559 lines
20 KiB
C#
559 lines
20 KiB
C#
#if REAL_T_IS_DOUBLE
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using real_t = System.Double;
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#else
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using real_t = System.Single;
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#endif
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using System;
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using System.Runtime.InteropServices;
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namespace Godot
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{
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/// <summary>
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/// A unit quaternion used for representing 3D rotations.
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/// Quaternions need to be normalized to be used for rotation.
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///
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/// It is similar to Basis, which implements matrix representation of
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/// rotations, and can be parametrized using both an axis-angle pair
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/// or Euler angles. Basis stores rotation, scale, and shearing,
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/// while Quaternion only stores rotation.
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///
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/// Due to its compactness and the way it is stored in memory, certain
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/// operations (obtaining axis-angle and performing SLERP, in particular)
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/// are more efficient and robust against floating-point errors.
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/// </summary>
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[Serializable]
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[StructLayout(LayoutKind.Sequential)]
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public struct Quaternion : IEquatable<Quaternion>
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{
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/// <summary>
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/// X component of the quaternion (imaginary `i` axis part).
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/// Quaternion components should usually not be manipulated directly.
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/// </summary>
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public real_t x;
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/// <summary>
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/// Y component of the quaternion (imaginary `j` axis part).
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/// Quaternion components should usually not be manipulated directly.
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/// </summary>
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public real_t y;
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/// <summary>
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/// Z component of the quaternion (imaginary `k` axis part).
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/// Quaternion components should usually not be manipulated directly.
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/// </summary>
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public real_t z;
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/// <summary>
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/// W component of the quaternion (real part).
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/// Quaternion components should usually not be manipulated directly.
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/// </summary>
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public real_t w;
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/// <summary>
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/// Access quaternion components using their index.
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/// </summary>
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/// <value>`[0]` is equivalent to `.x`, `[1]` is equivalent to `.y`, `[2]` is equivalent to `.z`, `[3]` is equivalent to `.w`.</value>
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public real_t this[int index]
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{
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get
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{
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switch (index)
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{
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case 0:
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return x;
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case 1:
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return y;
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case 2:
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return z;
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case 3:
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return w;
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default:
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throw new IndexOutOfRangeException();
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}
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}
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set
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{
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switch (index)
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{
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case 0:
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x = value;
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break;
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case 1:
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y = value;
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break;
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case 2:
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z = value;
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break;
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case 3:
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w = value;
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break;
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default:
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throw new IndexOutOfRangeException();
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}
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}
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}
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/// <summary>
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/// Returns the length (magnitude) of the quaternion.
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/// </summary>
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/// <value>Equivalent to `Mathf.Sqrt(LengthSquared)`.</value>
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public real_t Length
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{
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get { return Mathf.Sqrt(LengthSquared); }
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}
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/// <summary>
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/// Returns the squared length (squared magnitude) of the quaternion.
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/// This method runs faster than <see cref="Length"/>, so prefer it if
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/// you need to compare quaternions or need the squared length for some formula.
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/// </summary>
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/// <value>Equivalent to `Dot(this)`.</value>
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public real_t LengthSquared
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{
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get { return Dot(this); }
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}
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/// <summary>
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/// Returns the angle between this quaternion and `to`.
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/// This is the magnitude of the angle you would need to rotate
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/// by to get from one to the other.
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///
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/// Note: This method has an abnormally high amount
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/// of floating-point error, so methods such as
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/// <see cref="Mathf.IsZeroApprox"/> will not work reliably.
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/// </summary>
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/// <param name="to">The other quaternion.</param>
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/// <returns>The angle between the quaternions.</returns>
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public real_t AngleTo(Quaternion to)
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{
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real_t dot = Dot(to);
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return Mathf.Acos(Mathf.Clamp(dot * dot * 2 - 1, -1, 1));
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}
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/// <summary>
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/// Performs a cubic spherical interpolation between quaternions `preA`,
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/// this vector, `b`, and `postB`, by the given amount `t`.
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/// </summary>
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/// <param name="b">The destination quaternion.</param>
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/// <param name="preA">A quaternion before this quaternion.</param>
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/// <param name="postB">A quaternion after `b`.</param>
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/// <param name="weight">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param>
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/// <returns>The interpolated quaternion.</returns>
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public Quaternion CubicSlerp(Quaternion b, Quaternion preA, Quaternion postB, real_t weight)
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{
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real_t t2 = (1.0f - weight) * weight * 2f;
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Quaternion sp = Slerp(b, weight);
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Quaternion sq = preA.Slerpni(postB, weight);
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return sp.Slerpni(sq, t2);
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}
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/// <summary>
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/// Returns the dot product of two quaternions.
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/// </summary>
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/// <param name="b">The other quaternion.</param>
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/// <returns>The dot product.</returns>
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public real_t Dot(Quaternion b)
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{
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return x * b.x + y * b.y + z * b.z + w * b.w;
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}
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/// <summary>
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/// Returns Euler angles (in the YXZ convention: when decomposing,
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/// first Z, then X, and Y last) corresponding to the rotation
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/// represented by the unit quaternion. Returned vector contains
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/// the rotation angles in the format (X angle, Y angle, Z angle).
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/// </summary>
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/// <returns>The Euler angle representation of this quaternion.</returns>
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public Vector3 GetEuler()
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{
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#if DEBUG
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if (!IsNormalized())
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{
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throw new InvalidOperationException("Quaternion is not normalized");
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}
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#endif
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var basis = new Basis(this);
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return basis.GetEuler();
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}
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/// <summary>
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/// Returns the inverse of the quaternion.
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/// </summary>
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/// <returns>The inverse quaternion.</returns>
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public Quaternion Inverse()
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{
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#if DEBUG
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if (!IsNormalized())
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{
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throw new InvalidOperationException("Quaternion is not normalized");
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}
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#endif
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return new Quaternion(-x, -y, -z, w);
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}
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/// <summary>
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/// Returns whether the quaternion is normalized or not.
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/// </summary>
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/// <returns>A bool for whether the quaternion is normalized or not.</returns>
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public bool IsNormalized()
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{
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return Mathf.Abs(LengthSquared - 1) <= Mathf.Epsilon;
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}
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/// <summary>
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/// Returns a copy of the quaternion, normalized to unit length.
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/// </summary>
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/// <returns>The normalized quaternion.</returns>
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public Quaternion Normalized()
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{
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return this / Length;
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}
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/// <summary>
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/// Returns the result of the spherical linear interpolation between
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/// this quaternion and `to` by amount `weight`.
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///
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/// Note: Both quaternions must be normalized.
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/// </summary>
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/// <param name="to">The destination quaternion for interpolation. Must be normalized.</param>
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/// <param name="weight">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param>
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/// <returns>The resulting quaternion of the interpolation.</returns>
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public Quaternion Slerp(Quaternion to, real_t weight)
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{
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#if DEBUG
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if (!IsNormalized())
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{
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throw new InvalidOperationException("Quaternion is not normalized");
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}
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if (!to.IsNormalized())
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{
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throw new ArgumentException("Argument is not normalized", nameof(to));
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}
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#endif
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// Calculate cosine.
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real_t cosom = x * to.x + y * to.y + z * to.z + w * to.w;
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var to1 = new Quaternion();
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// Adjust signs if necessary.
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if (cosom < 0.0)
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{
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cosom = -cosom;
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to1.x = -to.x;
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to1.y = -to.y;
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to1.z = -to.z;
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to1.w = -to.w;
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}
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else
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{
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to1.x = to.x;
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to1.y = to.y;
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to1.z = to.z;
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to1.w = to.w;
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}
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real_t sinom, scale0, scale1;
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// Calculate coefficients.
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if (1.0 - cosom > Mathf.Epsilon)
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{
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// Standard case (Slerp).
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real_t omega = Mathf.Acos(cosom);
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sinom = Mathf.Sin(omega);
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scale0 = Mathf.Sin((1.0f - weight) * omega) / sinom;
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scale1 = Mathf.Sin(weight * omega) / sinom;
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}
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else
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{
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// Quaternions are very close so we can do a linear interpolation.
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scale0 = 1.0f - weight;
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scale1 = weight;
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}
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// Calculate final values.
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return new Quaternion
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(
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scale0 * x + scale1 * to1.x,
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scale0 * y + scale1 * to1.y,
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scale0 * z + scale1 * to1.z,
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scale0 * w + scale1 * to1.w
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);
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}
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/// <summary>
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/// Returns the result of the spherical linear interpolation between
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/// this quaternion and `to` by amount `weight`, but without
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/// checking if the rotation path is not bigger than 90 degrees.
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/// </summary>
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/// <param name="to">The destination quaternion for interpolation. Must be normalized.</param>
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/// <param name="weight">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param>
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/// <returns>The resulting quaternion of the interpolation.</returns>
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public Quaternion Slerpni(Quaternion to, real_t weight)
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{
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real_t dot = Dot(to);
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if (Mathf.Abs(dot) > 0.9999f)
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{
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return this;
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}
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real_t theta = Mathf.Acos(dot);
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real_t sinT = 1.0f / Mathf.Sin(theta);
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real_t newFactor = Mathf.Sin(weight * theta) * sinT;
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real_t invFactor = Mathf.Sin((1.0f - weight) * theta) * sinT;
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return new Quaternion
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(
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invFactor * x + newFactor * to.x,
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invFactor * y + newFactor * to.y,
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invFactor * z + newFactor * to.z,
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invFactor * w + newFactor * to.w
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);
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}
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/// <summary>
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/// Returns a vector transformed (multiplied) by this quaternion.
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/// </summary>
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/// <param name="v">A vector to transform.</param>
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/// <returns>The transformed vector.</returns>
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public Vector3 Xform(Vector3 v)
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{
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#if DEBUG
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if (!IsNormalized())
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{
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throw new InvalidOperationException("Quaternion is not normalized");
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}
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#endif
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var u = new Vector3(x, y, z);
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Vector3 uv = u.Cross(v);
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return v + ((uv * w) + u.Cross(uv)) * 2;
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}
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// Constants
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private static readonly Quaternion _identity = new Quaternion(0, 0, 0, 1);
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/// <summary>
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/// The identity quaternion, representing no rotation.
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/// Equivalent to an identity <see cref="Basis"/> matrix. If a vector is transformed by
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/// an identity quaternion, it will not change.
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/// </summary>
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/// <value>Equivalent to `new Quaternion(0, 0, 0, 1)`.</value>
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public static Quaternion Identity { get { return _identity; } }
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/// <summary>
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/// Constructs a quaternion defined by the given values.
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/// </summary>
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/// <param name="x">X component of the quaternion (imaginary `i` axis part).</param>
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/// <param name="y">Y component of the quaternion (imaginary `j` axis part).</param>
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/// <param name="z">Z component of the quaternion (imaginary `k` axis part).</param>
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/// <param name="w">W component of the quaternion (real part).</param>
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public Quaternion(real_t x, real_t y, real_t z, real_t w)
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{
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this.x = x;
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this.y = y;
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this.z = z;
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this.w = w;
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}
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/// <summary>
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/// Constructs a quaternion from the given quaternion.
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/// </summary>
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/// <param name="q">The existing quaternion.</param>
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public Quaternion(Quaternion q)
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{
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this = q;
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}
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/// <summary>
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/// Constructs a quaternion from the given <see cref="Basis"/>.
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/// </summary>
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/// <param name="basis">The basis to construct from.</param>
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public Quaternion(Basis basis)
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{
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this = basis.Quaternion();
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}
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/// <summary>
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/// Constructs a quaternion that will perform a rotation specified by
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/// Euler angles (in the YXZ convention: when decomposing,
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/// first Z, then X, and Y last),
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/// given in the vector format as (X angle, Y angle, Z angle).
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/// </summary>
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/// <param name="eulerYXZ"></param>
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public Quaternion(Vector3 eulerYXZ)
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{
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real_t half_a1 = eulerYXZ.y * 0.5f;
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real_t half_a2 = eulerYXZ.x * 0.5f;
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real_t half_a3 = eulerYXZ.z * 0.5f;
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// R = Y(a1).X(a2).Z(a3) convention for Euler angles.
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// Conversion to quaternion as listed in https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770024290.pdf (page A-6)
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// a3 is the angle of the first rotation, following the notation in this reference.
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real_t cos_a1 = Mathf.Cos(half_a1);
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real_t sin_a1 = Mathf.Sin(half_a1);
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real_t cos_a2 = Mathf.Cos(half_a2);
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real_t sin_a2 = Mathf.Sin(half_a2);
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real_t cos_a3 = Mathf.Cos(half_a3);
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real_t sin_a3 = Mathf.Sin(half_a3);
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x = sin_a1 * cos_a2 * sin_a3 + cos_a1 * sin_a2 * cos_a3;
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y = sin_a1 * cos_a2 * cos_a3 - cos_a1 * sin_a2 * sin_a3;
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z = cos_a1 * cos_a2 * sin_a3 - sin_a1 * sin_a2 * cos_a3;
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w = sin_a1 * sin_a2 * sin_a3 + cos_a1 * cos_a2 * cos_a3;
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}
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/// <summary>
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/// Constructs a quaternion that will rotate around the given axis
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/// by the specified angle. The axis must be a normalized vector.
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/// </summary>
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/// <param name="axis">The axis to rotate around. Must be normalized.</param>
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/// <param name="angle">The angle to rotate, in radians.</param>
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public Quaternion(Vector3 axis, real_t angle)
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{
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#if DEBUG
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if (!axis.IsNormalized())
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{
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throw new ArgumentException("Argument is not normalized", nameof(axis));
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}
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#endif
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real_t d = axis.Length();
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if (d == 0f)
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{
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x = 0f;
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y = 0f;
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z = 0f;
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w = 0f;
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}
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else
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{
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real_t sinAngle = Mathf.Sin(angle * 0.5f);
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real_t cosAngle = Mathf.Cos(angle * 0.5f);
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real_t s = sinAngle / d;
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x = axis.x * s;
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y = axis.y * s;
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z = axis.z * s;
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w = cosAngle;
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}
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}
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public static Quaternion operator *(Quaternion left, Quaternion right)
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{
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return new Quaternion
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(
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left.w * right.x + left.x * right.w + left.y * right.z - left.z * right.y,
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left.w * right.y + left.y * right.w + left.z * right.x - left.x * right.z,
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left.w * right.z + left.z * right.w + left.x * right.y - left.y * right.x,
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left.w * right.w - left.x * right.x - left.y * right.y - left.z * right.z
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);
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}
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public static Quaternion operator +(Quaternion left, Quaternion right)
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{
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return new Quaternion(left.x + right.x, left.y + right.y, left.z + right.z, left.w + right.w);
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}
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public static Quaternion operator -(Quaternion left, Quaternion right)
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{
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return new Quaternion(left.x - right.x, left.y - right.y, left.z - right.z, left.w - right.w);
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}
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public static Quaternion operator -(Quaternion left)
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{
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return new Quaternion(-left.x, -left.y, -left.z, -left.w);
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}
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public static Quaternion operator *(Quaternion left, Vector3 right)
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{
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return new Quaternion
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(
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left.w * right.x + left.y * right.z - left.z * right.y,
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left.w * right.y + left.z * right.x - left.x * right.z,
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left.w * right.z + left.x * right.y - left.y * right.x,
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-left.x * right.x - left.y * right.y - left.z * right.z
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);
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}
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public static Quaternion operator *(Vector3 left, Quaternion right)
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{
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return new Quaternion
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(
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right.w * left.x + right.y * left.z - right.z * left.y,
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right.w * left.y + right.z * left.x - right.x * left.z,
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right.w * left.z + right.x * left.y - right.y * left.x,
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-right.x * left.x - right.y * left.y - right.z * left.z
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);
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}
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public static Quaternion operator *(Quaternion left, real_t right)
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{
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return new Quaternion(left.x * right, left.y * right, left.z * right, left.w * right);
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}
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public static Quaternion operator *(real_t left, Quaternion right)
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{
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return new Quaternion(right.x * left, right.y * left, right.z * left, right.w * left);
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}
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public static Quaternion operator /(Quaternion left, real_t right)
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{
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return left * (1.0f / right);
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}
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public static bool operator ==(Quaternion left, Quaternion right)
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|
{
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return left.Equals(right);
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|
}
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|
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public static bool operator !=(Quaternion left, Quaternion right)
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|
{
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|
return !left.Equals(right);
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|
}
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public override bool Equals(object obj)
|
|
{
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|
if (obj is Quaternion)
|
|
{
|
|
return Equals((Quaternion)obj);
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|
}
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|
|
|
return false;
|
|
}
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|
|
|
public bool Equals(Quaternion other)
|
|
{
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|
return x == other.x && y == other.y && z == other.z && w == other.w;
|
|
}
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|
|
|
/// <summary>
|
|
/// Returns true if this quaternion and `other` are approximately equal, by running
|
|
/// <see cref="Mathf.IsEqualApprox(real_t, real_t)"/> on each component.
|
|
/// </summary>
|
|
/// <param name="other">The other quaternion to compare.</param>
|
|
/// <returns>Whether or not the quaternions are approximately equal.</returns>
|
|
public bool IsEqualApprox(Quaternion other)
|
|
{
|
|
return Mathf.IsEqualApprox(x, other.x) && Mathf.IsEqualApprox(y, other.y) && Mathf.IsEqualApprox(z, other.z) && Mathf.IsEqualApprox(w, other.w);
|
|
}
|
|
|
|
public override int GetHashCode()
|
|
{
|
|
return y.GetHashCode() ^ x.GetHashCode() ^ z.GetHashCode() ^ w.GetHashCode();
|
|
}
|
|
|
|
public override string ToString()
|
|
{
|
|
return String.Format("({0}, {1}, {2}, {3})", x.ToString(), y.ToString(), z.ToString(), w.ToString());
|
|
}
|
|
|
|
public string ToString(string format)
|
|
{
|
|
return String.Format("({0}, {1}, {2}, {3})", x.ToString(format), y.ToString(format), z.ToString(format), w.ToString(format));
|
|
}
|
|
}
|
|
}
|