public ConwayPoly Cylinderize(OpParams o)
{
var vertexPoints = new List <Vector3>();
var faceIndices = ListFacesByVertexIndices();
for (var vertexIndex = 0; vertexIndex < Vertices.Count; vertexIndex++)
{
float amount = o.GetValueA(this, vertexIndex);
var vertex = Vertices[vertexIndex];
if (IncludeVertex(vertexIndex, o.facesel, o.TagListFromString(), o.filterFunc))
{
var normalized = new Vector2(vertex.Position.x, vertex.Position.z).normalized;
var result = new Vector3(normalized.x, vertex.Position.y, normalized.y);
vertexPoints.Add(Vector3.LerpUnclamped(vertex.Position, result, amount));
VertexRoles[vertexIndex] = Roles.Existing;
}
else
{
vertexPoints.Add(vertex.Position);
VertexRoles[vertexIndex] = Roles.Ignored;
}
}
var conway = new ConwayPoly(vertexPoints, faceIndices, FaceRoles, VertexRoles, FaceTags);
return(conway);
}
/**
* Canonicalizes a polyhedron by adjusting its vertices iteratively.
*
* @param poly The polyhedron whose vertices to adjust.
* @param numIterations The number of iterations to adjust for.
*/
public static void Adjust(ConwayPoly poly, int numIterations)
{
var dual = poly.Dual();
for (int i = 0; i < numIterations; i++)
{
var newDualPositions = ReciprocalCenters(poly);
dual.SetVertexPositions(newDualPositions);
var newPositions = ReciprocalCenters(dual);
poly.SetVertexPositions(newPositions);
}
}
/**
* A port of the "reciprocalC" function written by George Hart. Reflects
* the centers of faces across the unit sphere.
*
* @param poly The polyhedron whose centers to invert.
* @return The list of inverted face centers.
*/
private static List <Vector3> ReciprocalCenters(ConwayPoly poly)
{
var faceCenters = new List <Vector3>();
for (var i = 0; i < poly.Faces.Count; i++)
{
var newCenter = poly.Faces[i].Centroid;
newCenter *= 1.0f / Mathf.Pow(newCenter.magnitude, 2);
faceCenters.Add(newCenter);
}
return(faceCenters);
}
/**
* A port of the "reciprocalN" function written by George Hart.
*
* @param poly The polyhedron to apply this canonicalization to.
* @return A list of the new vertices of the dual polyhedron.
*/
private static List <Vector3> ReciprocalVertices(ConwayPoly poly)
{
var newVertices = new List <Vector3>();
foreach (var face in poly.Faces)
{
// Initialize values which will be updated in the loop below
var centroid = face.Centroid;
var normalSum = new Vector3();
double avgEdgeDistance = 0.0;
// Retrieve the indices of the vertices defining this face
var faceVertices = face.GetVertices();
// Keep track of the "previous" two vertices in CCW order
var lastlastVertex = faceVertices[faceVertices.Count - 2];
var lastVertex = faceVertices[faceVertices.Count - 1];
for (var i = 0; i < faceVertices.Count; i++)
{
var vertex = faceVertices[i];
// Compute the normal of the plane defined by this vertex and
// the previous two
var v1 = lastlastVertex.Position;
v1 -= lastVertex.Position;
var v2 = vertex.Position;
v2 -= lastVertex.Position;
var normal = Vector3.Cross(v1, v2);
normalSum += normal;
// Compute distance from edge to origin
avgEdgeDistance += PointLineDist(new Vector3(), lastlastVertex.Position, lastVertex.Position);
// Update the previous vertices for the next iteration
lastlastVertex = lastVertex;
lastVertex = vertex;
}
normalSum = normalSum.normalized;
avgEdgeDistance /= faceVertices.Count;
var resultingVector = new Vector3();
resultingVector = Vector3.Dot(centroid, normalSum) * normalSum;
resultingVector *= Mathf.Pow(1.0f / resultingVector.magnitude, 2);
resultingVector *= (1.0f + (float)avgEdgeDistance) / 2.0f;
newVertices.Add(resultingVector);
}
return(newVertices);
}
/**
* A helper method for threshold-based termination in both planarizing and
* adjusting. If a vertex moves by an unexpectedly large amount, or if the
* new vertex position has an NaN component, the algorithm automatically
* terminates.
*
* @param poly The polyhedron to canonicalize.
* @param threshold The threshold of vertex movement after an iteration.
* @param planarize True if we are planarizing, false if we are adjusting.
* @return The number of iterations that were executed.
*/
private static int _Canonicalize(ConwayPoly poly, double threshold, bool planarize)
{
var dual = poly.Dual();
var currentPositions = poly.Vertices.Select(x => x.Position).ToList();
int iterations = 0;
while (true)
{
var newDualPositions = planarize ? ReciprocalVertices(poly) : ReciprocalCenters(poly);
dual.SetVertexPositions(newDualPositions);
var newPositions = planarize ? ReciprocalVertices(dual) : ReciprocalCenters(dual);
double maxChange = 0.0;
for (int i = 0; i < currentPositions.Count; i++)
{
var newPos = poly.Vertices[i].Position;
var diff = newPos - currentPositions[i];
maxChange = Math.Max(maxChange, diff.magnitude);
}
// Check if an error occurred in computation. If so, terminate
// immediately
if (Double.IsNaN(newPositions[0].x) || Double.IsNaN(newPositions[0].y) ||
Double.IsNaN(newPositions[0].z))
{
break;
}
// Check if the position changed by a significant amount so as to
// be erroneous. If so, terminate immediately
if (planarize && maxChange > MAX_VERTEX_CHANGE)
{
break;
}
poly.SetVertexPositions(newPositions);
if (maxChange < threshold)
{
break;
}
currentPositions = poly.Vertices.Select(x => x.Position).ToList();
iterations++;
}
return(iterations);
}
/**
* Canonicalizes this polyhedron until the change in position does not
* exceed the given threshold. That is, the algorithm terminates when no vertex
* moves more than the threshold after one iteration.
*
* @param thresholdAdjust The threshold for change in one "adjust"
* iteration.
* @param thresholdPlanarize The threshold for change in one "planarize"
* iteration.
* @return The canonicalized version of this polyhedron.
*/
public ConwayPoly Canonicalize(double thresholdAdjust, double thresholdPlanarize)
{
var previousFaceRoles = FaceRoles;
var previousVertexRoles = VertexRoles;
ConwayPoly canonicalized = Duplicate();
if (thresholdAdjust > 0)
{
Adjust(canonicalized, thresholdAdjust);
}
if (thresholdPlanarize > 0)
{
Planarize(canonicalized, thresholdPlanarize);
}
canonicalized.FaceRoles = previousFaceRoles;
canonicalized.VertexRoles = previousVertexRoles;
return(canonicalized);
}
/**
* Modifies a polyhedron's vertices such that faces are closer to planar.
* The more iterations, the closer the faces are to planar. If a vertex
* moves by an unexpectedly large amount, or if the new vertex position
* has an NaN component, the algorithm automatically terminates.
*
* @param poly The polyhedron whose faces to planarize.
* @param numIterations The number of iterations to planarize for.
*/
public static void Planarize(ConwayPoly poly, int numIterations)
{
var dual = poly.Dual();
for (int i = 0; i < numIterations; i++)
{
var newDualPositions = ReciprocalVertices(poly);
dual.SetVertexPositions(newDualPositions);
var newPositions = ReciprocalVertices(dual);
double maxChange = 0.0;
for (int j = 0; j < poly.Vertices.Count; j++)
{
var newPos = poly.Vertices[j].Position;
var diff = newPos - poly.Vertices[j].Position;
maxChange = Math.Max(maxChange, diff.magnitude);
}
// Check if an error occurred in computation. If so, terminate
// immediately. This likely occurs when faces are already planar.
if (Double.IsNaN(newPositions[0].x) || Double.IsNaN(newPositions[0].y) ||
Double.IsNaN(newPositions[0].z))
{
break;
}
// Check if the position changed by a significant amount so as to
// be erroneous. If so, terminate immediately
if (maxChange > MAX_VERTEX_CHANGE)
{
break;
}
poly.SetVertexPositions(newPositions);
}
}
/**
* Canonicalizes a polyhedron by adjusting its vertices iteratively. When
* no vertex moves more than the given threshold, the algorithm terminates.
*
* @param poly The polyhedron whose vertices to adjust.
* @param threshold The threshold of vertex movement after an iteration.
* @return The number of iterations that were executed.
*/
public static int Adjust(ConwayPoly poly, double threshold)
{
return(_Canonicalize(poly, threshold, false));
}
public MeshFaceList(ConwayPoly conwayPoly)
{
_mConwayPoly = conwayPoly;
}
/**
* Modifies a polyhedron's vertices such that faces are closer to planar.
* When no vertex moves more than the given threshold, the algorithm
* terminates.
*
* @param poly The polyhedron to canonicalize.
* @param threshold The threshold of vertex movement after an iteration.
* @return The number of iterations that were executed.
*/
public static int Planarize(ConwayPoly poly, double threshold)
{
return(_Canonicalize(poly, threshold, true));
}
/// <summary>
/// Convenience constructor, for use outside of the mesh class
/// </summary>
public MeshVertexList() : base()
{
_mConwayPoly = null;
}
/// <summary>
/// Creates a vertex list that is aware of its parent mesh
/// </summary>
/// <param name="conwayPoly"></param>
public MeshVertexList(ConwayPoly conwayPoly) : base()
{
_mConwayPoly = conwayPoly;
}
/// <summary>
/// Convenience constructor, for use outside of the mesh class
/// </summary>
public MeshHalfedgeList()
{
_mConwayPoly = null;
}
/// <summary>
/// Creates a halfedge list that is aware of its parent mesh
/// </summary>
/// <param name="conwayPoly"></param>
public MeshHalfedgeList(ConwayPoly conwayPoly)
: base()
{
_mConwayPoly = conwayPoly;
}
public float GetValueB(ConwayPoly poly, int index) => funcB?.Invoke(new FilterParams(poly, index)) ?? valueB;
