/**
* 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 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);
}
/**
* 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);
}
}