379 lines
10 KiB
C#
379 lines
10 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 Transform2D : IEquatable<Transform2D>
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{
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public Vector2 x;
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public Vector2 y;
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public Vector2 origin;
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public real_t Rotation
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{
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get
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{
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real_t det = BasisDeterminant();
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Transform2D t = Orthonormalized();
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if (det < 0)
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{
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t.ScaleBasis(new Vector2(1, -1));
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}
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return Mathf.Atan2(t.x.y, t.x.x);
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}
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set
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{
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Vector2 scale = Scale;
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x.x = y.y = Mathf.Cos(value);
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x.y = y.x = Mathf.Sin(value);
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y.x *= -1;
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Scale = scale;
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}
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}
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public Vector2 Scale
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{
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get
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{
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real_t detSign = Mathf.Sign(BasisDeterminant());
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return new Vector2(x.Length(), detSign * y.Length());
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}
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set
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{
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x = x.Normalized();
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y = y.Normalized();
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x *= value.x;
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y *= value.y;
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}
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}
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/// <summary>
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/// Access whole columns in the form of Vector2. The third column is the origin vector.
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/// </summary>
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/// <param name="column">Which column vector.</param>
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public Vector2 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 x;
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case 1:
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return y;
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case 2:
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return origin;
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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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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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origin = 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. The third column is the origin vector.
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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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Vector2 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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public Transform2D AffineInverse()
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{
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real_t det = BasisDeterminant();
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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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var inv = this;
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real_t temp = inv[0, 0];
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inv[0, 0] = inv[1, 1];
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inv[1, 1] = temp;
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real_t detInv = 1.0f / det;
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inv[0] *= new Vector2(detInv, -detInv);
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inv[1] *= new Vector2(-detInv, detInv);
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inv[2] = inv.BasisXform(-inv[2]);
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return inv;
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}
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private real_t BasisDeterminant()
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{
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return x.x * y.y - x.y * y.x;
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}
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public Vector2 BasisXform(Vector2 v)
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{
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return new Vector2(Tdotx(v), Tdoty(v));
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}
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public Vector2 BasisXformInv(Vector2 v)
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{
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return new Vector2(x.Dot(v), y.Dot(v));
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}
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public Transform2D InterpolateWith(Transform2D m, real_t c)
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{
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real_t r1 = Rotation;
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real_t r2 = m.Rotation;
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Vector2 s1 = Scale;
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Vector2 s2 = m.Scale;
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// Slerp rotation
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var v1 = new Vector2(Mathf.Cos(r1), Mathf.Sin(r1));
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var v2 = new Vector2(Mathf.Cos(r2), Mathf.Sin(r2));
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real_t dot = v1.Dot(v2);
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// Clamp dot to [-1, 1]
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dot = dot < -1.0f ? -1.0f : (dot > 1.0f ? 1.0f : dot);
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Vector2 v;
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if (dot > 0.9995f)
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{
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// Linearly interpolate to avoid numerical precision issues
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v = v1.Lerp(v2, c).Normalized();
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}
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else
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{
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real_t angle = c * Mathf.Acos(dot);
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Vector2 v3 = (v2 - v1 * dot).Normalized();
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v = v1 * Mathf.Cos(angle) + v3 * Mathf.Sin(angle);
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}
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// Extract parameters
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Vector2 p1 = origin;
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Vector2 p2 = m.origin;
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// Construct matrix
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var res = new Transform2D(Mathf.Atan2(v.y, v.x), p1.Lerp(p2, c));
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Vector2 scale = s1.Lerp(s2, c);
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res.x *= scale;
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res.y *= scale;
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return res;
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}
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public Transform2D Inverse()
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{
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var inv = this;
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// Swap
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real_t temp = inv.x.y;
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inv.x.y = inv.y.x;
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inv.y.x = temp;
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inv.origin = inv.BasisXform(-inv.origin);
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return inv;
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}
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public Transform2D Orthonormalized()
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{
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var on = this;
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Vector2 onX = on.x;
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Vector2 onY = on.y;
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onX.Normalize();
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onY = onY - onX * onX.Dot(onY);
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onY.Normalize();
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on.x = onX;
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on.y = onY;
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return on;
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}
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public Transform2D Rotated(real_t phi)
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{
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return this * new Transform2D(phi, new Vector2());
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}
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public Transform2D Scaled(Vector2 scale)
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{
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var copy = this;
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copy.x *= scale;
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copy.y *= scale;
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copy.origin *= scale;
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return copy;
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}
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private void ScaleBasis(Vector2 scale)
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{
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x.x *= scale.x;
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x.y *= scale.y;
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y.x *= scale.x;
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y.y *= scale.y;
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}
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private real_t Tdotx(Vector2 with)
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{
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return this[0, 0] * with[0] + this[1, 0] * with[1];
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}
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private real_t Tdoty(Vector2 with)
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{
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return this[0, 1] * with[0] + this[1, 1] * with[1];
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}
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public Transform2D Translated(Vector2 offset)
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{
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var copy = this;
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copy.origin += copy.BasisXform(offset);
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return copy;
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}
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public Vector2 Xform(Vector2 v)
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{
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return new Vector2(Tdotx(v), Tdoty(v)) + origin;
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}
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public Vector2 XformInv(Vector2 v)
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{
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Vector2 vInv = v - origin;
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return new Vector2(x.Dot(vInv), y.Dot(vInv));
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}
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// Constants
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private static readonly Transform2D _identity = new Transform2D(1, 0, 0, 1, 0, 0);
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private static readonly Transform2D _flipX = new Transform2D(-1, 0, 0, 1, 0, 0);
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private static readonly Transform2D _flipY = new Transform2D(1, 0, 0, -1, 0, 0);
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public static Transform2D Identity => _identity;
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public static Transform2D FlipX => _flipX;
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public static Transform2D FlipY => _flipY;
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// Constructors
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public Transform2D(Vector2 xAxis, Vector2 yAxis, Vector2 originPos)
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{
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x = xAxis;
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y = yAxis;
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origin = originPos;
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}
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// Arguments are named such that xy is equal to calling x.y
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public Transform2D(real_t xx, real_t xy, real_t yx, real_t yy, real_t ox, real_t oy)
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{
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x = new Vector2(xx, xy);
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y = new Vector2(yx, yy);
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origin = new Vector2(ox, oy);
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}
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public Transform2D(real_t rot, Vector2 pos)
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{
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x.x = y.y = Mathf.Cos(rot);
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x.y = y.x = Mathf.Sin(rot);
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y.x *= -1;
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origin = pos;
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}
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public static Transform2D operator *(Transform2D left, Transform2D right)
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{
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left.origin = left.Xform(right.origin);
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real_t x0 = left.Tdotx(right.x);
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real_t x1 = left.Tdoty(right.x);
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real_t y0 = left.Tdotx(right.y);
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real_t y1 = left.Tdoty(right.y);
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left.x.x = x0;
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left.x.y = x1;
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left.y.x = y0;
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left.y.y = y1;
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return left;
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}
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public static bool operator ==(Transform2D left, Transform2D 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 !=(Transform2D left, Transform2D 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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return obj is Transform2D transform2D && Equals(transform2D);
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}
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public bool Equals(Transform2D other)
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{
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return x.Equals(other.x) && y.Equals(other.y) && origin.Equals(other.origin);
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}
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public bool IsEqualApprox(Transform2D other)
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{
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return x.IsEqualApprox(other.x) && y.IsEqualApprox(other.y) && origin.IsEqualApprox(other.origin);
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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() ^ origin.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})", new object[]
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{
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x.ToString(),
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y.ToString(),
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origin.ToString()
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});
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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})", new object[]
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{
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x.ToString(format),
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y.ToString(format),
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origin.ToString(format)
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});
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}
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}
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}
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