urho3d/Source/Urho3D/Math/Quaternion.h

//
// Copyright (c) 2008-2020 the Urho3D project.
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
// THE SOFTWARE.
//

#pragma once

#include "../Math/Matrix3.h"

#ifdef URHO3D_SSE
#include <emmintrin.h>
#endif

namespace Urho3D
{

/// Rotation represented as a four-dimensional normalized vector.
class URHO3D_API Quaternion
{
public:
    /// Construct an identity quaternion.
    Quaternion() noexcept
#ifndef URHO3D_SSE
       :w_(1.0f),
        x_(0.0f),
        y_(0.0f),
        z_(0.0f)
#endif
    {
#ifdef URHO3D_SSE
        _mm_storeu_ps(&w_, _mm_set_ps(0.f, 0.f, 0.f, 1.f));
#endif
    }

    /// Copy-construct from another quaternion.
    Quaternion(const Quaternion& quat) noexcept
#if defined(URHO3D_SSE) && (!defined(_MSC_VER) || _MSC_VER >= 1700) /* Visual Studio 2012 and newer. VS2010 has a bug with these, see https://github.com/urho3d/Urho3D/issues/1044 */
    {
        _mm_storeu_ps(&w_, _mm_loadu_ps(&quat.w_));
    }
#else
       :w_(quat.w_),
        x_(quat.x_),
        y_(quat.y_),
        z_(quat.z_)
    {
    }
#endif

    /// Construct from values.
    Quaternion(float w, float x, float y, float z) noexcept
#ifndef URHO3D_SSE
       :w_(w),
        x_(x),
        y_(y),
        z_(z)
#endif
    {
#ifdef URHO3D_SSE
        _mm_storeu_ps(&w_, _mm_set_ps(z, y, x, w));
#endif
    }

    /// Construct from a float array.
    explicit Quaternion(const float* data) noexcept
#ifndef URHO3D_SSE
       :w_(data[0]),
        x_(data[1]),
        y_(data[2]),
        z_(data[3])
#endif
    {
#ifdef URHO3D_SSE
        _mm_storeu_ps(&w_, _mm_loadu_ps(data));
#endif
    }

    /// Construct from an angle (in degrees) and axis.
    Quaternion(float angle, const Vector3& axis) noexcept
    {
        FromAngleAxis(angle, axis);
    }

    /// Construct from an angle (in degrees, for Urho2D).
    explicit Quaternion(float angle) noexcept
    {
        FromAngleAxis(angle, Vector3::FORWARD);
    }

    /// Construct from Euler angles (in degrees). Equivalent to Y*X*Z.
    Quaternion(float x, float y, float z) noexcept
    {
        FromEulerAngles(x, y, z);
    }

    /// Construct from Euler angles (in degrees).
    explicit Quaternion(const Vector3& angles) noexcept
    {
        FromEulerAngles(angles.x_, angles.y_, angles.z_);
    }

    /// Construct from the rotation difference between two direction vectors.
    Quaternion(const Vector3& start, const Vector3& end) noexcept
    {
        FromRotationTo(start, end);
    }

    /// Construct from orthonormal axes.
    Quaternion(const Vector3& xAxis, const Vector3& yAxis, const Vector3& zAxis) noexcept
    {
        FromAxes(xAxis, yAxis, zAxis);
    }

    /// Construct from a rotation matrix.
    explicit Quaternion(const Matrix3& matrix) noexcept
    {
        FromRotationMatrix(matrix);
    }

#ifdef URHO3D_SSE
    explicit Quaternion(__m128 wxyz) noexcept
    {
        _mm_storeu_ps(&w_, wxyz);
    }
#endif

    /// Assign from another quaternion.
    Quaternion& operator =(const Quaternion& rhs) noexcept
    {
#if defined(URHO3D_SSE) && (!defined(_MSC_VER) || _MSC_VER >= 1700) /* Visual Studio 2012 and newer. VS2010 has a bug with these, see https://github.com/urho3d/Urho3D/issues/1044 */
        _mm_storeu_ps(&w_, _mm_loadu_ps(&rhs.w_));
#else
        w_ = rhs.w_;
        x_ = rhs.x_;
        y_ = rhs.y_;
        z_ = rhs.z_;
#endif
        return *this;
    }

    /// Add-assign a quaternion.
    Quaternion& operator +=(const Quaternion& rhs)
    {
#ifdef URHO3D_SSE
        _mm_storeu_ps(&w_, _mm_add_ps(_mm_loadu_ps(&w_), _mm_loadu_ps(&rhs.w_)));
#else
        w_ += rhs.w_;
        x_ += rhs.x_;
        y_ += rhs.y_;
        z_ += rhs.z_;
#endif
        return *this;
    }

    /// Multiply-assign a scalar.
    Quaternion& operator *=(float rhs)
    {
#ifdef URHO3D_SSE
        _mm_storeu_ps(&w_, _mm_mul_ps(_mm_loadu_ps(&w_), _mm_set1_ps(rhs)));
#else
        w_ *= rhs;
        x_ *= rhs;
        y_ *= rhs;
        z_ *= rhs;
#endif
        return *this;
    }

    /// Test for equality with another quaternion without epsilon.
    bool operator ==(const Quaternion& rhs) const
    {
#ifdef URHO3D_SSE
        __m128 c = _mm_cmpeq_ps(_mm_loadu_ps(&w_), _mm_loadu_ps(&rhs.w_));
        c = _mm_and_ps(c, _mm_movehl_ps(c, c));
        c = _mm_and_ps(c, _mm_shuffle_ps(c, c, _MM_SHUFFLE(1, 1, 1, 1)));
        return _mm_cvtsi128_si32(_mm_castps_si128(c)) == -1;
#else
        return w_ == rhs.w_ && x_ == rhs.x_ && y_ == rhs.y_ && z_ == rhs.z_;
#endif
    }

    /// Test for inequality with another quaternion without epsilon.
    bool operator !=(const Quaternion& rhs) const { return !(*this == rhs); }

    /// Multiply with a scalar.
    Quaternion operator *(float rhs) const
    {
#ifdef URHO3D_SSE
        return Quaternion(_mm_mul_ps(_mm_loadu_ps(&w_), _mm_set1_ps(rhs)));
#else
        return Quaternion(w_ * rhs, x_ * rhs, y_ * rhs, z_ * rhs);
#endif
    }

    /// Return negation.
    Quaternion operator -() const
    {
#ifdef URHO3D_SSE
        return Quaternion(_mm_xor_ps(_mm_loadu_ps(&w_), _mm_castsi128_ps(_mm_set1_epi32((int)0x80000000UL))));
#else
        return Quaternion(-w_, -x_, -y_, -z_);
#endif
    }

    /// Add a quaternion.
    Quaternion operator +(const Quaternion& rhs) const
    {
#ifdef URHO3D_SSE
        return Quaternion(_mm_add_ps(_mm_loadu_ps(&w_), _mm_loadu_ps(&rhs.w_)));
#else
        return Quaternion(w_ + rhs.w_, x_ + rhs.x_, y_ + rhs.y_, z_ + rhs.z_);
#endif
    }

    /// Subtract a quaternion.
    Quaternion operator -(const Quaternion& rhs) const
    {
#ifdef URHO3D_SSE
        return Quaternion(_mm_sub_ps(_mm_loadu_ps(&w_), _mm_loadu_ps(&rhs.w_)));
#else
        return Quaternion(w_ - rhs.w_, x_ - rhs.x_, y_ - rhs.y_, z_ - rhs.z_);
#endif
    }

    /// Multiply a quaternion.
    Quaternion operator *(const Quaternion& rhs) const
    {
#ifdef URHO3D_SSE
        __m128 q1 = _mm_loadu_ps(&w_);
        __m128 q2 = _mm_loadu_ps(&rhs.w_);
        q2 = _mm_shuffle_ps(q2, q2, _MM_SHUFFLE(0, 3, 2, 1));
        const __m128 signy = _mm_castsi128_ps(_mm_set_epi32((int)0x80000000UL, (int)0x80000000UL, 0, 0));
        const __m128 signx = _mm_shuffle_ps(signy, signy, _MM_SHUFFLE(2, 0, 2, 0));
        const __m128 signz = _mm_shuffle_ps(signy, signy, _MM_SHUFFLE(3, 0, 0, 3));
        __m128 out = _mm_mul_ps(_mm_shuffle_ps(q1, q1, _MM_SHUFFLE(1, 1, 1, 1)), _mm_shuffle_ps(q2, q2, _MM_SHUFFLE(0, 1, 2, 3)));
        out = _mm_add_ps(_mm_mul_ps(_mm_xor_ps(signy, _mm_shuffle_ps(q1, q1, _MM_SHUFFLE(2, 2, 2, 2))), _mm_shuffle_ps(q2, q2, _MM_SHUFFLE(1, 0, 3, 2))), _mm_xor_ps(signx, out));
        out = _mm_add_ps(_mm_mul_ps(_mm_xor_ps(signz, _mm_shuffle_ps(q1, q1, _MM_SHUFFLE(3, 3, 3, 3))), _mm_shuffle_ps(q2, q2, _MM_SHUFFLE(2, 3, 0, 1))), out);
        out = _mm_add_ps(_mm_mul_ps(_mm_shuffle_ps(q1, q1, _MM_SHUFFLE(0, 0, 0, 0)), q2), out);
        return Quaternion(_mm_shuffle_ps(out, out, _MM_SHUFFLE(2, 1, 0, 3)));
#else
        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_
        );
#endif
    }

    /// Multiply a Vector3.
    Vector3 operator *(const Vector3& rhs) const
    {
#ifdef URHO3D_SSE
        __m128 q = _mm_loadu_ps(&w_);
        q = _mm_shuffle_ps(q, q, _MM_SHUFFLE(0, 3, 2, 1));
        __m128 v = _mm_set_ps(0.f, rhs.z_, rhs.y_, rhs.x_);
        const __m128 W = _mm_shuffle_ps(q, q, _MM_SHUFFLE(3, 3, 3, 3));
        const __m128 a_yzx = _mm_shuffle_ps(q, q, _MM_SHUFFLE(3, 0, 2, 1));
        __m128 x = _mm_mul_ps(q, _mm_shuffle_ps(v, v, _MM_SHUFFLE(3, 0, 2, 1)));
        __m128 qxv = _mm_sub_ps(x, _mm_mul_ps(a_yzx, v));
        __m128 Wv = _mm_mul_ps(W, v);
        __m128 s = _mm_add_ps(qxv, _mm_shuffle_ps(Wv, Wv, _MM_SHUFFLE(3, 1, 0, 2)));
        __m128 qs = _mm_mul_ps(q, s);
        __m128 y = _mm_shuffle_ps(qs, qs, _MM_SHUFFLE(3, 1, 0, 2));
        s = _mm_sub_ps(_mm_mul_ps(a_yzx, s), y);
        s = _mm_add_ps(s, s);
        s = _mm_add_ps(s, v);

        return Vector3(
            _mm_cvtss_f32(s),
            _mm_cvtss_f32(_mm_shuffle_ps(s, s, _MM_SHUFFLE(1, 1, 1, 1))),
            _mm_cvtss_f32(_mm_movehl_ps(s, s)));
#else
        Vector3 qVec(x_, y_, z_);
        Vector3 cross1(qVec.CrossProduct(rhs));
        Vector3 cross2(qVec.CrossProduct(cross1));

        return rhs + 2.0f * (cross1 * w_ + cross2);
#endif
    }

    /// Define from an angle (in degrees) and axis.
    void FromAngleAxis(float angle, const Vector3& axis);
    /// Define from Euler angles (in degrees). Equivalent to Y*X*Z.
    void FromEulerAngles(float x, float y, float z);
    /// Define from the rotation difference between two direction 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);
    /// Define from a direction to look in and an up direction. Return true if successful, or false if would result in a NaN, in which case the current value remains.
    bool FromLookRotation(const Vector3& direction, const Vector3& up = Vector3::UP);

    /// Normalize to unit length.
    void Normalize()
    {
#ifdef URHO3D_SSE
        __m128 q = _mm_loadu_ps(&w_);
        __m128 n = _mm_mul_ps(q, q);
        n = _mm_add_ps(n, _mm_shuffle_ps(n, n, _MM_SHUFFLE(2, 3, 0, 1)));
        n = _mm_add_ps(n, _mm_shuffle_ps(n, n, _MM_SHUFFLE(0, 1, 2, 3)));
        __m128 e = _mm_rsqrt_ps(n);
        __m128 e3 = _mm_mul_ps(_mm_mul_ps(e, e), e);
        __m128 half = _mm_set1_ps(0.5f);
        n = _mm_add_ps(e, _mm_mul_ps(half, _mm_sub_ps(e, _mm_mul_ps(n, e3))));
        _mm_storeu_ps(&w_, _mm_mul_ps(q, n));
#else
        float lenSquared = LengthSquared();
        if (!Urho3D::Equals(lenSquared, 1.0f) && lenSquared > 0.0f)
        {
            float invLen = 1.0f / sqrtf(lenSquared);
            w_ *= invLen;
            x_ *= invLen;
            y_ *= invLen;
            z_ *= invLen;
        }
#endif
    }

    /// Return normalized to unit length.
    Quaternion Normalized() const
    {
#ifdef URHO3D_SSE
        __m128 q = _mm_loadu_ps(&w_);
        __m128 n = _mm_mul_ps(q, q);
        n = _mm_add_ps(n, _mm_shuffle_ps(n, n, _MM_SHUFFLE(2, 3, 0, 1)));
        n = _mm_add_ps(n, _mm_shuffle_ps(n, n, _MM_SHUFFLE(0, 1, 2, 3)));
        __m128 e = _mm_rsqrt_ps(n);
        __m128 e3 = _mm_mul_ps(_mm_mul_ps(e, e), e);
        __m128 half = _mm_set1_ps(0.5f);
        n = _mm_add_ps(e, _mm_mul_ps(half, _mm_sub_ps(e, _mm_mul_ps(n, e3))));
        return Quaternion(_mm_mul_ps(q, n));
#else
        float lenSquared = LengthSquared();
        if (!Urho3D::Equals(lenSquared, 1.0f) && lenSquared > 0.0f)
        {
            float invLen = 1.0f / sqrtf(lenSquared);
            return *this * invLen;
        }
        else
            return *this;
#endif
    }

    /// Return inverse.
    Quaternion Inverse() const
    {
#ifdef URHO3D_SSE
        __m128 q = _mm_loadu_ps(&w_);
        __m128 n = _mm_mul_ps(q, q);
        n = _mm_add_ps(n, _mm_shuffle_ps(n, n, _MM_SHUFFLE(2, 3, 0, 1)));
        n = _mm_add_ps(n, _mm_shuffle_ps(n, n, _MM_SHUFFLE(0, 1, 2, 3)));
        return Quaternion(_mm_div_ps(_mm_xor_ps(q, _mm_castsi128_ps(_mm_set_epi32((int)0x80000000UL, (int)0x80000000UL, (int)0x80000000UL, 0))), n));
#else
        float lenSquared = LengthSquared();
        if (lenSquared == 1.0f)
            return Conjugate();
        else if (lenSquared >= M_EPSILON)
            return Conjugate() * (1.0f / lenSquared);
        else
            return IDENTITY;
#endif
    }

    /// Return squared length.
    float LengthSquared() const
    {
#ifdef URHO3D_SSE
        __m128 q = _mm_loadu_ps(&w_);
        __m128 n = _mm_mul_ps(q, q);
        n = _mm_add_ps(n, _mm_shuffle_ps(n, n, _MM_SHUFFLE(2, 3, 0, 1)));
        n = _mm_add_ps(n, _mm_shuffle_ps(n, n, _MM_SHUFFLE(0, 1, 2, 3)));
        return _mm_cvtss_f32(n);
#else
        return w_ * w_ + x_ * x_ + y_ * y_ + z_ * z_;
#endif
    }

    /// Calculate dot product.
    float DotProduct(const Quaternion& rhs) const
    {
#ifdef URHO3D_SSE
        __m128 q1 = _mm_loadu_ps(&w_);
        __m128 q2 = _mm_loadu_ps(&rhs.w_);
        __m128 n = _mm_mul_ps(q1, q2);
        n = _mm_add_ps(n, _mm_shuffle_ps(n, n, _MM_SHUFFLE(2, 3, 0, 1)));
        n = _mm_add_ps(n, _mm_shuffle_ps(n, n, _MM_SHUFFLE(0, 1, 2, 3)));
        return _mm_cvtss_f32(n);
#else
        return w_ * rhs.w_ + x_ * rhs.x_ + y_ * rhs.y_ + z_ * rhs.z_;
#endif
    }

    /// 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 whether any element is NaN.
    bool IsNaN() const { return Urho3D::IsNaN(w_) || Urho3D::IsNaN(x_) || Urho3D::IsNaN(y_) || Urho3D::IsNaN(z_); }

    /// Return whether any element is Inf.
    bool IsInf() const { return Urho3D::IsInf(w_) || Urho3D::IsInf(x_) || Urho3D::IsInf(y_) || Urho3D::IsInf(z_); }

    /// Return conjugate.
    Quaternion Conjugate() const
    {
#ifdef URHO3D_SSE
        __m128 q = _mm_loadu_ps(&w_);
        return Quaternion(_mm_xor_ps(q, _mm_castsi128_ps(_mm_set_epi32((int)0x80000000UL, (int)0x80000000UL, (int)0x80000000UL, 0))));
#else
        return Quaternion(w_, -x_, -y_, -z_);
#endif
    }

    /// Return Euler angles in degrees.
    /// @property
    Vector3 EulerAngles() const;
    /// Return yaw angle in degrees.
    /// @property{get_yaw}
    float YawAngle() const;
    /// Return pitch angle in degrees.
    /// @property{get_pitch}
    float PitchAngle() const;
    /// Return roll angle in degrees.
    /// @property{get_roll}
    float RollAngle() const;
    /// Return rotation axis.
    /// @property
    Vector3 Axis() const;
    /// Return rotation angle.
    /// @property
    float Angle() const;
    /// Return the rotation matrix that corresponds to this quaternion.
    /// @property
    Matrix3 RotationMatrix() const;
    /// Spherical interpolation with another quaternion.
    Quaternion Slerp(const Quaternion& rhs, float t) const;
    /// Normalized linear interpolation with another quaternion.
    Quaternion Nlerp(const Quaternion& rhs, float t, bool shortestPath = false) const;

    /// Return float data.
    const float* Data() const { return &w_; }

    /// Return as string.
    String ToString() const;

    /// W coordinate.
    float w_;
    /// X coordinate.
    float x_;
    /// Y coordinate.
    float y_;
    /// Z coordinate.
    float z_;

    /// Identity quaternion.
    static const Quaternion IDENTITY;
};

}