, zAxis);
    }

    /// Construct from a rotation matrix.
    Quaternion(const Matrix3& matrix)
    {
        FromRotationMatrix(matrix);
    }
    
    /// Test for equality with another quaternion without epsilon.
    bool operator == (const Quaternion& rhs) const;
	
	/// Multiply with a scalar.
    Quaternion operator * (float rhs) const;
    
	/// Return negation.
    Quaternion operator - () const;
    
    /// Test for equality with another quaternion without epsilon.
    bool operator == (const Quaternion& rhs) const { return w_ == rhs.w_ && x_ == rhs.x_ && y_ == rhs.y_ && z_ == rhs.z_; }
    /// Multiply with a scalar.
    Quaternion operator * (float rhs) const { return Quaternion(w_ * rhs, x_ * rhs, y_ * rhs, z_ * rhs); }
    /// Return negation.
    Quaternion operator - () const { return Quaternion(-w_, -x_, -y_, -z_); }
    /// Add a quaternion.
    Quaternion operator + (const Quaternion& rhs) const { return Quaternion(w_ + rhs.w_, x_ + rhs.x_, y_ + rhs.y_, z_ + rhs.z_); }
    /// Subtract a quaternion.
    Quaternion operator - (const Quaternion& rhs) const { return Quaternion(w_ - rhs.w_, x_ - rhs.x_, y_ - rhs.y_, z_ - rhs.z_); }
    
    /// Multiply a quaternion.
    Quaternion operator * (const Quaternion& rhs) const
    {
        return Quaternion(
            w_ * rhs.w_ - x_ * rhs.x_ - y_ * rhs.y_ - z_ * rhs.z_,
            w_ * rhs.x_ + x_ * rhs.w_ + y_ * rhs.z_ - z_ * rhs.y_,
            w_ * rhs.y_ + y_ * rhs.w_ + z_ * rhs.x_ - x_ * rhs.z_,
            w_ * rhs.z_ + z_ * rhs.w_ + x_ * rhs.y_ - y_ * rhs.x_
        );
    }
    
    /// Multiply a Vector3.
    Vector3 operator * (const Vector3& rhs) const
    {
        Vector3 qVec(x_,y_,z_);
        Vector3 cross1(qVec.CrossProduct(rhs));
        Vector3 cross2(qVec.CrossProduct(cross1));
        
        return rhs + 2.0f * (cross1 * w_ + cross2);
    }
    
    /// Define from an angle (in degrees) and axis.
    void FromAngleAxis(float angle, const Vector3& axis);
    /// Define from Euler angles (in degrees.)
    void FromEulerAngles(float x, float y, float z);
    /// Define from the rotation difference between two vectors.
    void FromRotationTo(const Vector3& start, const Vector3& end);
    /// Define from orthonormal axes.
    void FromAxes(const Vector3& xAxis, const Vector3& yAxis, const Vector3& zAxis);
    /// Define from a rotation matrix.
    void FromRotationMatrix(const Matrix3& matrix);
    
    /// Normalize to unit length and return the previous length.
    float Normalize()
    {
        float len = sqrtf(LengthSquared());
        if (len >= M_EPSILON)
            *this *= (1.0f / len);

        return len;
    }
    
    /// Return normalized to unit length.
    Quaternion Normalized() const
    {
        float lenSquared = LengthSquared();
        if (lenSquared >= M_EPSILON * M_EPSILON)
            return *this * (1.0f / sqrtf(lenSquared));
        else
            return IDENTITY;
    }
    
    /// Return inverse.
    Quaternion Inverse() const
    {
        float lenSquared = LengthSquared();
        if (lenSquared == 1.0f)
            return Conjugate();
        else if (lenSquared >= M_EPSILON)
            return Conjugate() * (1.0f / lenSquared);
        else
            return IDENTITY;
    }
    
    /// Return squared length.
    float LengthSquared() const { return w_ * w_ + x_ * x_ + y_ * y_ + z_ * z_; }
    /// Calculate dot product.
    float DotProduct(const Quaternion& rhs) const { return w_ * rhs.w_ + x_ * rhs.x_ + y_ * rhs.y_ + z_ * rhs.z_; }
    /// Test for equality with another quaternion with epsilon.
    bool Equals(const Quaternion& rhs) const { return Urho3D::Equals(w_, rhs.w_) && Urho3D::Equals(x_, rhs.x_) && Urho3D::Equals(y_, rhs.y_) && Urho3D::Equals(z_, rhs.z_); }
    /// Return conjugate.
    Quaternion Conjugate() const { return Quaternion(w_, -x_, -y_, -z_); }
    
    /// Return Euler angles in degrees.
    Vector3 EulerAngles() const;
    /// Return yaw angle in degrees.
    float YawAngle() const;
    /// Return pitch angle in degrees.
    float PitchAngle() const;
    /// Return roll angle in degrees.
    float RollAngle() const;
    /// Return the rotation matrix that corresponds to this quaternion.
    Matrix3 RotationMatrix() const;
    /// Spherical interpolation with another quaternion.
    Quaternion Slerp(Quaternion rhs, float t) const;
    /// Return as string.
    String ToString() const;
    
    /// W coordinate.
    float w_ @ w;
    /// X coordinate.
    float x_ @ x;
    /// Y coordinate.
    float y_ @ y;
    /// Z coordinate.
    float z_ @ z;
    
    /// Identity quaternion.
    static const Quaternion IDENTITY;
};