/// <summary>
/// Solves the linear system A * x = b, where A is the original matrix (before the factorization),
/// b = <paramref name="rhsVector"/> and x is the solution vector, which will be returned.
/// </summary>
/// <param name="rhsVector">
/// The right hand side vector. Its <see cref="IIndexable1D.Length"/> must be equal to
/// <see cref="Matrices.IIndexable2D.NumRows"/> of the original matrix A.
/// </param>
/// Thrown if the length of <paramref name="rhsVector"/> is different than <see cref="Matrices.IIndexable2D.NumRows"/>
/// of the original matrix A.
/// </exception>
public static Vector SolveLinearSystem(this ITriangulation triangulation, Vector rhsVector)
{
var solution = Vector.CreateZero(triangulation.Order);
triangulation.SolveLinearSystem(rhsVector, solution);
return(solution);
}
public DelaunayTriangulationManager(ICoordinateValidator cv, ITriangulation triangulator)
{
_triangulator = triangulator;
this.x = cv.getX();
this.y = cv.getY();
this.z_as_fxy = cv.get_Z_as_fxy();
}
public void visualizeEdges(ITriangulation <Vector3Vertex, DefaultTriangulationCell <Vector3Vertex> > triangulation)
{
/*
*
* foreach (var edge in voronoiMesh.Edges)
* {
* calculateCircumsphere
* var from = edge.Source.Circumcenter;
* var to = edge.Target.Circumcenter;
* drawingCanvas.Children.Add(new Line { X1 = from.X, Y1 = from.Y, X2 = to.X, Y2 = to.Y, Stroke = Brushes.Black });
* }
*
* foreach (var cell in voronoiMesh.Vertices)
* {
* for (int i = 0; i < 3; i++)
* {
* if (cell.Adjacency[i] == null)
* {
* var from = cell.Circumcenter;
* var t = cell.Vertices.Where((_, j) => j != i).ToArray();
* var factor = 100 * IsLeft(t[0].ToPoint(), t[1].ToPoint(), from) * IsLeft(t[0].ToPoint(), t[1].ToPoint(), Center(cell));
* var dir = new Point(0.5 * (t[0].Position[0] + t[1].Position[0]), 0.5 * (t[0].Position[1] + t[1].Position[1])) - from;
* var to = from + factor * dir;
* drawingCanvas.Children.Add(new Line { X1 = from.X, Y1 = from.Y, X2 = to.X, Y2 = to.Y, Stroke = Brushes.Black });
* }
* }
* }
*
* ShowVertices(Vertices);
* drawingCanvas.Children.Add(new Rectangle { Width = drawingCanvas.ActualWidth, Height = drawingCanvas.ActualHeight, Stroke = Brushes.Black, StrokeThickness = 3 });
* }
*/
// visualize
foreach (var cell in triangulation.Cells)
{
for (int i = 0; i < cell.Adjacency.Length; i++)
{
var F = cell.Adjacency[i];
int sharedBoundaries = 0;
// vertices shared with F:
for (int j = 0; j < cell.Vertices.Length; j++)
{
if (i != j)
{
sharedBoundaries++;
//cell.Vertices[j]
}
}
Debug.Log("Shared vertices: " + sharedBoundaries);
}
// drawLine(lastPos, vertex.toVector3(), ColorAssistant.getQualitativeColor(0));
}
}
/// <summary>
/// Provide new values for the vertices that constitute the triangles of the specified face.
/// </summary>
/// <param name="face">The face whose triangle vertices should be udpated.</param>
/// <param name="triangulation">The triangulation method used for converting faces to triangles.</param>
/// <remarks>
/// <para>This method will update the vertex attribute values for this face, but will not
/// immediately push these changes to the mesh itself. Instead, it will simply mark the
/// relevant submesh as dirty. Call <see cref="RebuildMesh"/>() in order to commit all
/// changes and apply them to the mesh.</para>
///
/// <para>The <paramref name="triangulation"/> parameter is expected to match the kind of
/// triangulation used when first creating the dynamic mesh, but is permitted to set the
/// vertex attributes however it likes. That is, the number of triangles generated for
/// each face and the vertex indices used by each of these triangles cannot change, only
/// vertex attributes. Not all vertex attributes need or are always expected to be
/// changed either. In many cases, simply changing normals or uvs, for example, is
/// all that is needed, and all other vertex attribute values can remain the same.</para>
/// </remarks>
public void RebuildFace(Topology.Face face, ITriangulation triangulation)
{
var submesh = _submeshes[_faceSubmeshIndices[face.index]];
var vertexAttributeArrays = GetIndexedVertexAttributeArrays(submesh, _faceFirstVertexIndices[face.index]);
triangulation.RebuildFace(face, vertexAttributeArrays);
submesh.isDirty = true;
}
/// <summary>
/// Ring：划分Delaunay三角网，结果保存于tsData
/// </summary>
/// <param name="depth">深度</param>
/// <param name="interpolateFunc">插值函数</param>
public void MeshRing(
double depth,
Func <IList <Point>, double, double, double, double> interpolateFunc)
{
try
{
triangulations = Triangulation.CreateDelaunay(this.allVerticesList);
this.TsData.VerticesList = new List <Point3D>(this.allVerticesList.Count);
this.TsData.TriLinksList = new List <TriLink>(this.triangulations.Cells.Count());
// 以Dict记录三角形的编号
int num = 1;
foreach (var cell in this.triangulations.Cells)
{
for (int i = 0; i < 3; ++i)
{
var v = cell.Vertices[i];
if (!this.vertexnumDictionary.ContainsKey(v))
{
this.vertexnumDictionary.Add(v, num++);
}
}
// 根据编号写ts的TriLinksList
this.TsData.TriLinksList.Add(new TriLink
{
VertexA = this.vertexnumDictionary[cell.Vertices[0]],
VertexB = this.vertexnumDictionary[cell.Vertices[1]],
VertexC = this.vertexnumDictionary[cell.Vertices[2]]
});
}
// 写ts的VerticesList, 并插值Z
foreach (var kv in this.vertexnumDictionary.OrderBy(n => n.Value))
{
var vPos = kv.Key.Position;
var x = vPos[0];
var y = vPos[1];
var z = interpolateFunc(this.edgeVerticesList, depth, x, y);
this.TsData.VerticesList.Add(new Point3D(x, y, z));
}
}
catch (Exception ex)
{
MessageBox.Show(ex.Message);
return;
}
}
public void visualizeVertices(ITriangulation <Vector3Vertex, DefaultTriangulationCell <Vector3Vertex> > triangulation)
{
// visualize
foreach (var cell in triangulation.Cells)
{
foreach (var vertex in cell.Vertices)
{
GameObject sphere = GameObject.CreatePrimitive(PrimitiveType.Sphere);
sphere.transform.position = vertex.toVector3();
sphere.transform.localScale = new Vector3(0.1f, 0.1f, 0.1f);
sphere.transform.SetParent(_delaunay.transform);
setColor(sphere, ColorAssistant.getQualitativeColor(0));
}
}
}
/// <summary>
/// Creates a dynamic mesh instance for the given faces, using the specified vertex attributes and triangulation object to construct the vertex data and triangles.
/// </summary>
/// <param name="faces">The faces for which to generate triangle meshes.</param>
/// <param name="vertexAttributes">The types of vertex data to include in the meshes, such as position, color, and normal.</param>
/// <param name="triangulation">The object which is responsible for turning each individual face into triangles with a mesh.</param>
/// <param name="maxVerticesPerSubmesh">The maximum number of vertices allowed per submesh. Defaults to Unity's built-in maximum of 65534.</param>
/// <returns>A dynamic mesh instance created from the given faces and triangulation.</returns>
public static DynamicMesh Create(IEnumerable <Topology.Face> faces, VertexAttributes vertexAttributes, ITriangulation triangulation, int maxVerticesPerSubmesh = 65534)
{
var dynamicMesh = CreateInstance <DynamicMesh>();
dynamicMesh._vertexAttributes = vertexAttributes;
dynamicMesh._maxVerticesPerSubmesh = maxVerticesPerSubmesh;
dynamicMesh.Initialize(new IEnumerable <Topology.Face>[] { faces }, triangulation);
return(dynamicMesh);
}
private void Initialize(IEnumerable <IEnumerable <Topology.Face> > faceGroups, ITriangulation triangulation)
{
int maxFaceIndex = -1;
var dynamicFaceSubmeshIndicesArray = new int[65536];
var dynamicFaceFirstVertexIndicesArray = new int[65536];
_cachedIndexedVertexAttributeArrays = new IndexedVertexAttributeArrays();
var submeshList = new List <Submesh>();
var vertexAttributeArrays = new DynamicVertexAttributeArrays(_vertexAttributes, _maxVerticesPerSubmesh);
var triangleIndices = new List <int>();
foreach (var faceGroup in faceGroups)
{
foreach (var face in faceGroup)
{
var vertexCount = triangulation.GetVertexCount(face);
if (vertexAttributeArrays.index + vertexCount > _maxVerticesPerSubmesh)
{
triangulation.FinalizeSubmesh(submeshList.Count);
submeshList.Add(new Submesh(vertexAttributeArrays, triangleIndices));
vertexAttributeArrays.Reset();
triangleIndices.Clear();
}
maxFaceIndex = Mathf.Max(maxFaceIndex, face.index);
SetGrowableArrayElement(ref dynamicFaceSubmeshIndicesArray, face.index, submeshList.Count);
SetGrowableArrayElement(ref dynamicFaceFirstVertexIndicesArray, face.index, vertexAttributeArrays.index);
vertexAttributeArrays.Grow(vertexCount);
triangulation.BuildFace(face, vertexAttributeArrays, triangleIndices);
}
if (vertexAttributeArrays.index > 0)
{
triangulation.FinalizeSubmesh(submeshList.Count);
submeshList.Add(new Submesh(vertexAttributeArrays, triangleIndices));
vertexAttributeArrays.Reset();
triangleIndices.Clear();
}
}
_submeshes = submeshList.ToArray();
var faceCount = maxFaceIndex + 1;
_faceSubmeshIndices = new int[faceCount];
_faceFirstVertexIndices = new int[faceCount];
Array.Copy(dynamicFaceSubmeshIndicesArray, _faceSubmeshIndices, faceCount);
Array.Copy(dynamicFaceFirstVertexIndicesArray, _faceFirstVertexIndices, faceCount);
}
/// <summary>
/// Calculates the Schur complement of M/C = S = A - B^T * inv(C) * B, where M = [A B; B^T C].
/// This method constructs inv(C) * B one column at a time and uses that column to calculate the superdiagonal
/// entries of the corresponding column of B^T * inv(C) * B.
/// </summary>
public static SymmetricMatrix CalcSchurComplementSymmetric(SymmetricMatrix A, CscMatrix B, ITriangulation inverseC)
{ //TODO: Unfortunately this cannot take advantage of MKL for CSC^T * vector.
double[] valuesB = B.RawValues;
int[] rowIndicesB = B.RawRowIndices;
int[] colOffsetsB = B.RawColOffsets;
var S = SymmetricMatrix.CreateZero(A.Order);
for (int j = 0; j < B.NumColumns; ++j)
{
// column j of (inv(C) * B) = inv(C) * column j of B
Vector colB = B.GetColumn(j);
double[] colInvCB = inverseC.SolveLinearSystem(colB).RawData;
// column j of (B^T * inv(C) * B) = B^T * column j of (inv(C) * B)
// However we only need the superdiagonal part of this column.
// Thus we only multiply the rows i of B^T (stored as columns i of B) with i <= j.
for (int i = 0; i <= j; ++i)
{
double dot = 0.0;
int colStart = colOffsetsB[i]; //inclusive
int colEnd = colOffsetsB[i + 1]; //exclusive
for (int k = colStart; k < colEnd; ++k)
{
dot += valuesB[k] * colInvCB[rowIndicesB[k]];
}
// Perform the subtraction S = A - (B^T * inv(C) * B) for the current (i, j)
int indexS = S.Find1DIndex(i, j);
S.RawData[indexS] = A.RawData[indexS] - dot;
}
}
return(S);
}
