520 lines
15 KiB
C#
520 lines
15 KiB
C#
using System;
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using System.Runtime.InteropServices;
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namespace Godot
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{
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[StructLayout(LayoutKind.Sequential)]
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public struct Basis : IEquatable<Basis>
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{
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private static readonly Basis identity = new Basis
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(
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new Vector3(1f, 0f, 0f),
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new Vector3(0f, 1f, 0f),
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new Vector3(0f, 0f, 1f)
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);
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private static readonly Basis[] orthoBases = new Basis[24]
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{
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new Basis(1f, 0f, 0f, 0f, 1f, 0f, 0f, 0f, 1f),
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new Basis(0f, -1f, 0f, 1f, 0f, 0f, 0f, 0f, 1f),
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new Basis(-1f, 0f, 0f, 0f, -1f, 0f, 0f, 0f, 1f),
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new Basis(0f, 1f, 0f, -1f, 0f, 0f, 0f, 0f, 1f),
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new Basis(1f, 0f, 0f, 0f, 0f, -1f, 0f, 1f, 0f),
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new Basis(0f, 0f, 1f, 1f, 0f, 0f, 0f, 1f, 0f),
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new Basis(-1f, 0f, 0f, 0f, 0f, 1f, 0f, 1f, 0f),
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new Basis(0f, 0f, -1f, -1f, 0f, 0f, 0f, 1f, 0f),
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new Basis(1f, 0f, 0f, 0f, -1f, 0f, 0f, 0f, -1f),
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new Basis(0f, 1f, 0f, 1f, 0f, 0f, 0f, 0f, -1f),
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new Basis(-1f, 0f, 0f, 0f, 1f, 0f, 0f, 0f, -1f),
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new Basis(0f, -1f, 0f, -1f, 0f, 0f, 0f, 0f, -1f),
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new Basis(1f, 0f, 0f, 0f, 0f, 1f, 0f, -1f, 0f),
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new Basis(0f, 0f, -1f, 1f, 0f, 0f, 0f, -1f, 0f),
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new Basis(-1f, 0f, 0f, 0f, 0f, -1f, 0f, -1f, 0f),
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new Basis(0f, 0f, 1f, -1f, 0f, 0f, 0f, -1f, 0f),
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new Basis(0f, 0f, 1f, 0f, 1f, 0f, -1f, 0f, 0f),
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new Basis(0f, -1f, 0f, 0f, 0f, 1f, -1f, 0f, 0f),
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new Basis(0f, 0f, -1f, 0f, -1f, 0f, -1f, 0f, 0f),
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new Basis(0f, 1f, 0f, 0f, 0f, -1f, -1f, 0f, 0f),
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new Basis(0f, 0f, 1f, 0f, -1f, 0f, 1f, 0f, 0f),
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new Basis(0f, 1f, 0f, 0f, 0f, 1f, 1f, 0f, 0f),
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new Basis(0f, 0f, -1f, 0f, 1f, 0f, 1f, 0f, 0f),
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new Basis(0f, -1f, 0f, 0f, 0f, -1f, 1f, 0f, 0f)
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};
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public Vector3 x;
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public Vector3 y;
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public Vector3 z;
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public static Basis Identity
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{
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get { return identity; }
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}
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public Vector3 Scale
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{
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get
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{
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return new Vector3
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(
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new Vector3(this[0, 0], this[1, 0], this[2, 0]).Length(),
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new Vector3(this[0, 1], this[1, 1], this[2, 1]).Length(),
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new Vector3(this[0, 2], this[1, 2], this[2, 2]).Length()
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);
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}
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}
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public Vector3 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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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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return;
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case 1:
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y = value;
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return;
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case 2:
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z = value;
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return;
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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 float this[int index, int axis]
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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[axis];
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case 1:
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return y[axis];
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case 2:
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return z[axis];
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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[axis] = value;
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return;
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case 1:
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y[axis] = value;
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return;
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case 2:
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z[axis] = value;
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return;
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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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internal static Basis CreateFromAxes(Vector3 xAxis, Vector3 yAxis, Vector3 zAxis)
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{
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return new Basis
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(
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new Vector3(xAxis.x, yAxis.x, zAxis.x),
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new Vector3(xAxis.y, yAxis.y, zAxis.y),
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new Vector3(xAxis.z, yAxis.z, zAxis.z)
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);
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}
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public float Determinant()
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{
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return this[0, 0] * (this[1, 1] * this[2, 2] - this[2, 1] * this[1, 2]) -
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this[1, 0] * (this[0, 1] * this[2, 2] - this[2, 1] * this[0, 2]) +
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this[2, 0] * (this[0, 1] * this[1, 2] - this[1, 1] * this[0, 2]);
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}
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public Vector3 GetAxis(int axis)
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{
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return new Vector3(this[0, axis], this[1, axis], this[2, axis]);
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}
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public Vector3 GetEuler()
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{
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Basis m = this.Orthonormalized();
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Vector3 euler;
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euler.z = 0.0f;
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float mxy = m.y[2];
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if (mxy < 1.0f)
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{
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if (mxy > -1.0f)
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{
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euler.x = Mathf.Asin(-mxy);
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euler.y = Mathf.Atan2(m.x[2], m.z[2]);
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euler.z = Mathf.Atan2(m.y[0], m.y[1]);
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}
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else
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{
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euler.x = Mathf.PI * 0.5f;
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euler.y = -Mathf.Atan2(-m.x[1], m.x[0]);
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}
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}
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else
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{
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euler.x = -Mathf.PI * 0.5f;
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euler.y = -Mathf.Atan2(m.x[1], m.x[0]);
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}
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return euler;
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}
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public int GetOrthogonalIndex()
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{
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Basis orth = this;
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for (int i = 0; i < 3; i++)
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{
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for (int j = 0; j < 3; j++)
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{
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float v = orth[i, j];
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if (v > 0.5f)
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v = 1.0f;
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else if (v < -0.5f)
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v = -1.0f;
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else
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v = 0f;
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orth[i, j] = v;
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}
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}
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for (int i = 0; i < 24; i++)
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{
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if (orthoBases[i] == orth)
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return i;
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}
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return 0;
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}
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public Basis Inverse()
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{
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Basis inv = this;
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float[] co = new float[3]
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{
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inv[1, 1] * inv[2, 2] - inv[1, 2] * inv[2, 1],
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inv[1, 2] * inv[2, 0] - inv[1, 0] * inv[2, 2],
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inv[1, 0] * inv[2, 1] - inv[1, 1] * inv[2, 0]
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};
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float det = inv[0, 0] * co[0] + inv[0, 1] * co[1] + inv[0, 2] * co[2];
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if (det == 0)
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{
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return new Basis
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(
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float.NaN, float.NaN, float.NaN,
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float.NaN, float.NaN, float.NaN,
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float.NaN, float.NaN, float.NaN
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);
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}
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float s = 1.0f / det;
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inv = new Basis
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(
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co[0] * s,
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inv[0, 2] * inv[2, 1] - inv[0, 1] * inv[2, 2] * s,
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inv[0, 1] * inv[1, 2] - inv[0, 2] * inv[1, 1] * s,
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co[1] * s,
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inv[0, 0] * inv[2, 2] - inv[0, 2] * inv[2, 0] * s,
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inv[0, 2] * inv[1, 0] - inv[0, 0] * inv[1, 2] * s,
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co[2] * s,
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inv[0, 1] * inv[2, 0] - inv[0, 0] * inv[2, 1] * s,
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inv[0, 0] * inv[1, 1] - inv[0, 1] * inv[1, 0] * s
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);
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return inv;
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}
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public Basis Orthonormalized()
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{
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Vector3 xAxis = GetAxis(0);
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Vector3 yAxis = GetAxis(1);
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Vector3 zAxis = GetAxis(2);
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xAxis.Normalize();
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yAxis = (yAxis - xAxis * (xAxis.Dot(yAxis)));
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yAxis.Normalize();
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zAxis = (zAxis - xAxis * (xAxis.Dot(zAxis)) - yAxis * (yAxis.Dot(zAxis)));
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zAxis.Normalize();
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return Basis.CreateFromAxes(xAxis, yAxis, zAxis);
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}
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public Basis Rotated(Vector3 axis, float phi)
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{
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return new Basis(axis, phi) * this;
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}
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public Basis Scaled(Vector3 scale)
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{
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Basis m = this;
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m[0, 0] *= scale.x;
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m[0, 1] *= scale.x;
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m[0, 2] *= scale.x;
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m[1, 0] *= scale.y;
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m[1, 1] *= scale.y;
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m[1, 2] *= scale.y;
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m[2, 0] *= scale.z;
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m[2, 1] *= scale.z;
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m[2, 2] *= scale.z;
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return m;
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}
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public float Tdotx(Vector3 with)
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{
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return this[0, 0] * with[0] + this[1, 0] * with[1] + this[2, 0] * with[2];
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}
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public float Tdoty(Vector3 with)
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{
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return this[0, 1] * with[0] + this[1, 1] * with[1] + this[2, 1] * with[2];
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}
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public float Tdotz(Vector3 with)
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{
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return this[0, 2] * with[0] + this[1, 2] * with[1] + this[2, 2] * with[2];
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}
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public Basis Transposed()
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{
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Basis tr = this;
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float temp = this[0, 1];
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this[0, 1] = this[1, 0];
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this[1, 0] = temp;
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temp = this[0, 2];
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this[0, 2] = this[2, 0];
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this[2, 0] = temp;
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temp = this[1, 2];
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this[1, 2] = this[2, 1];
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this[2, 1] = temp;
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return tr;
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}
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public Vector3 Xform(Vector3 v)
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{
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return new Vector3
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(
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this[0].Dot(v),
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this[1].Dot(v),
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this[2].Dot(v)
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);
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}
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public Vector3 XformInv(Vector3 v)
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{
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return new Vector3
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(
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(this[0, 0] * v.x) + (this[1, 0] * v.y) + (this[2, 0] * v.z),
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(this[0, 1] * v.x) + (this[1, 1] * v.y) + (this[2, 1] * v.z),
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(this[0, 2] * v.x) + (this[1, 2] * v.y) + (this[2, 2] * v.z)
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);
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}
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public Quat Quat() {
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float trace = x[0] + y[1] + z[2];
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if (trace > 0.0f) {
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float s = Mathf.Sqrt(trace + 1.0f) * 2f;
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float inv_s = 1f / s;
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return new Quat(
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(z[1] - y[2]) * inv_s,
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(x[2] - z[0]) * inv_s,
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(y[0] - x[1]) * inv_s,
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s * 0.25f
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);
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} else if (x[0] > y[1] && x[0] > z[2]) {
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float s = Mathf.Sqrt(x[0] - y[1] - z[2] + 1.0f) * 2f;
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float inv_s = 1f / s;
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return new Quat(
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s * 0.25f,
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(x[1] + y[0]) * inv_s,
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(x[2] + z[0]) * inv_s,
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(z[1] - y[2]) * inv_s
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);
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} else if (y[1] > z[2]) {
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float s = Mathf.Sqrt(-x[0] + y[1] - z[2] + 1.0f) * 2f;
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float inv_s = 1f / s;
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return new Quat(
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(x[1] + y[0]) * inv_s,
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s * 0.25f,
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(y[2] + z[1]) * inv_s,
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(x[2] - z[0]) * inv_s
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);
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} else {
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float s = Mathf.Sqrt(-x[0] - y[1] + z[2] + 1.0f) * 2f;
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float inv_s = 1f / s;
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return new Quat(
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(x[2] + z[0]) * inv_s,
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(y[2] + z[1]) * inv_s,
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s * 0.25f,
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(y[0] - x[1]) * inv_s
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);
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}
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}
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public Basis(Quat quat)
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{
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float s = 2.0f / quat.LengthSquared();
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float xs = quat.x * s;
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float ys = quat.y * s;
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float zs = quat.z * s;
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float wx = quat.w * xs;
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float wy = quat.w * ys;
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float wz = quat.w * zs;
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float xx = quat.x * xs;
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float xy = quat.x * ys;
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float xz = quat.x * zs;
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float yy = quat.y * ys;
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float yz = quat.y * zs;
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float zz = quat.z * zs;
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this.x = new Vector3(1.0f - (yy + zz), xy - wz, xz + wy);
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this.y = new Vector3(xy + wz, 1.0f - (xx + zz), yz - wx);
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this.z = new Vector3(xz - wy, yz + wx, 1.0f - (xx + yy));
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}
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public Basis(Vector3 axis, float phi)
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{
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Vector3 axis_sq = new Vector3(axis.x * axis.x, axis.y * axis.y, axis.z * axis.z);
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float cosine = Mathf.Cos(phi);
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float sine = Mathf.Sin(phi);
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this.x = new Vector3
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(
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axis_sq.x + cosine * (1.0f - axis_sq.x),
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axis.x * axis.y * (1.0f - cosine) - axis.z * sine,
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axis.z * axis.x * (1.0f - cosine) + axis.y * sine
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);
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this.y = new Vector3
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(
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axis.x * axis.y * (1.0f - cosine) + axis.z * sine,
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axis_sq.y + cosine * (1.0f - axis_sq.y),
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axis.y * axis.z * (1.0f - cosine) - axis.x * sine
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);
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this.z = new Vector3
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(
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axis.z * axis.x * (1.0f - cosine) - axis.y * sine,
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axis.y * axis.z * (1.0f - cosine) + axis.x * sine,
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axis_sq.z + cosine * (1.0f - axis_sq.z)
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);
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}
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public Basis(Vector3 xAxis, Vector3 yAxis, Vector3 zAxis)
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{
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this.x = xAxis;
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this.y = yAxis;
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this.z = zAxis;
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}
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public Basis(float xx, float xy, float xz, float yx, float yy, float yz, float zx, float zy, float zz)
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{
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this.x = new Vector3(xx, yx, zx);
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this.y = new Vector3(xy, yy, zy);
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this.z = new Vector3(xz, yz, zz);
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}
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public static Basis operator *(Basis left, Basis right)
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{
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return new Basis
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(
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right.Tdotx(left[0]), right.Tdoty(left[0]), right.Tdotz(left[0]),
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right.Tdotx(left[1]), right.Tdoty(left[1]), right.Tdotz(left[1]),
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right.Tdotx(left[2]), right.Tdoty(left[2]), right.Tdotz(left[2])
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);
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}
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public static bool operator ==(Basis left, Basis 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 !=(Basis left, Basis 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 Basis)
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{
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return Equals((Basis)obj);
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}
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return false;
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}
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public bool Equals(Basis other)
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{
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return x.Equals(other.x) && y.Equals(other.y) && z.Equals(other.z);
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}
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public override int GetHashCode()
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{
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return x.GetHashCode() ^ y.GetHashCode() ^ z.GetHashCode();
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|
}
|
|
|
|
public override string ToString()
|
|
{
|
|
return String.Format("({0}, {1}, {2})", new object[]
|
|
{
|
|
this.x.ToString(),
|
|
this.y.ToString(),
|
|
this.z.ToString()
|
|
});
|
|
}
|
|
|
|
public string ToString(string format)
|
|
{
|
|
return String.Format("({0}, {1}, {2})", new object[]
|
|
{
|
|
this.x.ToString(format),
|
|
this.y.ToString(format),
|
|
this.z.ToString(format)
|
|
});
|
|
}
|
|
}
|
|
}
|