671 lines
20 KiB
C#
671 lines
20 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 Basis : IEquatable<Basis>
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{
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// NOTE: x, y and z are public-only. Use Column0, Column1 and Column2 internally.
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/// <summary>
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/// Returns the basis matrix’s x vector.
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/// This is equivalent to <see cref="Column0"/>.
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/// </summary>
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public Vector3 x
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{
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get => Column0;
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set => Column0 = value;
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}
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/// <summary>
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/// Returns the basis matrix’s y vector.
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/// This is equivalent to <see cref="Column1"/>.
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/// </summary>
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public Vector3 y
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{
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get => Column1;
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set => Column1 = value;
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}
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/// <summary>
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/// Returns the basis matrix’s z vector.
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/// This is equivalent to <see cref="Column2"/>.
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/// </summary>
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public Vector3 z
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{
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get => Column2;
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set => Column2 = value;
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}
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public Vector3 Row0;
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public Vector3 Row1;
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public Vector3 Row2;
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public Vector3 Column0
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{
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get => new Vector3(Row0.x, Row1.x, Row2.x);
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set
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{
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this.Row0.x = value.x;
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this.Row1.x = value.y;
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this.Row2.x = value.z;
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}
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}
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public Vector3 Column1
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{
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get => new Vector3(Row0.y, Row1.y, Row2.y);
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set
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{
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this.Row0.y = value.x;
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this.Row1.y = value.y;
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this.Row2.y = value.z;
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}
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}
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public Vector3 Column2
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{
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get => new Vector3(Row0.z, Row1.z, Row2.z);
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set
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{
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this.Row0.z = value.x;
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this.Row1.z = value.y;
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this.Row2.z = value.z;
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}
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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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real_t detSign = Mathf.Sign(Determinant());
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return detSign * new Vector3
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(
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new Vector3(this.Row0[0], this.Row1[0], this.Row2[0]).Length(),
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new Vector3(this.Row0[1], this.Row1[1], this.Row2[1]).Length(),
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new Vector3(this.Row0[2], this.Row1[2], this.Row2[2]).Length()
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);
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}
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}
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/// <summary>
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/// Access whole columns in the form of Vector3.
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/// </summary>
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/// <param name="column">Which column vector.</param>
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public Vector3 this[int column]
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{
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get
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{
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switch (column)
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{
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case 0:
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return Column0;
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case 1:
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return Column1;
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case 2:
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return Column2;
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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 (column)
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{
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case 0:
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Column0 = value;
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return;
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case 1:
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Column1 = value;
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return;
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case 2:
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Column2 = 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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/// <summary>
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/// Access matrix elements in column-major order.
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/// </summary>
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/// <param name="column">Which column, the matrix horizontal position.</param>
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/// <param name="row">Which row, the matrix vertical position.</param>
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public real_t this[int column, int row]
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{
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get
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{
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return this[column][row];
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}
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set
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{
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Vector3 columnVector = this[column];
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columnVector[row] = value;
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this[column] = columnVector;
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}
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}
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internal Quat RotationQuat()
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{
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Basis orthonormalizedBasis = Orthonormalized();
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real_t det = orthonormalizedBasis.Determinant();
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if (det < 0)
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{
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// Ensure that the determinant is 1, such that result is a proper rotation matrix which can be represented by Euler angles.
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orthonormalizedBasis = orthonormalizedBasis.Scaled(Vector3.NegOne);
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}
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return orthonormalizedBasis.Quat();
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}
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internal void SetQuatScale(Quat quat, Vector3 scale)
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{
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SetDiagonal(scale);
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Rotate(quat);
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}
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private void Rotate(Quat quat)
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{
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this *= new Basis(quat);
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}
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private void SetDiagonal(Vector3 diagonal)
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{
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Row0 = new Vector3(diagonal.x, 0, 0);
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Row1 = new Vector3(0, diagonal.y, 0);
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Row2 = new Vector3(0, 0, diagonal.z);
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}
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public real_t Determinant()
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{
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real_t cofac00 = Row1[1] * Row2[2] - Row1[2] * Row2[1];
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real_t cofac10 = Row1[2] * Row2[0] - Row1[0] * Row2[2];
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real_t cofac20 = Row1[0] * Row2[1] - Row1[1] * Row2[0];
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return Row0[0] * cofac00 + Row0[1] * cofac10 + Row0[2] * cofac20;
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}
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public Vector3 GetEuler()
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{
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Basis m = Orthonormalized();
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Vector3 euler;
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euler.z = 0.0f;
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real_t mzy = m.Row1[2];
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if (mzy < 1.0f)
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{
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if (mzy > -1.0f)
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{
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euler.x = Mathf.Asin(-mzy);
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euler.y = Mathf.Atan2(m.Row0[2], m.Row2[2]);
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euler.z = Mathf.Atan2(m.Row1[0], m.Row1[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.Row0[1], m.Row0[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.Row0[1], m.Row0[0]);
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}
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return euler;
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}
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public Vector3 GetRow(int index)
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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 Row0;
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case 1:
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return Row1;
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case 2:
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return Row2;
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default:
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throw new IndexOutOfRangeException();
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}
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}
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public void SetRow(int index, Vector3 value)
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{
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switch (index)
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{
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case 0:
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Row0 = value;
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return;
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case 1:
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Row1 = value;
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return;
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case 2:
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Row2 = 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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public Vector3 GetColumn(int index)
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{
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return this[index];
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}
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public void SetColumn(int index, Vector3 value)
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{
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this[index] = value;
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}
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public int GetOrthogonalIndex()
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{
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var 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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var row = orth.GetRow(i);
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real_t v = row[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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row[j] = v;
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orth.SetRow(i, row);
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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 (orth == _orthoBases[i])
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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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real_t cofac00 = Row1[1] * Row2[2] - Row1[2] * Row2[1];
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real_t cofac10 = Row1[2] * Row2[0] - Row1[0] * Row2[2];
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real_t cofac20 = Row1[0] * Row2[1] - Row1[1] * Row2[0];
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real_t det = Row0[0] * cofac00 + Row0[1] * cofac10 + Row0[2] * cofac20;
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if (det == 0)
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throw new InvalidOperationException("Matrix determinant is zero and cannot be inverted.");
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real_t detInv = 1.0f / det;
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real_t cofac01 = Row0[2] * Row2[1] - Row0[1] * Row2[2];
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real_t cofac02 = Row0[1] * Row1[2] - Row0[2] * Row1[1];
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real_t cofac11 = Row0[0] * Row2[2] - Row0[2] * Row2[0];
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real_t cofac12 = Row0[2] * Row1[0] - Row0[0] * Row1[2];
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real_t cofac21 = Row0[1] * Row2[0] - Row0[0] * Row2[1];
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real_t cofac22 = Row0[0] * Row1[1] - Row0[1] * Row1[0];
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return new Basis
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(
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cofac00 * detInv, cofac01 * detInv, cofac02 * detInv,
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cofac10 * detInv, cofac11 * detInv, cofac12 * detInv,
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cofac20 * detInv, cofac21 * detInv, cofac22 * detInv
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);
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}
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public Basis Orthonormalized()
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{
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Vector3 column0 = GetColumn(0);
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Vector3 column1 = GetColumn(1);
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Vector3 column2 = GetColumn(2);
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column0.Normalize();
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column1 = column1 - column0 * column0.Dot(column1);
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column1.Normalize();
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column2 = column2 - column0 * column0.Dot(column2) - column1 * column1.Dot(column2);
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column2.Normalize();
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return new Basis(column0, column1, column2);
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}
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public Basis Rotated(Vector3 axis, real_t 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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var b = this;
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b.Row0 *= scale.x;
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b.Row1 *= scale.y;
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b.Row2 *= scale.z;
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return b;
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}
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public Basis Slerp(Basis target, real_t t)
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{
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var from = new Quat(this);
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var to = new Quat(target);
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var b = new Basis(from.Slerp(to, t));
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b.Row0 *= Mathf.Lerp(Row0.Length(), target.Row0.Length(), t);
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b.Row1 *= Mathf.Lerp(Row1.Length(), target.Row1.Length(), t);
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b.Row2 *= Mathf.Lerp(Row2.Length(), target.Row2.Length(), t);
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return b;
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}
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public real_t Tdotx(Vector3 with)
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{
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return this.Row0[0] * with[0] + this.Row1[0] * with[1] + this.Row2[0] * with[2];
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}
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public real_t Tdoty(Vector3 with)
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{
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return this.Row0[1] * with[0] + this.Row1[1] * with[1] + this.Row2[1] * with[2];
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}
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public real_t Tdotz(Vector3 with)
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{
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return this.Row0[2] * with[0] + this.Row1[2] * with[1] + this.Row2[2] * with[2];
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}
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public Basis Transposed()
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{
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var tr = this;
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real_t temp = tr.Row0[1];
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tr.Row0[1] = tr.Row1[0];
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tr.Row1[0] = temp;
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temp = tr.Row0[2];
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tr.Row0[2] = tr.Row2[0];
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tr.Row2[0] = temp;
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temp = tr.Row1[2];
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tr.Row1[2] = tr.Row2[1];
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tr.Row2[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.Row0.Dot(v),
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this.Row1.Dot(v),
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this.Row2.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.Row0[0] * v.x + this.Row1[0] * v.y + this.Row2[0] * v.z,
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this.Row0[1] * v.x + this.Row1[1] * v.y + this.Row2[1] * v.z,
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this.Row0[2] * v.x + this.Row1[2] * v.y + this.Row2[2] * v.z
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);
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}
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public Quat Quat()
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{
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real_t trace = Row0[0] + Row1[1] + Row2[2];
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if (trace > 0.0f)
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{
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real_t s = Mathf.Sqrt(trace + 1.0f) * 2f;
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real_t inv_s = 1f / s;
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return new Quat(
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(Row2[1] - Row1[2]) * inv_s,
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(Row0[2] - Row2[0]) * inv_s,
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(Row1[0] - Row0[1]) * inv_s,
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s * 0.25f
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);
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}
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if (Row0[0] > Row1[1] && Row0[0] > Row2[2])
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{
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real_t s = Mathf.Sqrt(Row0[0] - Row1[1] - Row2[2] + 1.0f) * 2f;
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real_t inv_s = 1f / s;
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return new Quat(
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s * 0.25f,
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(Row0[1] + Row1[0]) * inv_s,
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(Row0[2] + Row2[0]) * inv_s,
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(Row2[1] - Row1[2]) * inv_s
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);
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}
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if (Row1[1] > Row2[2])
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{
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real_t s = Mathf.Sqrt(-Row0[0] + Row1[1] - Row2[2] + 1.0f) * 2f;
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real_t inv_s = 1f / s;
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return new Quat(
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(Row0[1] + Row1[0]) * inv_s,
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s * 0.25f,
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(Row1[2] + Row2[1]) * inv_s,
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(Row0[2] - Row2[0]) * inv_s
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);
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}
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else
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{
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real_t s = Mathf.Sqrt(-Row0[0] - Row1[1] + Row2[2] + 1.0f) * 2f;
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real_t inv_s = 1f / s;
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return new Quat(
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(Row0[2] + Row2[0]) * inv_s,
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(Row1[2] + Row2[1]) * inv_s,
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s * 0.25f,
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(Row1[0] - Row0[1]) * inv_s
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);
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}
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}
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private static readonly Basis[] _orthoBases = {
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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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private static readonly Basis _identity = new Basis(1, 0, 0, 0, 1, 0, 0, 0, 1);
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private static readonly Basis _flipX = new Basis(-1, 0, 0, 0, 1, 0, 0, 0, 1);
|
||
private static readonly Basis _flipY = new Basis(1, 0, 0, 0, -1, 0, 0, 0, 1);
|
||
private static readonly Basis _flipZ = new Basis(1, 0, 0, 0, 1, 0, 0, 0, -1);
|
||
|
||
public static Basis Identity { get { return _identity; } }
|
||
public static Basis FlipX { get { return _flipX; } }
|
||
public static Basis FlipY { get { return _flipY; } }
|
||
public static Basis FlipZ { get { return _flipZ; } }
|
||
|
||
public Basis(Quat quat)
|
||
{
|
||
real_t s = 2.0f / quat.LengthSquared;
|
||
|
||
real_t xs = quat.x * s;
|
||
real_t ys = quat.y * s;
|
||
real_t zs = quat.z * s;
|
||
real_t wx = quat.w * xs;
|
||
real_t wy = quat.w * ys;
|
||
real_t wz = quat.w * zs;
|
||
real_t xx = quat.x * xs;
|
||
real_t xy = quat.x * ys;
|
||
real_t xz = quat.x * zs;
|
||
real_t yy = quat.y * ys;
|
||
real_t yz = quat.y * zs;
|
||
real_t zz = quat.z * zs;
|
||
|
||
Row0 = new Vector3(1.0f - (yy + zz), xy - wz, xz + wy);
|
||
Row1 = new Vector3(xy + wz, 1.0f - (xx + zz), yz - wx);
|
||
Row2 = new Vector3(xz - wy, yz + wx, 1.0f - (xx + yy));
|
||
}
|
||
|
||
public Basis(Vector3 euler)
|
||
{
|
||
real_t c;
|
||
real_t s;
|
||
|
||
c = Mathf.Cos(euler.x);
|
||
s = Mathf.Sin(euler.x);
|
||
var xmat = new Basis(1, 0, 0, 0, c, -s, 0, s, c);
|
||
|
||
c = Mathf.Cos(euler.y);
|
||
s = Mathf.Sin(euler.y);
|
||
var ymat = new Basis(c, 0, s, 0, 1, 0, -s, 0, c);
|
||
|
||
c = Mathf.Cos(euler.z);
|
||
s = Mathf.Sin(euler.z);
|
||
var zmat = new Basis(c, -s, 0, s, c, 0, 0, 0, 1);
|
||
|
||
this = ymat * xmat * zmat;
|
||
}
|
||
|
||
public Basis(Vector3 axis, real_t phi)
|
||
{
|
||
Vector3 axisSq = new Vector3(axis.x * axis.x, axis.y * axis.y, axis.z * axis.z);
|
||
real_t cosine = Mathf.Cos(phi);
|
||
Row0.x = axisSq.x + cosine * (1.0f - axisSq.x);
|
||
Row1.y = axisSq.y + cosine * (1.0f - axisSq.y);
|
||
Row2.z = axisSq.z + cosine * (1.0f - axisSq.z);
|
||
|
||
real_t sine = Mathf.Sin(phi);
|
||
real_t t = 1.0f - cosine;
|
||
|
||
real_t xyzt = axis.x * axis.y * t;
|
||
real_t zyxs = axis.z * sine;
|
||
Row0.y = xyzt - zyxs;
|
||
Row1.x = xyzt + zyxs;
|
||
|
||
xyzt = axis.x * axis.z * t;
|
||
zyxs = axis.y * sine;
|
||
Row0.z = xyzt + zyxs;
|
||
Row2.x = xyzt - zyxs;
|
||
|
||
xyzt = axis.y * axis.z * t;
|
||
zyxs = axis.x * sine;
|
||
Row1.z = xyzt - zyxs;
|
||
Row2.y = xyzt + zyxs;
|
||
}
|
||
|
||
public Basis(Vector3 column0, Vector3 column1, Vector3 column2)
|
||
{
|
||
Row0 = new Vector3(column0.x, column1.x, column2.x);
|
||
Row1 = new Vector3(column0.y, column1.y, column2.y);
|
||
Row2 = new Vector3(column0.z, column1.z, column2.z);
|
||
// Same as:
|
||
// Column0 = column0;
|
||
// Column1 = column1;
|
||
// Column2 = column2;
|
||
// We need to assign the struct fields here first so we can't do it that way...
|
||
}
|
||
|
||
// Arguments are named such that xy is equal to calling x.y
|
||
internal Basis(real_t xx, real_t yx, real_t zx, real_t xy, real_t yy, real_t zy, real_t xz, real_t yz, real_t zz)
|
||
{
|
||
Row0 = new Vector3(xx, yx, zx);
|
||
Row1 = new Vector3(xy, yy, zy);
|
||
Row2 = new Vector3(xz, yz, zz);
|
||
}
|
||
|
||
public static Basis operator *(Basis left, Basis right)
|
||
{
|
||
return new Basis
|
||
(
|
||
right.Tdotx(left.Row0), right.Tdoty(left.Row0), right.Tdotz(left.Row0),
|
||
right.Tdotx(left.Row1), right.Tdoty(left.Row1), right.Tdotz(left.Row1),
|
||
right.Tdotx(left.Row2), right.Tdoty(left.Row2), right.Tdotz(left.Row2)
|
||
);
|
||
}
|
||
|
||
public static bool operator ==(Basis left, Basis right)
|
||
{
|
||
return left.Equals(right);
|
||
}
|
||
|
||
public static bool operator !=(Basis left, Basis right)
|
||
{
|
||
return !left.Equals(right);
|
||
}
|
||
|
||
public override bool Equals(object obj)
|
||
{
|
||
if (obj is Basis)
|
||
{
|
||
return Equals((Basis)obj);
|
||
}
|
||
|
||
return false;
|
||
}
|
||
|
||
public bool Equals(Basis other)
|
||
{
|
||
return Row0.Equals(other.Row0) && Row1.Equals(other.Row1) && Row2.Equals(other.Row2);
|
||
}
|
||
|
||
public bool IsEqualApprox(Basis other)
|
||
{
|
||
return Row0.IsEqualApprox(other.Row0) && Row1.IsEqualApprox(other.Row1) && Row2.IsEqualApprox(other.Row2);
|
||
}
|
||
|
||
public override int GetHashCode()
|
||
{
|
||
return Row0.GetHashCode() ^ Row1.GetHashCode() ^ Row2.GetHashCode();
|
||
}
|
||
|
||
public override string ToString()
|
||
{
|
||
return String.Format("({0}, {1}, {2})", new object[]
|
||
{
|
||
Row0.ToString(),
|
||
Row1.ToString(),
|
||
Row2.ToString()
|
||
});
|
||
}
|
||
|
||
public string ToString(string format)
|
||
{
|
||
return String.Format("({0}, {1}, {2})", new object[]
|
||
{
|
||
Row0.ToString(format),
|
||
Row1.ToString(format),
|
||
Row2.ToString(format)
|
||
});
|
||
}
|
||
}
|
||
}
|