/// <summary>
/// Barycentric Parameterization
/// Covers barycentric methods which need a fully defined boundary
/// A particular method can be chosen by creating an appropriate Laplacian matrix
/// See also (Floater 2003)
/// </summary>
/// <param name="meshin">input mesh, after solving its texture coordinates in vertex traits will be adjusted</param>
/// <param name="meshout">an flattened output mesh with only X,Y coordinates set, Z is set to 0</param>
private void BarycentricMapping(TriangleMesh meshin, out TriangleMesh meshout)
{
/// init an mesh that serves for output of the 2d parametrized mesh
meshout = meshin.Copy();
//meshOut = meshIn;
/// get lenghts
var vertexCount = meshout.Vertices.Count;
var boundaryVertices = meshout.Vertices.Where(x => x.OnBoundary).ToList();
/// right hand side (RHS)
var bu = new double[vertexCount];
var bv = new double[vertexCount];
var b0 = new double[vertexCount];
// TODO : For geometry images, L mapped edges require splitting. Adaptive length parameterization should be sufficient for crack prediction however
FixBoundaryToShape(boundaryVertices, bu, bv);
var laplacian = MeshLaplacian.SelectedLaplacian == MeshLaplacian.Type.Harmonic ?
MeshLaplacian.CreateBoundedHarmonicLaplacian(meshin, 1d, 0d, true) :
MeshLaplacian.SelectedLaplacian == MeshLaplacian.Type.MeanValue ?
MeshLaplacian.CreateBoundedMeanLaplacian(meshin, 1d, 0d, true) :
MeshLaplacian.CreateBoundedUniformLaplacian(meshin, 1d, 0d, true);
var qrSolver = QR.Create(laplacian.Compress());
var success = qrSolver.Solve(bu) && qrSolver.Solve(bv);
/// update mesh positions
MeshLaplacian.UpdateMesh(meshout, bu, bv, b0, bu, bv);
MeshLaplacian.UpdateMesh(meshin, bu, bv);
}
