388 lines
11 KiB
C#
388 lines
11 KiB
C#
using System;
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using System.Runtime.InteropServices;
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#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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namespace Godot
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{
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[Serializable]
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[StructLayout(LayoutKind.Sequential)]
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public struct Quat : IEquatable<Quat>
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{
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public real_t x;
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public real_t y;
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public real_t z;
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public real_t w;
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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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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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public real_t LengthSquared
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{
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get { return Dot(this); }
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}
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public Quat CubicSlerp(Quat b, Quat preA, Quat postB, real_t t)
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{
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real_t t2 = (1.0f - t) * t * 2f;
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Quat sp = Slerp(b, t);
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Quat sq = preA.Slerpni(postB, t);
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return sp.Slerpni(sq, t2);
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}
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public real_t Dot(Quat 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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public Vector3 GetEuler()
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{
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#if DEBUG
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if (!IsNormalized())
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throw new InvalidOperationException("Quat is not normalized");
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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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public Quat Inverse()
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{
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#if DEBUG
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if (!IsNormalized())
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throw new InvalidOperationException("Quat is not normalized");
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#endif
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return new Quat(-x, -y, -z, w);
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}
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public Quat Normalized()
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{
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return this / Length;
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}
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public Quat Slerp(Quat b, real_t t)
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{
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#if DEBUG
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if (!IsNormalized())
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throw new InvalidOperationException("Quat is not normalized");
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if (!b.IsNormalized())
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throw new ArgumentException("Argument is not normalized", nameof(b));
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#endif
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// Calculate cosine
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real_t cosom = x * b.x + y * b.y + z * b.z + w * b.w;
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var to1 = new Quat();
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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 = -b.x;
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to1.y = -b.y;
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to1.z = -b.z;
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to1.w = -b.w;
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}
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else
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{
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to1.x = b.x;
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to1.y = b.y;
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to1.z = b.z;
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to1.w = b.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 - t) * omega) / sinom;
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scale1 = Mathf.Sin(t * 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 - t;
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scale1 = t;
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}
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// Calculate final values
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return new Quat
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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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public Quat Slerpni(Quat b, real_t t)
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{
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real_t dot = Dot(b);
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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(t * theta) * sinT;
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real_t invFactor = Mathf.Sin((1.0f - t) * theta) * sinT;
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return new Quat
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(
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invFactor * x + newFactor * b.x,
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invFactor * y + newFactor * b.y,
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invFactor * z + newFactor * b.z,
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invFactor * w + newFactor * b.w
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);
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}
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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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throw new InvalidOperationException("Quat is not normalized");
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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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// Static Readonly Properties
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public static Quat Identity { get; } = new Quat(0f, 0f, 0f, 1f);
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// Constructors
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public Quat(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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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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public Quat(Quat q)
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{
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this = q;
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}
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public Quat(Basis basis)
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{
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this = basis.Quat();
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}
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public Quat(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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public Quat(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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throw new ArgumentException("Argument is not normalized", nameof(axis));
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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 Quat operator *(Quat left, Quat right)
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{
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return new Quat
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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 Quat operator +(Quat left, Quat right)
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{
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return new Quat(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 Quat operator -(Quat left, Quat right)
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{
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return new Quat(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 Quat operator -(Quat left)
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{
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return new Quat(-left.x, -left.y, -left.z, -left.w);
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}
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public static Quat operator *(Quat left, Vector3 right)
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{
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return new Quat
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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 Quat operator *(Vector3 left, Quat right)
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{
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return new Quat
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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 Quat operator *(Quat left, real_t right)
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{
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return new Quat(left.x * right, left.y * right, left.z * right, left.w * right);
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}
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public static Quat operator *(real_t left, Quat right)
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{
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return new Quat(right.x * left, right.y * left, right.z * left, right.w * left);
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}
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public static Quat operator /(Quat 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 ==(Quat left, Quat right)
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{
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return left.Equals(right);
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}
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public static bool operator !=(Quat left, Quat 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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{
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if (obj is Quat)
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{
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return Equals((Quat)obj);
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}
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return false;
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}
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public bool Equals(Quat other)
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{
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return x == other.x && y == other.y && z == other.z && w == other.w;
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}
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public bool IsEqualApprox(Quat other)
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{
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return Mathf.IsEqualApprox(x, other.x) && Mathf.IsEqualApprox(y, other.y) && Mathf.IsEqualApprox(z, other.z) && Mathf.IsEqualApprox(w, other.w);
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}
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public override int GetHashCode()
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{
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return y.GetHashCode() ^ x.GetHashCode() ^ z.GetHashCode() ^ w.GetHashCode();
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}
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public override string ToString()
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{
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return String.Format("({0}, {1}, {2}, {3})", x.ToString(), y.ToString(), z.ToString(), w.ToString());
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}
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public string ToString(string format)
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{
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return String.Format("({0}, {1}, {2}, {3})", x.ToString(format), y.ToString(format), z.ToString(format), w.ToString(format));
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}
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}
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}
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