public static void Scale(ref Triangular3x3Wide m, ref Vector <float> scale, out Triangular3x3Wide result)
{
result.M11 = m.M11 * scale;
result.M21 = m.M21 * scale;
result.M22 = m.M22 * scale;
result.M31 = m.M31 * scale;
result.M32 = m.M32 * scale;
result.M33 = m.M33 * scale;
}
public static void Add(ref Triangular3x3Wide a, ref Triangular3x3Wide b, out Triangular3x3Wide sum)
{
sum.M11 = a.M11 + b.M11;
sum.M21 = a.M21 + b.M21;
sum.M22 = a.M22 + b.M22;
sum.M31 = a.M31 + b.M31;
sum.M32 = a.M32 + b.M32;
sum.M33 = a.M33 + b.M33;
}
public static void VectorSandwich(ref Vector3Wide v, ref Triangular3x3Wide m, out Vector <float> sandwich)
{
//This isn't actually fewer flops than the equivalent explicit operation, but it does avoid some struct locals and it's a pretty common operation.
//(And at the moment, avoiding struct locals is unfortunately helpful for codegen reasons.)
var x = v.X * m.M11 + v.Y * m.M21 + v.Z * m.M31;
var y = v.X * m.M21 + v.Y * m.M22 + v.Z * m.M32;
var z = v.X * m.M31 + v.Y * m.M32 + v.Z * m.M33;
sandwich = x * v.X + y * v.Y + z * v.Z;
}
public static void MatrixSandwich(ref Matrix2x3Wide m, ref Triangular3x3Wide t, out Triangular2x2Wide result)
{
var i11 = m.X.X * t.M11 + m.X.Y * t.M21 + m.X.Z * t.M31;
var i12 = m.X.X * t.M21 + m.X.Y * t.M22 + m.X.Z * t.M32;
var i13 = m.X.X * t.M31 + m.X.Y * t.M32 + m.X.Z * t.M33;
var i21 = m.Y.X * t.M11 + m.Y.Y * t.M21 + m.Y.Z * t.M31;
var i22 = m.Y.X * t.M21 + m.Y.Y * t.M22 + m.Y.Z * t.M32;
var i23 = m.Y.X * t.M31 + m.Y.Y * t.M32 + m.Y.Z * t.M33;
result.M11 = i11 * m.X.X + i12 * m.X.Y + i13 * m.X.Z;
result.M21 = i21 * m.X.X + i22 * m.X.Y + i23 * m.X.Z;
result.M22 = i21 * m.Y.X + i22 * m.Y.Y + i23 * m.Y.Z;
}
public static void SymmetricInvert(ref Triangular3x3Wide m, out Triangular3x3Wide inverse)
{
var m11 = m.M22 * m.M33 - m.M32 * m.M32;
var m21 = m.M32 * m.M31 - m.M33 * m.M21;
var m31 = m.M21 * m.M32 - m.M31 * m.M22;
var determinantInverse = Vector <float> .One / (m11 * m.M11 + m21 * m.M21 + m31 * m.M31);
var m22 = m.M33 * m.M11 - m.M31 * m.M31;
var m32 = m.M31 * m.M21 - m.M11 * m.M32;
var m33 = m.M11 * m.M22 - m.M21 * m.M21;
inverse.M11 = m11 * determinantInverse;
inverse.M21 = m21 * determinantInverse;
inverse.M31 = m31 * determinantInverse;
inverse.M22 = m22 * determinantInverse;
inverse.M32 = m32 * determinantInverse;
inverse.M33 = m33 * determinantInverse;
}
public static void RotationSandwich(ref Matrix3x3Wide r, ref Triangular3x3Wide m, out Triangular3x3Wide sandwich)
{
var i11 = r.X.X * m.M11 + r.Y.X * m.M21 + r.Z.X * m.M31;
var i12 = r.X.X * m.M21 + r.Y.X * m.M22 + r.Z.X * m.M32;
var i13 = r.X.X * m.M31 + r.Y.X * m.M32 + r.Z.X * m.M33;
var i21 = r.X.Y * m.M11 + r.Y.Y * m.M21 + r.Z.Y * m.M31;
var i22 = r.X.Y * m.M21 + r.Y.Y * m.M22 + r.Z.Y * m.M32;
var i23 = r.X.Y * m.M31 + r.Y.Y * m.M32 + r.Z.Y * m.M33;
var i31 = r.X.Z * m.M11 + r.Y.Z * m.M21 + r.Z.Z * m.M31;
var i32 = r.X.Z * m.M21 + r.Y.Z * m.M22 + r.Z.Z * m.M32;
var i33 = r.X.Z * m.M31 + r.Y.Z * m.M32 + r.Z.Z * m.M33;
sandwich.M11 = i11 * r.X.X + i12 * r.Y.X + i13 * r.Z.X;
sandwich.M21 = i21 * r.X.X + i22 * r.Y.X + i23 * r.Z.X;
sandwich.M22 = i21 * r.X.Y + i22 * r.Y.Y + i23 * r.Z.Y;
sandwich.M31 = i31 * r.X.X + i32 * r.Y.X + i33 * r.Z.X;
sandwich.M32 = i31 * r.X.Y + i32 * r.Y.Y + i33 * r.Z.Y;
sandwich.M33 = i31 * r.X.Z + i32 * r.Y.Z + i33 * r.Z.Z;
}
public static void SkewSandwichWithoutOverlap(ref Vector3Wide v, ref Triangular3x3Wide m, out Triangular3x3Wide sandwich)
{
//27 muls, 15 adds.
var x32 = v.X * m.M32;
var y31 = v.Y * m.M31;
var z21 = v.Z * m.M21;
var i11 = y31 - z21;
var i12 = v.Y * m.M32 - v.Z * m.M22;
var i13 = v.Y * m.M33 - v.Z * m.M32;
var i21 = v.Z * m.M11 - v.X * m.M31;
var i22 = z21 - x32;
var i23 = v.Z * m.M31 - v.X * m.M33;
var i31 = v.X * m.M21 - v.Y * m.M11;
var i32 = v.X * m.M22 - v.Y * m.M21;
var i33 = x32 - y31;
sandwich.M11 = v.Y * i13 - v.Z * i12;
sandwich.M21 = v.Y * i23 - v.Z * i22;
sandwich.M22 = v.Z * i21 - v.X * i23;
sandwich.M31 = v.Y * i33 - v.Z * i32;
sandwich.M32 = v.Z * i31 - v.X * i33;
sandwich.M33 = v.X * i32 - v.Y * i31;
}
public static void TransformBySymmetricWithoutOverlap(ref Vector3Wide v, ref Triangular3x3Wide m, out Vector3Wide result)
{
result.X = v.X * m.M11 + v.Y * m.M21 + v.Z * m.M31;
result.Y = v.X * m.M21 + v.Y * m.M22 + v.Z * m.M32;
result.Z = v.X * m.M31 + v.Y * m.M32 + v.Z * m.M33;
}