using System; using System.Runtime.InteropServices; #if REAL_T_IS_DOUBLE using real_t = System.Double; #else using real_t = System.Single; #endif namespace Godot { [StructLayout(LayoutKind.Sequential)] public struct Basis : IEquatable { private static readonly Basis identity = new Basis ( new Vector3(1f, 0f, 0f), new Vector3(0f, 1f, 0f), new Vector3(0f, 0f, 1f) ); private static readonly Basis[] orthoBases = { new Basis(1f, 0f, 0f, 0f, 1f, 0f, 0f, 0f, 1f), new Basis(0f, -1f, 0f, 1f, 0f, 0f, 0f, 0f, 1f), new Basis(-1f, 0f, 0f, 0f, -1f, 0f, 0f, 0f, 1f), new Basis(0f, 1f, 0f, -1f, 0f, 0f, 0f, 0f, 1f), new Basis(1f, 0f, 0f, 0f, 0f, -1f, 0f, 1f, 0f), new Basis(0f, 0f, 1f, 1f, 0f, 0f, 0f, 1f, 0f), new Basis(-1f, 0f, 0f, 0f, 0f, 1f, 0f, 1f, 0f), new Basis(0f, 0f, -1f, -1f, 0f, 0f, 0f, 1f, 0f), new Basis(1f, 0f, 0f, 0f, -1f, 0f, 0f, 0f, -1f), new Basis(0f, 1f, 0f, 1f, 0f, 0f, 0f, 0f, -1f), new Basis(-1f, 0f, 0f, 0f, 1f, 0f, 0f, 0f, -1f), new Basis(0f, -1f, 0f, -1f, 0f, 0f, 0f, 0f, -1f), new Basis(1f, 0f, 0f, 0f, 0f, 1f, 0f, -1f, 0f), new Basis(0f, 0f, -1f, 1f, 0f, 0f, 0f, -1f, 0f), new Basis(-1f, 0f, 0f, 0f, 0f, -1f, 0f, -1f, 0f), new Basis(0f, 0f, 1f, -1f, 0f, 0f, 0f, -1f, 0f), new Basis(0f, 0f, 1f, 0f, 1f, 0f, -1f, 0f, 0f), new Basis(0f, -1f, 0f, 0f, 0f, 1f, -1f, 0f, 0f), new Basis(0f, 0f, -1f, 0f, -1f, 0f, -1f, 0f, 0f), new Basis(0f, 1f, 0f, 0f, 0f, -1f, -1f, 0f, 0f), new Basis(0f, 0f, 1f, 0f, -1f, 0f, 1f, 0f, 0f), new Basis(0f, 1f, 0f, 0f, 0f, 1f, 1f, 0f, 0f), new Basis(0f, 0f, -1f, 0f, 1f, 0f, 1f, 0f, 0f), new Basis(0f, -1f, 0f, 0f, 0f, -1f, 1f, 0f, 0f) }; public Vector3 x { get { return GetAxis(0); } set { SetAxis(0, value); } } public Vector3 y { get { return GetAxis(1); } set { SetAxis(1, value); } } public Vector3 z { get { return GetAxis(2); } set { SetAxis(2, value); } } private Vector3 _x; private Vector3 _y; private Vector3 _z; public static Basis Identity { get { return identity; } } public Vector3 Scale { get { return new Vector3 ( new Vector3(this[0, 0], this[1, 0], this[2, 0]).Length(), new Vector3(this[0, 1], this[1, 1], this[2, 1]).Length(), new Vector3(this[0, 2], this[1, 2], this[2, 2]).Length() ); } } public Vector3 this[int index] { get { switch (index) { case 0: return _x; case 1: return _y; case 2: return _z; default: throw new IndexOutOfRangeException(); } } set { switch (index) { case 0: _x = value; return; case 1: _y = value; return; case 2: _z = value; return; default: throw new IndexOutOfRangeException(); } } } public real_t this[int index, int axis] { get { switch (index) { case 0: return _x[axis]; case 1: return _y[axis]; case 2: return _z[axis]; default: throw new IndexOutOfRangeException(); } } set { switch (index) { case 0: _x[axis] = value; return; case 1: _y[axis] = value; return; case 2: _z[axis] = value; return; default: throw new IndexOutOfRangeException(); } } } internal static Basis CreateFromAxes(Vector3 xAxis, Vector3 yAxis, Vector3 zAxis) { return new Basis ( new Vector3(xAxis.x, yAxis.x, zAxis.x), new Vector3(xAxis.y, yAxis.y, zAxis.y), new Vector3(xAxis.z, yAxis.z, zAxis.z) ); } public real_t Determinant() { return this[0, 0] * (this[1, 1] * this[2, 2] - this[2, 1] * this[1, 2]) - this[1, 0] * (this[0, 1] * this[2, 2] - this[2, 1] * this[0, 2]) + this[2, 0] * (this[0, 1] * this[1, 2] - this[1, 1] * this[0, 2]); } public Vector3 GetAxis(int axis) { return new Vector3(this[0, axis], this[1, axis], this[2, axis]); } public void SetAxis(int axis, Vector3 value) { this[0, axis] = value.x; this[1, axis] = value.y; this[2, axis] = value.z; } public Vector3 GetEuler() { Basis m = Orthonormalized(); Vector3 euler; euler.z = 0.0f; real_t mxy = m[1, 2]; if (mxy < 1.0f) { if (mxy > -1.0f) { euler.x = Mathf.Asin(-mxy); euler.y = Mathf.Atan2(m[0, 2], m[2, 2]); euler.z = Mathf.Atan2(m[1, 0], m[1, 1]); } else { euler.x = Mathf.Pi * 0.5f; euler.y = -Mathf.Atan2(-m[0, 1], m[0, 0]); } } else { euler.x = -Mathf.Pi * 0.5f; euler.y = -Mathf.Atan2(-m[0, 1], m[0, 0]); } return euler; } public int GetOrthogonalIndex() { var orth = this; for (int i = 0; i < 3; i++) { for (int j = 0; j < 3; j++) { real_t v = orth[i, j]; if (v > 0.5f) v = 1.0f; else if (v < -0.5f) v = -1.0f; else v = 0f; orth[i, j] = v; } } for (int i = 0; i < 24; i++) { if (orthoBases[i] == orth) return i; } return 0; } public Basis Inverse() { var inv = this; real_t[] co = { inv[1, 1] * inv[2, 2] - inv[1, 2] * inv[2, 1], inv[1, 2] * inv[2, 0] - inv[1, 0] * inv[2, 2], inv[1, 0] * inv[2, 1] - inv[1, 1] * inv[2, 0] }; real_t det = inv[0, 0] * co[0] + inv[0, 1] * co[1] + inv[0, 2] * co[2]; if (det == 0) { return new Basis ( real_t.NaN, real_t.NaN, real_t.NaN, real_t.NaN, real_t.NaN, real_t.NaN, real_t.NaN, real_t.NaN, real_t.NaN ); } real_t s = 1.0f / det; inv = new Basis ( co[0] * s, inv[0, 2] * inv[2, 1] - inv[0, 1] * inv[2, 2] * s, inv[0, 1] * inv[1, 2] - inv[0, 2] * inv[1, 1] * s, co[1] * s, inv[0, 0] * inv[2, 2] - inv[0, 2] * inv[2, 0] * s, inv[0, 2] * inv[1, 0] - inv[0, 0] * inv[1, 2] * s, co[2] * s, inv[0, 1] * inv[2, 0] - inv[0, 0] * inv[2, 1] * s, inv[0, 0] * inv[1, 1] - inv[0, 1] * inv[1, 0] * s ); return inv; } public Basis Orthonormalized() { Vector3 xAxis = GetAxis(0); Vector3 yAxis = GetAxis(1); Vector3 zAxis = GetAxis(2); xAxis.Normalize(); yAxis = yAxis - xAxis * xAxis.Dot(yAxis); yAxis.Normalize(); zAxis = zAxis - xAxis * xAxis.Dot(zAxis) - yAxis * yAxis.Dot(zAxis); zAxis.Normalize(); return CreateFromAxes(xAxis, yAxis, zAxis); } public Basis Rotated(Vector3 axis, real_t phi) { return new Basis(axis, phi) * this; } public Basis Scaled(Vector3 scale) { var m = this; m[0, 0] *= scale.x; m[0, 1] *= scale.x; m[0, 2] *= scale.x; m[1, 0] *= scale.y; m[1, 1] *= scale.y; m[1, 2] *= scale.y; m[2, 0] *= scale.z; m[2, 1] *= scale.z; m[2, 2] *= scale.z; return m; } public real_t Tdotx(Vector3 with) { return this[0, 0] * with[0] + this[1, 0] * with[1] + this[2, 0] * with[2]; } public real_t Tdoty(Vector3 with) { return this[0, 1] * with[0] + this[1, 1] * with[1] + this[2, 1] * with[2]; } public real_t Tdotz(Vector3 with) { return this[0, 2] * with[0] + this[1, 2] * with[1] + this[2, 2] * with[2]; } public Basis Transposed() { var tr = this; real_t temp = this[0, 1]; this[0, 1] = this[1, 0]; this[1, 0] = temp; temp = this[0, 2]; this[0, 2] = this[2, 0]; this[2, 0] = temp; temp = this[1, 2]; this[1, 2] = this[2, 1]; this[2, 1] = temp; return tr; } public Vector3 Xform(Vector3 v) { return new Vector3 ( this[0].Dot(v), this[1].Dot(v), this[2].Dot(v) ); } public Vector3 XformInv(Vector3 v) { return new Vector3 ( this[0, 0] * v.x + this[1, 0] * v.y + this[2, 0] * v.z, this[0, 1] * v.x + this[1, 1] * v.y + this[2, 1] * v.z, this[0, 2] * v.x + this[1, 2] * v.y + this[2, 2] * v.z ); } public Quat Quat() { real_t trace = _x[0] + _y[1] + _z[2]; if (trace > 0.0f) { real_t s = Mathf.Sqrt(trace + 1.0f) * 2f; real_t inv_s = 1f / s; return new Quat( (_z[1] - _y[2]) * inv_s, (_x[2] - _z[0]) * inv_s, (_y[0] - _x[1]) * inv_s, s * 0.25f ); } if (_x[0] > _y[1] && _x[0] > _z[2]) { real_t s = Mathf.Sqrt(_x[0] - _y[1] - _z[2] + 1.0f) * 2f; real_t inv_s = 1f / s; return new Quat( s * 0.25f, (_x[1] + _y[0]) * inv_s, (_x[2] + _z[0]) * inv_s, (_z[1] - _y[2]) * inv_s ); } if (_y[1] > _z[2]) { real_t s = Mathf.Sqrt(-_x[0] + _y[1] - _z[2] + 1.0f) * 2f; real_t inv_s = 1f / s; return new Quat( (_x[1] + _y[0]) * inv_s, s * 0.25f, (_y[2] + _z[1]) * inv_s, (_x[2] - _z[0]) * inv_s ); } else { real_t s = Mathf.Sqrt(-_x[0] - _y[1] + _z[2] + 1.0f) * 2f; real_t inv_s = 1f / s; return new Quat( (_x[2] + _z[0]) * inv_s, (_y[2] + _z[1]) * inv_s, s * 0.25f, (_y[0] - _x[1]) * inv_s ); } } 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; _x = new Vector3(1.0f - (yy + zz), xy - wz, xz + wy); _y = new Vector3(xy + wz, 1.0f - (xx + zz), yz - wx); _z = 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) { var axis_sq = new Vector3(axis.x * axis.x, axis.y * axis.y, axis.z * axis.z); real_t cosine = Mathf.Cos( phi); real_t sine = Mathf.Sin( phi); _x = new Vector3 ( axis_sq.x + cosine * (1.0f - axis_sq.x), axis.x * axis.y * (1.0f - cosine) - axis.z * sine, axis.z * axis.x * (1.0f - cosine) + axis.y * sine ); _y = new Vector3 ( axis.x * axis.y * (1.0f - cosine) + axis.z * sine, axis_sq.y + cosine * (1.0f - axis_sq.y), axis.y * axis.z * (1.0f - cosine) - axis.x * sine ); _z = new Vector3 ( axis.z * axis.x * (1.0f - cosine) - axis.y * sine, axis.y * axis.z * (1.0f - cosine) + axis.x * sine, axis_sq.z + cosine * (1.0f - axis_sq.z) ); } public Basis(Vector3 xAxis, Vector3 yAxis, Vector3 zAxis) { _x = xAxis; _y = yAxis; _z = zAxis; } public Basis(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz) { _x = new Vector3(xx, xy, xz); _y = new Vector3(yx, yy, yz); _z = new Vector3(zx, zy, zz); } public static Basis operator *(Basis left, Basis right) { return new Basis ( right.Tdotx(left[0]), right.Tdoty(left[0]), right.Tdotz(left[0]), right.Tdotx(left[1]), right.Tdoty(left[1]), right.Tdotz(left[1]), right.Tdotx(left[2]), right.Tdoty(left[2]), right.Tdotz(left[2]) ); } 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 _x.Equals(other[0]) && _y.Equals(other[1]) && _z.Equals(other[2]); } public override int GetHashCode() { return _x.GetHashCode() ^ _y.GetHashCode() ^ _z.GetHashCode(); } public override string ToString() { return String.Format("({0}, {1}, {2})", new object[] { _x.ToString(), _y.ToString(), _z.ToString() }); } public string ToString(string format) { return String.Format("({0}, {1}, {2})", new object[] { _x.ToString(format), _y.ToString(format), _z.ToString(format) }); } } }