public void Transpose_Instance()
{
var mat = new float3x3(1, 1, 1, 2, 2, 2, 3, 3, 3);
var actual = mat.Transpose();
Assert.Equal(new float3x3(1, 2, 3, 1, 2, 3, 1, 2, 3), actual);
}
/// <summary>
/// Calculates the vertex position so that it is parallel to the x-y plane.
/// </summary>
/// <param name="vertPos">Original vertex position.</param>
/// <param name="normal">The normal of the polygon the vertex belongs to. Used as new Z axis.</param>
/// <returns></returns>
internal static float3 Reduce2D(this float3 vertPos, float3 normal)
{
normal = normal.Normalize(); //New z axis
//If the normal equals the z axis of the world coodrinate system: reflect the point on the y axis.
if (normal == float3.UnitZ)
{
var rot = new float3x3(-1, 0, 0,
0, 1, 0,
0, 0, 1);
return(vertPos * rot);
}
//If the normal equals the negative z axis of the world coodrinate system: use the original coordinates.
if (normal == float3.UnitZ * -1)
{
return(vertPos);
}
var v2 = float3.Cross(normal, float3.UnitZ); //rotation axis - new x axis
v2 = v2.Normalize();
var v3 = float3.Cross(normal, v2); //new y axis
v3 = v3.Normalize();
//Calculate change-of-basis matrix (orthonormal matrix).
var row1 = new float3(v3.x, v2.x, normal.x);
var row2 = new float3(v3.y, v2.y, normal.y);
var row3 = new float3(v3.z, v2.z, normal.z);
//vector in new basis * changeOfBasisMat = vector in old basis
var changeOfBasisMat = new float3x3(row1, row2, row3);
//In an orthonomal matrix the inverse equals the transpose, thus the transpose can be used to calculate vector in new basis (transpose * vector = vector in new basis).
var transposeMat = new float3x3(changeOfBasisMat.Row0, changeOfBasisMat.Row1, changeOfBasisMat.Row2);
transposeMat = transposeMat.Transpose();
var newVert = transposeMat * vertPos;
//Round, to get rid of potential exponent representation.
var vecX = System.Math.Round(newVert.x, 5);
var vecY = System.Math.Round(newVert.y, 5);
var vecZ = System.Math.Round(newVert.z, 5);
newVert = new float3((float)vecX, (float)vecY, (float)vecZ);
return(newVert);
}