private static int GetBestCutPlane(List <Plane> planes, DcelMesh mesh)
{
// The plane cost is inspired by Stan Melax's convex hull implementation.
// It can be found in John Ratcliff's Convex Decomposition library.
float bestPlaneCost = 0;
int bestPlane = -1;
for (int i = 0; i < planes.Count; i++)
{
var plane = planes[i];
// Get min and max distance.
float minDistance = 0;
float maxDistance = 0;
foreach (var v in mesh.Vertices)
{
float distance = Vector3F.Dot(v.Position, plane.Normal) - plane.DistanceFromOrigin;
minDistance = Math.Min(distance, minDistance);
maxDistance = Math.Max(distance, maxDistance);
}
float diff = maxDistance - minDistance;
// The plane cost is the normalized maxDistance.
float planeCost = maxDistance / diff;
if (planeCost > bestPlaneCost)
{
bestPlaneCost = planeCost;
bestPlane = i;
}
}
return(bestPlane);
}
/// <summary>
/// Initializes a new instance of the <see cref="VertexAdjacency"/> class.
/// </summary>
/// <param name="mesh">The mesh for which the adjacency information is built.</param>
/// <exception cref="NotSupportedException">
/// Too many vertices in convex hull. Max. 65534 vertices in convex hull are supported.
/// </exception>
public VertexAdjacency(DcelMesh mesh)
{
if (mesh == null)
{
throw new ArgumentNullException("mesh");
}
int numberOfVertices = mesh.Vertices.Count;
if (numberOfVertices >= ushort.MaxValue)
{
throw new NotSupportedException("Too many vertices in convex hull. Max. 65534 vertices in convex hull are supported.");
}
Debug.Assert(mesh.Vertices.All(v => v.Tag == 0), "Tags of DcelMesh should be cleared.");
// Store the index of each vertex in its tag for fast lookup.
for (int i = 0; i < numberOfVertices; i++)
{
mesh.Vertices[i].Tag = i;
}
ListIndices = new ushort[numberOfVertices + 1];
List <ushort> adjacencyLists = new List <ushort>(numberOfVertices * 4);
for (int i = 0; i < numberOfVertices; i++)
{
DcelVertex vertex = mesh.Vertices[i];
ListIndices[i] = (ushort)adjacencyLists.Count;
// Gather all adjacent vertices.
DcelEdge startEdge = vertex.Edge;
DcelEdge edge = startEdge;
do
{
DcelVertex adjacentVertex = edge.Next.Origin;
int adjacentIndex = adjacentVertex.Tag;
Debug.Assert(mesh.Vertices[adjacentIndex] == adjacentVertex, "Indices stored in DcelVertex.Tag are invalid.");
adjacencyLists.Add((ushort)adjacentIndex);
edge = edge.Twin.Next;
} while (edge != startEdge);
}
// Add one additional entry which determines the end of the last adjacency list.
ListIndices[numberOfVertices] = (ushort)adjacencyLists.Count;
// Copy adjacency lists into static array.
Lists = adjacencyLists.ToArray();
}
/// <summary>
/// Initializes a new instance of the <see cref="VertexAdjacency"/> class.
/// </summary>
/// <param name="mesh">The mesh for which the adjacency information is built.</param>
/// <exception cref="NotSupportedException">
/// Too many vertices in convex hull. Max. 65534 vertices in convex hull are supported.
/// </exception>
public VertexAdjacency(DcelMesh mesh)
{
if (mesh == null)
throw new ArgumentNullException("mesh");
int numberOfVertices = mesh.Vertices.Count;
if (numberOfVertices >= ushort.MaxValue)
throw new NotSupportedException("Too many vertices in convex hull. Max. 65534 vertices in convex hull are supported.");
Debug.Assert(mesh.Vertices.All(v => v.Tag == 0), "Tags of DcelMesh should be cleared.");
// Store the index of each vertex in its tag for fast lookup.
for (int i = 0; i < numberOfVertices; i++)
mesh.Vertices[i].Tag = i;
ListIndices = new ushort[numberOfVertices + 1];
List<ushort> adjacencyLists = new List<ushort>(numberOfVertices * 4);
for (int i = 0; i < numberOfVertices; i++)
{
DcelVertex vertex = mesh.Vertices[i];
ListIndices[i] = (ushort)adjacencyLists.Count;
// Gather all adjacent vertices.
DcelEdge startEdge = vertex.Edge;
DcelEdge edge = startEdge;
do
{
DcelVertex adjacentVertex = edge.Next.Origin;
int adjacentIndex = adjacentVertex.Tag;
Debug.Assert(mesh.Vertices[adjacentIndex] == adjacentVertex, "Indices stored in DcelVertex.Tag are invalid.");
adjacencyLists.Add((ushort)adjacentIndex);
edge = edge.Twin.Next;
} while (edge != startEdge);
}
// Add one additional entry which determines the end of the last adjacency list.
ListIndices[numberOfVertices] = (ushort)adjacencyLists.Count;
// Copy adjacency lists into static array.
Lists = adjacencyLists.ToArray();
}
public static DcelMesh FromTriangleMesh(TriangleMesh mesh)
{
// TODO: To optimize, check tricks of TriangleMeshShape.ComputeNeighbors.
if (mesh == null)
throw new ArgumentNullException("mesh");
if (mesh.Vertices == null || mesh.Indices == null)
throw new ArgumentException("Input mesh has no vertices or vertex indices.");
// Create vertices.
int numberOfVertices = mesh.Vertices.Count;
var vertices = new List<DcelVertex>(numberOfVertices);
foreach (var position in mesh.Vertices)
vertices.Add(new DcelVertex(position, null));
// Weld similar vertices.
for (int i = 0; i < numberOfVertices; i++)
for (int j = i + 1; j < numberOfVertices; j++)
if (Vector3F.AreNumericallyEqual(vertices[i].Position, vertices[j].Position))
vertices[i] = vertices[j];
// Create edges and faces for each triangle.
// We need at least 3 edges for each triangle. We might need more edges if we have to
// connect unconnected islands of triangles.
var edges = new List<DcelEdge>(mesh.NumberOfTriangles * 3 * 2);
var faces = new List<DcelFace>(mesh.NumberOfTriangles);
for (int i = 0; i < mesh.NumberOfTriangles; i++)
{
// Get triangle indices.
var index0 = mesh.Indices[i * 3 + 0];
var index1 = mesh.Indices[i * 3 + 1];
var index2 = mesh.Indices[i * 3 + 2];
// Get DCEL vertices.
var vertex0 = vertices[index0];
var vertex1 = vertices[index1];
var vertex2 = vertices[index2];
// Create 3 edges.
var edge0 = new DcelEdge();
var edge1 = new DcelEdge();
var edge2 = new DcelEdge();
// Create 1 face.
var face = new DcelFace();
// Fill out face info.
face.Boundary = edge0;
// Fill out vertex info.
vertex0.Edge = edge0;
vertex1.Edge = edge1;
vertex2.Edge = edge2;
// Fill out edge info.
// Twin links are created later.
edge0.Face = face;
edge0.Origin = vertex0;
edge0.Next = edge1;
edge0.Previous = edge2;
edge1.Face = face;
edge1.Origin = vertex1;
edge1.Next = edge2;
edge1.Previous = edge0;
edge2.Face = face;
edge2.Origin = vertex2;
edge2.Next = edge0;
edge2.Previous = edge1;
// Add to lists.
edges.Add(edge0);
edges.Add(edge1);
edges.Add(edge2);
faces.Add(face);
}
// Connect triangles that share an edge.
for (int i = 0; i < faces.Count; i++)
{
// Get face and its 3 edges.
var faceI = faces[i];
var edgeI0 = faceI.Boundary;
var edgeI1 = edgeI0.Next;
var edgeI2 = edgeI1.Next;
Debug.Assert(edgeI2.Next == edgeI0);
for (int j = i + 1; j < faces.Count; j++)
{
// Get face and its 3 edges.
var faceJ = faces[j];
var edgeJ0 = faceJ.Boundary;
var edgeJ1 = edgeJ0.Next;
var edgeJ2 = edgeJ1.Next;
Debug.Assert(edgeJ2.Next == edgeJ0);
TryLink(edgeI0, edgeJ0);
TryLink(edgeI0, edgeJ1);
TryLink(edgeI0, edgeJ2);
TryLink(edgeI1, edgeJ0);
TryLink(edgeI1, edgeJ1);
TryLink(edgeI1, edgeJ2);
TryLink(edgeI2, edgeJ0);
TryLink(edgeI2, edgeJ1);
TryLink(edgeI2, edgeJ2);
}
}
// If the mesh is not closed, we have to add twin edges at the boundaries
foreach (var edge in edges.ToArray())
{
if (edge.Twin == null)
{
var twin = new DcelEdge();
twin.Origin = edge.Next.Origin;
twin.Twin = edge;
edge.Twin = twin;
edges.Add(twin);
}
}
// Yet, twin.Next/Previous were not set.
foreach (var edge in edges)
{
if (edge.Previous == null)
{
// The previous edge has not been set.
// Search the edges around the origin until we find the previous unconnected edge.
var origin = edge.Origin;
var originEdge = edge.Twin.Next; // Another edge with the same origin.
while (originEdge.Twin.Next != null)
{
Debug.Assert(originEdge.Origin == origin);
originEdge = originEdge.Twin.Next;
}
var previous = originEdge.Twin;
previous.Next = edge;
edge.Previous = previous;
}
}
// Check if we have one connected mesh.
if (vertices.Count > 0)
{
const int Tag = 1;
TagLinkedComponents(vertices[0], Tag);
// Check if all components were reached.
if (vertices.Any(v => v.Tag != Tag)
|| edges.Any(e => e.Tag != Tag)
|| faces.Any(f => f.Tag != Tag))
{
throw new NotSupportedException("The triangle mesh consists of several unconnected components or sub-meshes.");
}
}
var dcelMesh = new DcelMesh { Vertex = vertices.FirstOrDefault() };
dcelMesh.ResetTags();
return dcelMesh;
}
public static DcelMesh FromTriangleMesh(TriangleMesh mesh)
{
// TODO: To optimize, check tricks of TriangleMeshShape.ComputeNeighbors.
if (mesh == null)
{
throw new ArgumentNullException("mesh");
}
if (mesh.Vertices == null || mesh.Indices == null)
{
throw new ArgumentException("Input mesh has no vertices or vertex indices.");
}
// Create vertices.
int numberOfVertices = mesh.Vertices.Count;
var vertices = new List <DcelVertex>(numberOfVertices);
foreach (var position in mesh.Vertices)
{
vertices.Add(new DcelVertex(position, null));
}
// Weld similar vertices.
for (int i = 0; i < numberOfVertices; i++)
{
for (int j = i + 1; j < numberOfVertices; j++)
{
if (Vector3F.AreNumericallyEqual(vertices[i].Position, vertices[j].Position))
{
vertices[i] = vertices[j];
}
}
}
// Create edges and faces for each triangle.
// We need at least 3 edges for each triangle. We might need more edges if we have to
// connect unconnected islands of triangles.
var edges = new List <DcelEdge>(mesh.NumberOfTriangles * 3 * 2);
var faces = new List <DcelFace>(mesh.NumberOfTriangles);
for (int i = 0; i < mesh.NumberOfTriangles; i++)
{
// Get triangle indices.
var index0 = mesh.Indices[i * 3 + 0];
var index1 = mesh.Indices[i * 3 + 1];
var index2 = mesh.Indices[i * 3 + 2];
// Get DCEL vertices.
var vertex0 = vertices[index0];
var vertex1 = vertices[index1];
var vertex2 = vertices[index2];
// Create 3 edges.
var edge0 = new DcelEdge();
var edge1 = new DcelEdge();
var edge2 = new DcelEdge();
// Create 1 face.
var face = new DcelFace();
// Fill out face info.
face.Boundary = edge0;
// Fill out vertex info.
vertex0.Edge = edge0;
vertex1.Edge = edge1;
vertex2.Edge = edge2;
// Fill out edge info.
// Twin links are created later.
edge0.Face = face;
edge0.Origin = vertex0;
edge0.Next = edge1;
edge0.Previous = edge2;
edge1.Face = face;
edge1.Origin = vertex1;
edge1.Next = edge2;
edge1.Previous = edge0;
edge2.Face = face;
edge2.Origin = vertex2;
edge2.Next = edge0;
edge2.Previous = edge1;
// Add to lists.
edges.Add(edge0);
edges.Add(edge1);
edges.Add(edge2);
faces.Add(face);
}
// Connect triangles that share an edge.
for (int i = 0; i < faces.Count; i++)
{
// Get face and its 3 edges.
var faceI = faces[i];
var edgeI0 = faceI.Boundary;
var edgeI1 = edgeI0.Next;
var edgeI2 = edgeI1.Next;
Debug.Assert(edgeI2.Next == edgeI0);
for (int j = i + 1; j < faces.Count; j++)
{
// Get face and its 3 edges.
var faceJ = faces[j];
var edgeJ0 = faceJ.Boundary;
var edgeJ1 = edgeJ0.Next;
var edgeJ2 = edgeJ1.Next;
Debug.Assert(edgeJ2.Next == edgeJ0);
TryLink(edgeI0, edgeJ0);
TryLink(edgeI0, edgeJ1);
TryLink(edgeI0, edgeJ2);
TryLink(edgeI1, edgeJ0);
TryLink(edgeI1, edgeJ1);
TryLink(edgeI1, edgeJ2);
TryLink(edgeI2, edgeJ0);
TryLink(edgeI2, edgeJ1);
TryLink(edgeI2, edgeJ2);
}
}
// If the mesh is not closed, we have to add twin edges at the boundaries
foreach (var edge in edges.ToArray())
{
if (edge.Twin == null)
{
var twin = new DcelEdge();
twin.Origin = edge.Next.Origin;
twin.Twin = edge;
edge.Twin = twin;
edges.Add(twin);
}
}
// Yet, twin.Next/Previous were not set.
foreach (var edge in edges)
{
if (edge.Previous == null)
{
// The previous edge has not been set.
// Search the edges around the origin until we find the previous unconnected edge.
var origin = edge.Origin;
var originEdge = edge.Twin.Next; // Another edge with the same origin.
while (originEdge.Twin.Next != null)
{
Debug.Assert(originEdge.Origin == origin);
originEdge = originEdge.Twin.Next;
}
var previous = originEdge.Twin;
previous.Next = edge;
edge.Previous = previous;
}
}
// Check if we have one connected mesh.
if (vertices.Count > 0)
{
const int Tag = 1;
TagLinkedComponents(vertices[0], Tag);
// Check if all components were reached.
if (vertices.Any(v => v.Tag != Tag) ||
edges.Any(e => e.Tag != Tag) ||
faces.Any(f => f.Tag != Tag))
{
throw new NotSupportedException("The triangle mesh consists of several unconnected components or sub-meshes.");
}
}
var dcelMesh = new DcelMesh {
Vertex = vertices.FirstOrDefault()
};
dcelMesh.ResetTags();
return(dcelMesh);
}
private void BuildVertexAdjacencyLists(DcelMesh convexHull)
{
_vertexAdjacency = new VertexAdjacency(convexHull);
}
private static int GetBestCutPlane(List<Plane> planes, DcelMesh mesh)
{
// The plane cost is inspired by Stan Melax's convex hull implementation.
// It can be found in John Ratcliff's Convex Decomposition library.
float bestPlaneCost = 0;
int bestPlane = -1;
for (int i = 0; i < planes.Count; i++)
{
var plane = planes[i];
// Get min and max distance.
float minDistance = 0;
float maxDistance = 0;
foreach (var v in mesh.Vertices)
{
float distance = Vector3F.Dot(v.Position, plane.Normal) - plane.DistanceFromOrigin;
minDistance = Math.Min(distance, minDistance);
maxDistance = Math.Max(distance, maxDistance);
}
float diff = maxDistance - minDistance;
// The plane cost is the normalized maxDistance.
float planeCost = maxDistance / diff;
if (planeCost > bestPlaneCost)
{
bestPlaneCost = planeCost;
bestPlane = i;
}
}
return bestPlane;
}
/// <summary>
/// Initializes a new instance of the <see cref="DcelMesh" /> class that is a copy of the given
/// mesh.
/// </summary>
/// <param name="mesh">
/// The source mesh to copy. Can be <see langword="null"/> to create an empty
/// <see cref="DcelMesh"/>.
/// </param>
/// <remarks>
/// This constructor creates a new <see cref="DcelMesh"/> which is a copy of the given
/// <paramref name="mesh"/>.
/// </remarks>
public DcelMesh(DcelMesh mesh)
{
if (mesh == null)
{
return;
}
var originalVertices = mesh.Vertices;
var originalEdges = mesh.Edges;
var originalFaces = mesh.Faces;
// 3 empty lists.
_vertices = new List <DcelVertex>(originalVertices.Count);
_edges = new List <DcelEdge>(originalEdges.Count);
_faces = new List <DcelFace>(originalFaces.Count);
// Use the internal tags to store list indices.
for (int i = 0; i < originalVertices.Count; i++)
{
originalVertices[i].InternalTag = i;
}
for (int i = 0; i < originalEdges.Count; i++)
{
originalEdges[i].InternalTag = i;
}
for (int i = 0; i < originalFaces.Count; i++)
{
originalFaces[i].InternalTag = i;
}
// Add empty instances to the new lists.
for (int i = 0; i < originalVertices.Count; i++)
{
_vertices.Add(new DcelVertex());
}
for (int i = 0; i < originalEdges.Count; i++)
{
_edges.Add(new DcelEdge());
}
for (int i = 0; i < originalFaces.Count; i++)
{
_faces.Add(new DcelFace());
}
// Clone the DCEL parts.
for (int i = 0; i < originalVertices.Count; i++)
{
var s = originalVertices[i]; // source
var t = _vertices[i]; // target
t.Position = s.Position;
if (s.Edge != null)
{
t.Edge = _edges[s.Edge.InternalTag];
}
t.Tag = s.Tag;
t.UserData = s.UserData;
}
for (int i = 0; i < originalEdges.Count; i++)
{
var s = originalEdges[i];
var t = _edges[i];
if (s.Origin != null)
{
t.Origin = _vertices[s.Origin.InternalTag];
}
if (s.Twin != null)
{
t.Twin = _edges[s.Twin.InternalTag];
}
if (s.Face != null)
{
t.Face = _faces[s.Face.InternalTag];
}
if (s.Next != null)
{
t.Next = _edges[s.Next.InternalTag];
}
if (s.Previous != null)
{
t.Previous = _edges[s.Previous.InternalTag];
}
t.Tag = s.Tag;
t.UserData = s.UserData;
}
for (int i = 0; i < originalFaces.Count; i++)
{
var s = originalFaces[i];
var t = _faces[i];
if (s.Boundary != null)
{
t.Boundary = _edges[s.Boundary.InternalTag];
}
if (s.Holes != null)
{
t.Holes = new List <DcelEdge>(s.Holes.Count);
for (int j = 0; j < s.Holes.Count; j++)
{
if (s.Holes[j] != null)
{
t.Holes.Add(_edges[s.Holes[j].InternalTag]);
}
}
}
t.Tag = s.Tag;
t.UserData = s.UserData;
}
Dirty = false;
if (mesh.Vertex != null)
{
Vertex = _vertices[mesh.Vertex.InternalTag];
}
mesh.ResetInternalTags();
Debug.Assert(_vertices.Count == mesh._vertices.Count, "Cloning of DcelMesh failed. Clone has different number of vertices.");
Debug.Assert(_edges.Count == mesh._edges.Count, "Cloning of DcelMesh failed. Clone has different number of edges.");
Debug.Assert(_faces.Count == mesh._faces.Count, "Cloning of DcelMesh failed. Clone has different number of faces.");
}
public void Reset()
{
// Reset fields.
_faces = new List<DcelFace>();
_taggedEdges = new List<DcelEdge>();
_isPlanar = false;
_type = ConvexHullType.Empty;
_mesh = new DcelMesh();
}
