/// <summary>
/// Generate a debug mesh containing the centroids of the primary mesh's triangles as points.
/// </summary>
/// <returns>A new mesh for debug</returns>
public Mesh <Vertex3D> GenerateCentroidPointMesh()
{
// Doesn't rely on topology
int numTriangles = indices.Length / 3;
Vertex3D[] centroidVerts = new Vertex3D[numTriangles];
Vertex3D centroidVertex = new Vertex3D();
Mesh <Vertex3D> centroidMesh = new Mesh <Vertex3D>(centroidVerts);
int triangleIndex = 0;
for (int i = 0; i < numTriangles; ++i)
{
Vector3 centroid = Topology.CalculateCentroid(i);
IPositionVertex ipv = centroidVertex as IPositionVertex;
if (ipv != null)
{
ipv.SetPosition(centroid);
}
centroidMesh.vertices[triangleIndex++] = (Vertex3D)ipv;
}
return(centroidMesh);
}
public float RelaxTriangles(float multiplier)
{
NeedsUpdate = true;
double totalSurfaceArea = 4.0 * Math.PI;
double idealFaceArea = totalSurfaceArea / (indices.Length / 3);
double idealEdgeLength = Math.Sqrt(idealFaceArea * 4.0 / Math.Sqrt(3.0));
double idealDistanceToCentroid = idealEdgeLength * Math.Sqrt(3) / 3.0 * 0.9;
Vector3[] shiftPositions = new Vector3[mesh.vertices.Length];
for (int i = 0; i < mesh.vertices.Length; ++i)
{
shiftPositions[i] = new Vector3(Vector3.Zero);
}
int numIndices = indices.Length;
TVertex[] centroidVerts = new TVertex[numIndices / 3];
TVertex centroidVertex = new TVertex();
for (int i = 0; i < numIndices; i += 3)
{
Vector3 centroid = Topology.CalculateCentroid(i / 3);
centroid.Normalize();
MeshAttr.SetPosition(ref centroidVertex, ref centroid);
Vector3[] oldPositions = new Vector3[3]
{
new Vector3(MeshAttr.GetPosition(ref mesh.vertices[indices[i]])),
new Vector3(MeshAttr.GetPosition(ref mesh.vertices[indices[i + 1]])),
new Vector3(MeshAttr.GetPosition(ref mesh.vertices[indices[i + 2]])),
};
for (int j = 0; j < 3; ++j)
{
Vector3 midLine = centroid - oldPositions[j];
float midLength = midLine.Length;
midLine *= (float)(multiplier * (midLength - idealDistanceToCentroid) / midLength);
shiftPositions[indices[i + j]] += midLine;
}
}
var origin = Vector3.Zero;
Plane p = new Plane(Vector3.UnitY, Vector3.Zero);
for (int i = 0; i < mesh.vertices.Length; ++i)
{
Vector3 vertexPosition = MeshAttr.GetPosition(ref mesh.vertices[i]);
p.Redefine(vertexPosition, origin);
shiftPositions[i] = vertexPosition + p.ProjectPoint(shiftPositions[i]);
shiftPositions[i].Normalize();
}
// Stop poylgons rotating about their centroid.
// Doesn't stop triangles flipping.
float[] rotationSuppressions = new float[mesh.vertices.Length];
rotationSuppressions.Initialize();
Topology.GenerateEdges();
float minEdgeLength = (float)idealEdgeLength * 0.8f;
float maxEdgeLength = (float)idealEdgeLength * 1.2f;
foreach (var iter in Topology.Edges)
{
Int64 key = iter.Key;
int index1 = (int)(key & 0xffffffff);
int index2 = (int)((key >> 32) & 0xffffffff);
Vector3 oldPos1 = MeshAttr.GetPosition(ref mesh.vertices[index1]);
Vector3 oldPos2 = MeshAttr.GetPosition(ref mesh.vertices[index2]);
Vector3 newPos1 = shiftPositions[index1];
Vector3 newPos2 = shiftPositions[index2];
Vector3 oldEdge = oldPos2 - oldPos1;
Vector3 newEdge = newPos2 - newPos1;
if (newEdge.Length < minEdgeLength)
{
// Move shift positions back out to ensure that the edge is never too small.
Vector3 midPt = newPos1 + 0.5f * newEdge;
newEdge.Normalize();
newEdge *= minEdgeLength * 0.5f;
shiftPositions[index1] = midPt - newEdge;
shiftPositions[index2] = midPt + newEdge;
newEdge = shiftPositions[index2] - shiftPositions[index1];
}
if (newEdge.Length > maxEdgeLength)
{
// Move shift positions back in to ensure that the edge is never too large.
Vector3 midPt = newPos1 + 0.5f * newEdge;
newEdge.Normalize();
newEdge *= (maxEdgeLength * 0.5f);
shiftPositions[index1] = midPt - newEdge;
shiftPositions[index2] = midPt + newEdge;
newEdge = shiftPositions[index2] - shiftPositions[index1];
}
oldEdge.Normalize();
newEdge.Normalize();
float suppression = (1.0f - Vector3.Dot(oldEdge, newEdge)) * 0.5f;
rotationSuppressions[index1] = Math.Max(suppression, rotationSuppressions[index1]);
rotationSuppressions[index2] = Math.Max(suppression, rotationSuppressions[index2]);
}
for (int i = 0; i < mesh.vertices.Length; ++i)
{
Vector3 pos = MeshAttr.GetPosition(ref mesh.vertices[i]);
Vector3 delta = pos;
pos = Math2.Lerp(pos, shiftPositions[i], (float)(1.0f - Math.Sqrt(rotationSuppressions[i])));
pos.Normalize();
shiftPositions[i] = pos;
}
float totalShift = 0;
for (int i = 0; i < mesh.vertices.Length; ++i)
{
Vector3 delta = MeshAttr.GetPosition(ref mesh.vertices[i]);
MeshAttr.SetPosition(ref mesh.vertices[i], ref shiftPositions[i]);
delta -= shiftPositions[i];
totalShift += delta.Length;
}
Topology.Regenerate();
return(totalShift);
}
// Alternative algorithm
// for each triangle
// find normal
// find centroid radius
// Tilt triangle towards centroid radius
// moving edges towards symmetry.
// generate new point for each tri vert
// for each vert, calc average of all new verts, normalise and apply
// Algorithm is nearly there, but on some triangles, there is a potential that converging on
// centroid tilts through random moves away from centroidal radius, and they become thin / start overlapping.
public float RelaxTriangles1(float multiplier)
{
NeedsUpdate = true;
double totalSurfaceArea = 4.0 * Math.PI;
double idealFaceArea = totalSurfaceArea / (indices.Length / 3);
double idealEdgeLength = Math.Sqrt(idealFaceArea * 4.0 / Math.Sqrt(3.0));
double idealDistanceToCentroid = idealEdgeLength * Math.Sqrt(3) / 3.0 * 0.9;
int numIndices = indices.Length;
Vector3[] shiftPositions = new Vector3[mesh.vertices.Length];
for (int i = 0; i < mesh.vertices.Length; ++i)
{
shiftPositions[i] = new Vector3(Vector3.Zero);
}
for (int i = 0; i < numIndices; i += 3)
{
if (1 == 1)//TooThin(i))
{
Vector3 centroid = Topology.CalculateCentroid(i / 3);
centroid.Normalize();
// Compare each corner to the centroid
// if too far off some ideal length ( the centroid of an equilateral triangle ),
// pull vertex closer to centroid, (without buggering up the other triangles using
// this point.)
Vector3[] oldPositions = new Vector3[3]
{
new Vector3(MeshAttr.GetPosition(ref mesh.vertices[indices[i]])),
new Vector3(MeshAttr.GetPosition(ref mesh.vertices[indices[i + 1]])),
new Vector3(MeshAttr.GetPosition(ref mesh.vertices[indices[i + 2]])),
};
Vector3[] newPositions = new Vector3[3];
for (int j = 0; j < 3; ++j)
{
TVertex v1 = mesh.vertices[indices[i + j]];
Vector3 v1Pos = MeshAttr.GetPosition(ref v1);
Vector3 e1 = centroid - v1Pos;
if (e1.Length > idealDistanceToCentroid * 1.1)
{
// Move vertex closer to centroid
float factor = 1.0f - (float)idealDistanceToCentroid / e1.Length;
float fraction = (multiplier * (1.0f - (float)idealDistanceToCentroid / e1.Length));
factor = factor * fraction;
v1Pos = Vector3.Normalize(v1Pos + e1 * factor);
}
else if (e1.Length < idealDistanceToCentroid * 0.9)
{
// Move vertex away from the centroid
float factor = 1 - e1.Length / (float)idealDistanceToCentroid;
float fraction = (multiplier * (e1.Length / (float)idealDistanceToCentroid));
factor = factor * fraction;
v1Pos = Vector3.Normalize(v1Pos - e1 * factor);
}
newPositions[j] = v1Pos;
}
// If this makes the triangle less parallel to the sphere, don't do it.
Vector3 a = newPositions[1] - newPositions[0];
Vector3 b = newPositions[2] - newPositions[1];
Vector3 normal = Vector3.Cross(a, b);
normal.Normalize();
float dot = Vector3.Dot(centroid, normal);
double phi = Math.Acos(dot);
a = oldPositions[1] - oldPositions[0];
b = oldPositions[2] - oldPositions[1];
normal = Vector3.Cross(a, b);
normal.Normalize();
dot = Vector3.Dot(centroid, normal);
double theta = Math.Acos(dot);
if (phi < dot)
{
for (int j = 0; j < 3; ++j)
{
//SetPosition(ref mesh.vertices[indices[i + j]], ref newPositions[j]);
shiftPositions[indices[i + j]] = newPositions[j];
}
}
// If any surrounding triangles would be less parallel to the sphere than
// this is more parallel, don't do it.
}
}
TVertex[] vertices = new TVertex[mesh.vertices.Length];
float totalShift = 0;
for (int i = 0; i < mesh.vertices.Length; ++i)
{
Vector3 delta = shiftPositions[i] - MeshAttr.GetPosition(ref mesh.vertices[i]);
MeshAttr.SetPosition(ref mesh.vertices[i], ref shiftPositions[i]);
totalShift += delta.Length;
}
Topology.Regenerate();
return(totalShift);
}