/// <summary> /// Quaternions are added. /// </summary> /// <param name="quaternion1">The first quaternion.</param> /// <param name="quaternion2">The second quaternion.</param> /// <param name="result">The sum of both quaternions.</param> public static void Add(ref Fixed64Quaternion quaternion1, ref Fixed64Quaternion quaternion2, out Fixed64Quaternion result) { result.x = quaternion1.x + quaternion2.x; result.y = quaternion1.y + quaternion2.y; result.z = quaternion1.z + quaternion2.z; result.w = quaternion1.w + quaternion2.w; }
/// <summary> /// Quaternions are subtracted. /// </summary> /// <param name="quaternion1">The first quaternion.</param> /// <param name="quaternion2">The second quaternion.</param> /// <param name="result">The difference of both quaternions.</param> public static void Subtract(ref Fixed64Quaternion quaternion1, ref Fixed64Quaternion quaternion2, out Fixed64Quaternion result) { result.x = quaternion1.x - quaternion2.x; result.y = quaternion1.y - quaternion2.y; result.z = quaternion1.z - quaternion2.z; result.w = quaternion1.w - quaternion2.w; }
/// <summary> /// Scale a quaternion /// </summary> /// <param name="quaternion1">The quaternion to scale.</param> /// <param name="scaleFactor">Scale factor.</param> /// <param name="result">The scaled quaternion.</param> public static void Multiply(ref Fixed64Quaternion quaternion1, Fixed64 scaleFactor, out Fixed64Quaternion result) { result.x = quaternion1.x * scaleFactor; result.y = quaternion1.y * scaleFactor; result.z = quaternion1.z * scaleFactor; result.w = quaternion1.w * scaleFactor; }
public static Fixed64Quaternion LerpUnclamped(Fixed64Quaternion a, Fixed64Quaternion b, Fixed64 t) { Fixed64Quaternion result = Multiply(a, (1 - t)) + Multiply(b, t); result.Normalize(); return(result); }
public static Fixed64Quaternion Conjugate(Fixed64Quaternion value) { Fixed64Quaternion quaternion; quaternion.x = -value.x; quaternion.y = -value.y; quaternion.z = -value.z; quaternion.w = value.w; return(quaternion); }
public static Fixed64Quaternion FromToRotation(Fixed64Vector3 fromVector, Fixed64Vector3 toVector) { Fixed64Vector3 w = Fixed64Vector3.Cross(fromVector, toVector); Fixed64Quaternion q = new Fixed64Quaternion(w.x, w.y, w.z, Fixed64Vector3.Dot(fromVector, toVector)); q.w += Fixed64.Sqrt(fromVector.SqrMagnitude * toVector.SqrMagnitude); q.Normalize(); return(q); }
public static Fixed64 Angle(Fixed64Quaternion a, Fixed64Quaternion b) { Fixed64Quaternion aInv = Inverse(a); Fixed64Quaternion f = b * aInv; Fixed64 angle = Fixed64.Acos(f.w) * 2 * Fixed64.Rad2Deg; if (angle > 180) { angle = 360 - angle; } return(angle); }
public static Fixed64Quaternion Slerp(Fixed64Quaternion from, Fixed64Quaternion to, Fixed64 t) { t = FixedMath.Clamp(t, 0, 1); Fixed64 dot = Dot(from, to); if (dot < 0.0f) { to = Multiply(to, -1); dot = -dot; } Fixed64 halfTheta = Fixed64.Acos(dot); return(Multiply(Multiply(from, Fixed64.Sin((1 - t) * halfTheta)) + Multiply(to, Fixed64.Sin(t * halfTheta)), 1 / Fixed64.Sin(halfTheta))); }
/// <summary> /// Multiply two quaternions. /// </summary> /// <param name="quaternion1">The first quaternion.</param> /// <param name="quaternion2">The second quaternion.</param> /// <param name="result">The product of both quaternions.</param> public static void Multiply(ref Fixed64Quaternion quaternion1, ref Fixed64Quaternion quaternion2, out Fixed64Quaternion result) { Fixed64 x = quaternion1.x; Fixed64 y = quaternion1.y; Fixed64 z = quaternion1.z; Fixed64 w = quaternion1.w; Fixed64 num4 = quaternion2.x; Fixed64 num3 = quaternion2.y; Fixed64 num2 = quaternion2.z; Fixed64 num = quaternion2.w; Fixed64 num12 = (y * num2) - (z * num3); Fixed64 num11 = (z * num4) - (x * num2); Fixed64 num10 = (x * num3) - (y * num4); Fixed64 num9 = ((x * num4) + (y * num3)) + (z * num2); result.x = ((x * num) + (num4 * w)) + num12; result.y = ((y * num) + (num3 * w)) + num11; result.z = ((z * num) + (num2 * w)) + num10; result.w = (w * num) - num9; }
/// <summary> /// Creates a quaternion from a matrix. /// </summary> /// <param name="matrix">A matrix representing an orientation.</param> /// <param name="result">JQuaternion representing an orientation.</param> public static void CreateFromMatrix(ref Fixed64Matrix matrix, out Fixed64Quaternion result) { Fixed64 num8 = (matrix.M11 + matrix.M22) + matrix.M33; if (num8 > Fixed64.Zero) { Fixed64 num = Fixed64.Sqrt((num8 + Fixed64.One)); result.w = num * Fixed64.Half; num = Fixed64.Half / num; result.x = (matrix.M23 - matrix.M32) * num; result.y = (matrix.M31 - matrix.M13) * num; result.z = (matrix.M12 - matrix.M21) * num; } else if ((matrix.M11 >= matrix.M22) && (matrix.M11 >= matrix.M33)) { Fixed64 num7 = Fixed64.Sqrt((((Fixed64.One + matrix.M11) - matrix.M22) - matrix.M33)); Fixed64 num4 = Fixed64.Half / num7; result.x = Fixed64.Half * num7; result.y = (matrix.M12 + matrix.M21) * num4; result.z = (matrix.M13 + matrix.M31) * num4; result.w = (matrix.M23 - matrix.M32) * num4; } else if (matrix.M22 > matrix.M33) { Fixed64 num6 = Fixed64.Sqrt((((Fixed64.One + matrix.M22) - matrix.M11) - matrix.M33)); Fixed64 num3 = Fixed64.Half / num6; result.x = (matrix.M21 + matrix.M12) * num3; result.y = Fixed64.Half * num6; result.z = (matrix.M32 + matrix.M23) * num3; result.w = (matrix.M31 - matrix.M13) * num3; } else { Fixed64 num5 = Fixed64.Sqrt((((Fixed64.One + matrix.M33) - matrix.M11) - matrix.M22)); Fixed64 num2 = Fixed64.Half / num5; result.x = (matrix.M31 + matrix.M13) * num2; result.y = (matrix.M32 + matrix.M23) * num2; result.z = Fixed64.Half * num5; result.w = (matrix.M12 - matrix.M21) * num2; } }
public static Fixed64Quaternion RotateTowards(Fixed64Quaternion from, Fixed64Quaternion to, Fixed64 maxDegreesDelta) { Fixed64 dot = Dot(from, to); if (dot < 0.0f) { to = Multiply(to, -1); dot = -dot; } Fixed64 halfTheta = Fixed64.Acos(dot); Fixed64 theta = halfTheta * 2; maxDegreesDelta *= Fixed64.Deg2Rad; if (maxDegreesDelta >= theta) { return(to); } maxDegreesDelta /= theta; return(Multiply(Multiply(from, Fixed64.Sin((1 - maxDegreesDelta) * halfTheta)) + Multiply(to, Fixed64.Sin(maxDegreesDelta * halfTheta)), 1 / Fixed64.Sin(halfTheta))); }
static Fixed64Quaternion() { identity = new Fixed64Quaternion(0, 0, 0, 1); }
/// <summary> /// Scale a quaternion /// </summary> /// <param name="quaternion1">The quaternion to scale.</param> /// <param name="scaleFactor">Scale factor.</param> /// <returns>The scaled quaternion.</returns> #region public static JQuaternion Multiply(JQuaternion quaternion1, FP scaleFactor) public static Fixed64Quaternion Multiply(Fixed64Quaternion quaternion1, Fixed64 scaleFactor) { Multiply(ref quaternion1, scaleFactor, out Fixed64Quaternion result); return(result); }
/// <summary> /// Multiply two quaternions. /// </summary> /// <param name="quaternion1">The first quaternion.</param> /// <param name="quaternion2">The second quaternion.</param> /// <returns>The product of both quaternions.</returns> #region public static JQuaternion Multiply(JQuaternion quaternion1, JQuaternion quaternion2) public static Fixed64Quaternion Multiply(Fixed64Quaternion quaternion1, Fixed64Quaternion quaternion2) { Multiply(ref quaternion1, ref quaternion2, out Fixed64Quaternion result); return(result); }
/// <summary> /// Quaternions are subtracted. /// </summary> /// <param name="quaternion1">The first quaternion.</param> /// <param name="quaternion2">The second quaternion.</param> /// <returns>The difference of both quaternions.</returns> #region public static JQuaternion Subtract(JQuaternion quaternion1, JQuaternion quaternion2) public static Fixed64Quaternion Subtract(Fixed64Quaternion quaternion1, Fixed64Quaternion quaternion2) { Subtract(ref quaternion1, ref quaternion2, out Fixed64Quaternion result); return(result); }
public static void CreateFromYawPitchRoll(Fixed64 yaw, Fixed64 pitch, Fixed64 roll, out Fixed64Quaternion result) { Fixed64 num9 = roll * Fixed64.Half; Fixed64 num6 = Fixed64.Sin(num9); Fixed64 num5 = Fixed64.Cos(num9); Fixed64 num8 = pitch * Fixed64.Half; Fixed64 num4 = Fixed64.Sin(num8); Fixed64 num3 = Fixed64.Cos(num8); Fixed64 num7 = yaw * Fixed64.Half; Fixed64 num2 = Fixed64.Sin(num7); Fixed64 num = Fixed64.Cos(num7); result.x = ((num * num4) * num5) + ((num2 * num3) * num6); result.y = ((num2 * num3) * num5) - ((num * num4) * num6); result.z = ((num * num3) * num6) - ((num2 * num4) * num5); result.w = ((num * num3) * num5) + ((num2 * num4) * num6); }
/// <summary> /// Quaternions are added. /// </summary> /// <param name="quaternion1">The first quaternion.</param> /// <param name="quaternion2">The second quaternion.</param> /// <returns>The sum of both quaternions.</returns> #region public static JQuaternion Add(JQuaternion quaternion1, JQuaternion quaternion2) public static Fixed64Quaternion Add(Fixed64Quaternion quaternion1, Fixed64Quaternion quaternion2) { Add(ref quaternion1, ref quaternion2, out Fixed64Quaternion result); return(result); }
public static Fixed64Quaternion Inverse(Fixed64Quaternion rotation) { Fixed64 invNorm = Fixed64.One / ((rotation.x * rotation.x) + (rotation.y * rotation.y) + (rotation.z * rotation.z) + (rotation.w * rotation.w)); return(Multiply(Conjugate(rotation), invNorm)); }
public static Fixed64 Dot(Fixed64Quaternion a, Fixed64Quaternion b) { return(a.w * b.w + a.x * b.x + a.y * b.y + a.z * b.z); }
public void SetFromToRotation(Fixed64Vector3 fromDirection, Fixed64Vector3 toDirection) { Fixed64Quaternion targetRotation = FromToRotation(fromDirection, toDirection); Set(targetRotation.x, targetRotation.y, targetRotation.z, targetRotation.w); }
public static Fixed64Quaternion Lerp(Fixed64Quaternion a, Fixed64Quaternion b, Fixed64 t) { t = FixedMath.Clamp(t, Fixed64.Zero, Fixed64.One); return(LerpUnclamped(a, b, t)); }