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MeshUtils.prejava
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#include "macros.h"
import com.donhatchsw.compat.ArrayList;
import com.donhatchsw.compat.IntArrayList;
import com.donhatchsw.util.Arrays;
import com.donhatchsw.util.ConvexHull;
import com.donhatchsw.util.FuzzyPointHashSet;
import com.donhatchsw.util.MergeFind;
import com.donhatchsw.util.MyMath;
import com.donhatchsw.util.SortStuff;
import com.donhatchsw.util.VecMath;
final public class MeshUtils
{
private MeshUtils(){ throw new AssertionError(); } // non-instantiatable util class
public static double[][/*2*/] getMeshVertsXY(Mesh mesh)
{
int nVerts = mesh.verts.size();
double answer[][] = new double[nVerts][2];
FORI (iVert, nVerts)
{
Mesh.Vertex v = mesh.getVert(iVert);
answer[iVert][0] = v.x();
answer[iVert][1] = v.y();
}
return answer;
}
public static double[][/*3*/] getMeshVertsXYH(Mesh mesh)
{
int nVerts = mesh.verts.size();
double answer[][] = new double[nVerts][3];
FORI (iVert, nVerts)
{
Mesh.Vertex v = mesh.getVert(iVert);
answer[iVert][0] = v.x();
answer[iVert][1] = v.y();
answer[iVert][2] = v.h();
}
return answer;
}
public static double[][/*3*/] getMeshVertsXYZW(Mesh mesh)
{
int nVerts = mesh.verts.size();
double answer[][] = new double[nVerts][4];
FORI (iVert, nVerts)
{
Mesh.Vertex v = mesh.getVert(iVert);
answer[iVert][0] = v.X();
answer[iVert][1] = v.Y();
answer[iVert][2] = v.Z();
answer[iVert][3] = v.W();
}
return answer;
}
// If canonicalOrder flag, order each face so that least-index vertex is first,
// and then sort faces by increasing size and then increasing contents.
// and then sort faces by increasing size and then contents.
public static int[][] getMeshFaces(Mesh mesh, boolean canonicalOrderFlag)
{
boolean seenEdge[] = new boolean[mesh.edges.size()]; // all false initially
int[][] faces = new int[mesh.edges.size()][];
int[] scratchFace = new int[mesh.edges.size()]; // probably safer than mesh.verts.size()
int nFaces = 0;
FORIDOWN(iEdge, mesh.edges.size())
{
if (seenEdge[iEdge]) continue;
Mesh.Edge edge0 = mesh.getEdge(iEdge);
int faceSize = 0;
Mesh.Edge edge = edge0;
do {
seenEdge[edge.myIndex()] = true;
scratchFace[faceSize++] = edge.initialVertex().myIndex();
} while ((edge = edge.next()) != edge0);
faces[nFaces++] = (int[])Arrays.subarray(scratchFace, 0, faceSize);
}
faces = (int[][])Arrays.subarray(faces, 0, nFaces);
if (canonicalOrderFlag)
{
FORIDOWN(iFace, faces.length)
{
int face[] = faces[iFace];
int mini = VecMath.mini(face);
System.arraycopy(face, mini,
scratchFace, 0,
face.length - mini);
System.arraycopy(face, 0,
scratchFace, face.length - mini,
mini);
System.arraycopy(scratchFace, 0,
face, 0,
face.length);
}
SortStuff.sort(faces, new SortStuff.Comparator() {
@Override public int compare(Object a, Object b)
{
// TODO: call it aFace, bFace
int aFace[] = (int[])a;
int bFace[] = (int[])b;
if (aFace.length < bFace.length) return -1;
if (aFace.length > bFace.length) return 1;
for (int i = 0; i < aFace.length; ++i)
{
if (aFace[i] < bFace[i]) return -1;
if (aFace[i] > bFace[i]) return 1;
}
return 0;
}
});
}
return faces;
} // getMeshFaces
// CBB: assumes mesh is triangulated
public static int[] findPrimalFaceFromDualVert(Mesh mesh, Mesh dualMesh, int iDualVert)
{
int nEdges = dualMesh.edges.size();
CHECK_EQ(nEdges, mesh.edges.size());
FORI (iEdge, nEdges)
{
Mesh.Edge dualEdge = dualMesh.getEdge(iEdge);
Mesh.Vertex initialVertex = dualEdge.initialVertex();
if (initialVertex != null
&& initialVertex.myIndex() == iDualVert)
{
Mesh.Edge primalEdge = (mesh.getEdge(iEdge)).opposite();
assumpt(primalEdge.next().next().next() == primalEdge);
// advance around triangle til initial vertex is smallest
while (primalEdge.initialVertex().myIndex() > primalEdge.finalVertex().myIndex()
|| primalEdge.initialVertex().myIndex() > primalEdge.prev().initialVertex().myIndex())
primalEdge = primalEdge.next();
int i0 = primalEdge.initialVertex().myIndex();
int i1 = primalEdge.finalVertex().myIndex();
int i2 = primalEdge.prev().initialVertex().myIndex();
return new int[] {i0,i1,i2};
}
}
return null;
} // findPrimalFaceFromDualVert
private static double detDouble(int n, java.math.BigInteger M[/*n*/][/*n*/])
{
int verboseLevel = 1;
if (verboseLevel >= 1) OUT(" in detDouble(n="+n+")");
long t0millis = System.currentTimeMillis();
double Mdouble[][] = new double[n][n];
for (int i = 0; i < n; ++i)
for (int j = 0; j < n; ++j)
Mdouble[i][j] = M[i][j].doubleValue();
double answer = VecMath.detDestructive(Mdouble);
long t1millis = System.currentTimeMillis();
if (verboseLevel >= 1) OUT(" out detDouble(n="+n+"), returning "+answer+" in "+(t1millis-t0millis)/1000.+" secs.");
return answer;
}
// https://en.wikipedia.org/wiki/Bareiss_algorithm
// http://www.ams.org/journals/mcom/1968-22-103/S0025-5718-1968-0226829-0/S0025-5718-1968-0226829-0.pdf
// http://cs.nyu.edu/exact/core/download/core_v1.4/core_v1.4/progs/bareiss/bareiss.cpp
// Crazy good and simple! I was previously reducing to upper-triangular form using egcd at each step,
// but it was way more complicated and blew up unless I did strange heuristics.
// Hmm, it claims to do pivoting, but doesn't, and suffers from zero-divides.
// there's some analysis here:
// http://www.math.usm.edu/perry/Research/Thesis_DRL.pdf
/*
double Matrix::determinant() const {
Matrix A = *this;
double det;
int i, j, k;
for (i = 0; i < n-1; i++) {
// CHECK_EQ(a(i, i), 0);
for (j = i + 1; j < n; j++)
for (k = i + 1; k < n; k++) {
A(j,k) = (A(j,k)*A(i,i)-A(j,i)*A(i,k));
if (i) A(j, k) /= A(i-1,i-1);
}
}
return A(n-1,n-1);
}
*/
private static java.math.BigInteger detDestructive(int n, java.math.BigInteger M[][])
{
int verboseLevel = 0;
if (verboseLevel >= 1) OUT(" in detDestructive(n="+n+")");
long t0millis = System.currentTimeMillis();
int maxBitLength = 0;
java.math.BigInteger answer;
if (n == 0)
answer = java.math.BigInteger.ONE;
else
{
int sign = 1;
FORI (i, n-1)
{
if (M[i][i].signum() == 0)
{
// "standard workaround" for zero-divide in bareiss's algorithm, according to thesis.
// algorithm is on p.26, this comment is on p.34.
// Swap with any row that will make this entry nonzero.
int jPivot = -1;
for (int j = i+1; j < n; ++j)
if (M[j][i].signum() != 0)
{
jPivot = j;
break;
}
if (jPivot == -1)
return java.math.BigInteger.ZERO;
OUT("HEY! working around bareiss problem");
java.math.BigInteger temp[];
SWAP(M[i], M[jPivot], temp);
sign *= -1;
}
//CHECK_EQ(M[i][i].signum(), 0); XXX what is this?? it fails
for (int j = i+1; j < n; ++j)
for (int k = i+1; k < n; ++k)
{
// jk = jk*ii-ji*ik
M[j][k] = M[j][k].multiply(M[i][i]).subtract(M[j][i].multiply(M[i][k]));
maxBitLength = MAX(maxBitLength, M[j][k].bitLength());
if (i > 0)
{
java.math.BigInteger quotientAndRemainder[/*2*/] = M[j][k].divideAndRemainder(M[i-1][i-1]);
M[j][k] = quotientAndRemainder[0];
CHECK_EQ(quotientAndRemainder[1].signum(), 0);
// that didn't increase the bitlength, so don't need to update maxBitLength
}
}
}
answer = M[n-1][n-1];
if (sign < 0)
answer = answer.negate();
}
long t1millis = System.currentTimeMillis();
if (verboseLevel >= 1) OUT(" maxBitLength = "+maxBitLength);
if (verboseLevel >= 1) OUT(" out detDestructive(n="+n+"), returning "+answer+" in "+(t1millis-t0millis)/1000.+" secs.");
return answer;
} // detDestructive
private static java.math.BigInteger[][] copymat(int nRows, int nCols, java.math.BigInteger M[][])
{
java.math.BigInteger answer[][] = new java.math.BigInteger[nRows][nCols];
FORI (iRow, nRows)
FORI (iCol, nCols)
answer[iRow][iCol] = M[iRow][iCol];
return answer;
}
private static java.math.BigInteger det(int n, java.math.BigInteger M[][])
{
return detDestructive(n, copymat(n, n, M));
} // det
private static java.math.BigInteger det(int n, long M[][])
{
java.math.BigInteger bigM[][] = new java.math.BigInteger[n][n];
FORI (i, n)
FORI (j, n)
bigM[i][j] = java.math.BigInteger.valueOf(M[i][j]);
return detDestructive(n, bigM);
}
private static double detDouble(int n, long M[][])
{
double Mdouble[][] = new double[n][n];
FORI (i, n)
FORI (j, n)
Mdouble[i][j] = (double)M[i][j];
return VecMath.detDestructive(Mdouble);
}
private static java.math.BigInteger det(long M[][])
{
return det(M.length, M);
}
public static int detConfidenceTest1(long M[][])
{
java.math.BigInteger detBig = det(M);
double detDouble = detDouble(M.length, M);
boolean same = EQ(detBig.doubleValue(), detDouble, 1e-12);
OUT(" det("+Arrays.toStringCompact(M)+") = "+detBig+" "+(same?"==":"!=")+" "+detDouble+" "+(same?"yay!":" OH NO!!!!!!!!!!!!!"));
int nFailures = same ? 0 : 1;
return nFailures;
}
public static void detConfidenceTest()
{
int nFailures = 0;
// Nonzero determinant
nFailures += detConfidenceTest1(new long[][]{});
nFailures += detConfidenceTest1(new long[][]{{1}});
nFailures += detConfidenceTest1(new long[][]{{2}});
nFailures += detConfidenceTest1(new long[][]{{-1}});
nFailures += detConfidenceTest1(new long[][]{{1,0},{0,1}});
nFailures += detConfidenceTest1(new long[][]{{1,2},{3,4}});
nFailures += detConfidenceTest1(new long[][]{{0,1},{1,0}});
nFailures += detConfidenceTest1(new long[][]{{1,0,0},{0,1,0},{0,0,1}});
nFailures += detConfidenceTest1(new long[][]{{1,0,0},{0,0,1},{0,1,0}});
// Example from the thesis cited above, where bareiss leads to zero-divide. answer is 245.
nFailures += detConfidenceTest1(new long[][]{
{1,-4,1,2},
{-1,4,4,1},
{3,3,3,4},
{2,5,2,-1},
});
// Nonzero determinant, messes up without pivoting
nFailures += detConfidenceTest1(new long[][]{{0,1,0},{0,0,1},{1,0,0}}); // messes up!
nFailures += detConfidenceTest1(new long[][]{{0,1,0},{1,0,0},{0,0,1}});
nFailures += detConfidenceTest1(new long[][]{{0,0,1},{1,0,0},{0,1,0}});
nFailures += detConfidenceTest1(new long[][]{{0,0,1},{0,1,0},{1,0,0}});
// Zero determinant
nFailures += detConfidenceTest1(new long[][]{{0}});
nFailures += detConfidenceTest1(new long[][]{{0,0},{0,0}});
nFailures += detConfidenceTest1(new long[][]{{1,0},{0,0}});
nFailures += detConfidenceTest1(new long[][]{{0,1},{0,0}});
nFailures += detConfidenceTest1(new long[][]{{0,0},{1,0}});
nFailures += detConfidenceTest1(new long[][]{{0,0},{0,1}});
nFailures += detConfidenceTest1(new long[][]{{0,0,0},{0,0,0},{0,0,0}});
nFailures += detConfidenceTest1(new long[][]{{1,2,3},{4,5,6},{0,0,0}});
nFailures += detConfidenceTest1(new long[][]{{1,1,1},{2,2,2},{3,3,3}});
if (true)
{
for (int n = 1; n <= 4; ++n)
{
FORI (i, 1<<(n*n))
{
long M[][] = new long[n][n];
FORI (j, n*n)
M[j/n][j%n] = BIT(i, j);
nFailures += detConfidenceTest1(M);
}
}
}
CHECK_EQ(nFailures, 0);
OUT("detConfidenceTest PASSED! hooray!");
}
// Uses Kirchoff's theorem. https://en.wikipedia.org/wiki/Kirchhoff%27s_theorem,
// with Bareiss's algorithm for exact integer determinant.
public static java.math.BigInteger countSpanningTrees(Mesh mesh, boolean withAnalysis)
{
SimplerMeshDataStructure simplerMeshDataStructure = new SimplerMeshDataStructure(mesh, /*mergeInsideOutVertsIntoInfiniteVert=*/false);
int v2e[][] = simplerMeshDataStructure.v2e;
int e2v[][] = simplerMeshDataStructure.e2v;
return countSpanningTrees(v2e.length, e2v, withAnalysis);
} // countSpanningTrees
public static java.math.BigInteger countSpanningTrees(int nVerts, int e2v[][], boolean withAnalysis)
{
if (withAnalysis) OUT(" in countSpanningTrees");
if (withAnalysis) OUT(" nVerts="+nVerts);
if (withAnalysis) OUT(" e2v="+Arrays.toStringCompact(e2v));
if (nVerts == 0) return java.math.BigInteger.ZERO; // special case to avoid determinant of size -1
java.math.BigInteger laplacianCofactor[][] = new java.math.BigInteger[nVerts-1][nVerts-1];
for (int i = 0; i < laplacianCofactor.length; ++i)
for (int j = 0; j < laplacianCofactor[0].length; ++j)
laplacianCofactor[i][j] = java.math.BigInteger.ZERO;
int nEdges = e2v.length;
for (int iEdge = 0; iEdge < nEdges; ++iEdge)
{
int i0 = e2v[iEdge][0];
int i1 = e2v[iEdge][1];
if (i0 != i1) // self-loops are irrelevant
{
if (i0 != nVerts-1) // if in range
{
laplacianCofactor[i0][i0] = laplacianCofactor[i0][i0].add(java.math.BigInteger.ONE);
if (i1 != nVerts-1) // if in range
laplacianCofactor[i0][i1] = laplacianCofactor[i0][i1].subtract(java.math.BigInteger.ONE);
}
}
}
if (withAnalysis)
{
PRINTMAT(laplacianCofactor);
double detDouble = detDouble(nVerts-1, laplacianCofactor);
OUT(" detDouble="+detDouble);
CHECK_GE(detDouble, 0);
java.math.BigInteger detBigInt = det(nVerts-1, laplacianCofactor);
OUT(" detBigInt="+detBigInt);
OUT(" detBigInt.doubleValue()="+detBigInt.doubleValue());
OUT(" detDouble="+detDouble); // again
CHECK_GE(detBigInt.signum(), 0);
CHECK_ALMOST_EQ_REL(detBigInt.doubleValue(), detDouble, 1e-12);
OUT(" out countSpanningTrees, returning "+detBigInt);
return detBigInt;
}
else
{
return detDestructive(nVerts-1, laplacianCofactor);
}
} // countSpanningTrees
// TODO: this paper: https://pdfs.semanticscholar.org/208b/71b285804d96897731d41f9a4079d0523068.pdf
// says "Colbourn et al. in [9] have proposed an algorithm which runs in O(n^2) time for an n-vertex planar graph!"
// The Colbourn paper is:
// C.J. Colbourn, J.S. Provan, and D. Vertigan: A new approach to solving three combinatorial enumeration problems on planar graphs. Discrete Appl. Math. 60, 119–129 (1995)
// Cool, found it here: http://www.sciencedirect.com/science/article/pii/0166218X95E01113
// So let's code it up!
// Oh argh, does it not use integer arithmetic? I'm afraid this will blow up immensely.
// Ah I see, they claim O(n log n) digits accuracy is sufficient. Hmm.
//
// Okay how do I guide the search?
// Can't seem to find any of the papers that show how to reduce any planar graph
// in O(n^2) operations, but there is this: https://en.wikipedia.org/wiki/Y-%CE%94_transform
// which gives some clues...
// Oh wait! Check out http://www.wikiwand.com/en/Steinitz's_theorem .
// It says any convex polyhedron can be transformed to a tetrahedron
// by delta-Y and Y-deltas?
public static void messAroundWithDeltaWye(Mesh mesh)
{
int verboseLevel = 2;
if (verboseLevel >= 1) OUT(" in messAroundWithDeltaWye");
if (verboseLevel >= 3) OUT(" mesh = "+mesh);
if (false) mesh.sanityCheckTopology(); // XXX woops! dual mesh flunks because of the null endpoints!
Mesh scratchMesh = new Mesh(mesh);
if (verboseLevel >= 3) OUT(" scratchMesh = "+scratchMesh);
if (false) scratchMesh.sanityCheckTopology(); // XXX woops! dual mesh flunks because of the null endpoints!
// Hack-- get rid of that nonexistent vertex.
// (CBB: should something like this be in Mesh?)
{
int nEdges = scratchMesh.edges.size();
boolean hasInfiniteVertex = false;
FORI (iEdge, nEdges)
if (scratchMesh.getEdge(iEdge).initialVertex() == null)
{
hasInfiniteVertex = true;
break;
}
if (hasInfiniteVertex)
{
Mesh.Vertex vert = scratchMesh.newVertex(0.,0.,0.,0.); // meaningless
FORI (iEdge, nEdges)
{
Mesh.Edge edge = scratchMesh.getEdge(iEdge);
if (edge.initialVertex() == null)
edge.setInitialVertex(vert);
}
if (verboseLevel >= 3) OUT(" after fixing: scratchMesh = "+scratchMesh);
}
FORI (iEdge, nEdges)
{
CHECK_NE(scratchMesh.getEdge(iEdge).initialVertex(), null);
CHECK_NE(scratchMesh.getEdge(iEdge).next(), null);
}
}
scratchMesh.sanityCheckTopology(); // finally it's sane
while (true)
{
if (verboseLevel >= 2) OUT(" top of loop: nVerts="+scratchMesh.verts.size()+" nEdges="+scratchMesh.edges.size());
// Always go from simpler to more complicated,
// so that we don't get confused, e.g. a pendant satisfies condition of a series
// reduction.
// loop deletion
{
if (verboseLevel >= 2) OUT(" checking for loops...");
Mesh.Edge loop = null;
{
int nEdges = scratchMesh.edges.size();
FORI (iEdge, nEdges)
{
Mesh.Edge edge = scratchMesh.getEdge(iEdge);
if (edge.initialVertex() == edge.finalVertex())
{
loop = edge;
break;
}
}
}
if (loop != null)
{
if (verboseLevel >= 2) OUT(" found a loop! deleting it");
scratchMesh.deleteEdge(loop);
continue;
}
}
// pendant edge deletion
{
if (verboseLevel >= 2) OUT(" checking for pendants...");
Mesh.Edge pendant = null;
{
int nEdges = scratchMesh.edges.size();
FORI (iEdge, nEdges)
{
Mesh.Edge edge = scratchMesh.getEdge(iEdge);
Mesh.Edge nextEdge = edge.next();
CHECK_NE(nextEdge, edge); // since no loops
CHECK_EQ(nextEdge==edge.opposite(),
edge.finalVertex().arity == 1);
if (edge.finalVertex().arity == 1)
{
pendant = edge;
break;
}
}
}
if (pendant != null)
{
if (verboseLevel >= 2) OUT(" found a pendant! deleting it");
Mesh.Vertex vert = pendant.finalVertex();
// just deleting the vert would do it, but deleting the edge first
// is potentially more efficient
CHECK_EQ(vert.arity, 1);
scratchMesh.deleteEdge(pendant);
CHECK_EQ(vert.arity, 0);
scratchMesh.deleteVertex(vert, null, null);
continue;
}
}
// parallel reduction
{
if (verboseLevel >= 2) OUT(" checking for parallels...");
Mesh.Edge parallel = null;
{
int nEdges = scratchMesh.edges.size();
FORI (iEdge, nEdges)
{
Mesh.Edge edge = scratchMesh.getEdge(iEdge);
Mesh.Edge nextEdge = edge.next();
CHECK_NE(nextEdge, edge); // since no loops
CHECK_NE(nextEdge, edge.opposite()); // since no pendants
if (nextEdge.finalVertex() == edge.initialVertex())
{
parallel = edge;
break;
}
}
}
if (parallel != null)
{
if (verboseLevel >= 2) OUT(" found a parallel! "+parallel+" deleting it");
scratchMesh.deleteEdge(parallel);
continue;
}
}
// series reduction
{
if (verboseLevel >= 2) OUT(" checking for serieses...");
Mesh.Edge seriesStart = null;
{
int nEdges = scratchMesh.edges.size();
FORI (iEdge, nEdges)
{
Mesh.Edge edge = scratchMesh.getEdge(iEdge);
Mesh.Edge nextEdge = edge.next();
CHECK_NE(nextEdge, edge); // since no loops
CHECK_NE(nextEdge, edge.opposite()); // since no pendants
CHECK_NE(nextEdge.finalVertex(), edge.initialVertex()); // since no parallels
CHECK_EQ(edge.next().opposite().next().opposite()==edge,
edge.finalVertex().arity == 2);
if (edge.finalVertex().arity == 2)
{
seriesStart = edge;
break;
}
}
}
if (seriesStart != null)
{
if (verboseLevel >= 2) OUT(" found a series! deleting it");
if (verboseLevel >= 3) OUT(" before: "+scratchMesh);
// create a replacement edge,
// then delete the two originals and the vertex.
scratchMesh.sanityCheckTopology();
Mesh.Edge shortCut = scratchMesh.newEdge(true);
// can't call sanityCheckTopology again until after connected both endpoints
// see picture at insertEdgeBefore
CHECK_EQ(shortCut.prev(), shortCut.opposite());
scratchMesh.insertEdgeBefore(shortCut, seriesStart);
CHECK_NE(shortCut.prev(), shortCut.opposite());
CHECK_EQ(shortCut.opposite().prev(), shortCut);
scratchMesh.insertEdgeBefore(shortCut.opposite(), seriesStart.next().next());
scratchMesh.sanityCheckTopology();
Mesh.Vertex vert = seriesStart.finalVertex();
CHECK_EQ(vert.arity, 2);
scratchMesh.deleteEdge(seriesStart.next());
CHECK_EQ(vert.arity, 1);
scratchMesh.deleteEdge(seriesStart);
CHECK_EQ(vert.arity, 0);
scratchMesh.deleteVertex(vert, null, null);
scratchMesh.sanityCheckTopology();
if (verboseLevel >= 3) OUT(" after: "+scratchMesh);
continue;
}
}
// wye-delta transformation
{
if (verboseLevel >= 2) OUT(" checking for wyes...");
Mesh.Edge towardsWye = null;
{
int nEdges = scratchMesh.edges.size();
FORI (iEdge, nEdges)
{
Mesh.Edge edge = scratchMesh.getEdge(iEdge);
CHECK_EQ(edge.next().opposite().next().opposite().next().opposite()==edge,
edge.finalVertex().arity == 3);
if (edge.finalVertex().arity == 3)
{
towardsWye = edge;
break;
}
}
}
if (towardsWye != null)
{
if (verboseLevel >= 2) OUT(" found a wye! changing it to a delta");
Mesh.Edge A = towardsWye;
Mesh.Edge B = A.next().opposite();
Mesh.Edge C = B.next().opposite();
CHECK_EQ(A, C.next().opposite());
Mesh.Edge AB = scratchMesh.newEdge(true);
Mesh.Edge BC = scratchMesh.newEdge(true);
Mesh.Edge CA = scratchMesh.newEdge(true);
scratchMesh.insertEdgeBefore(AB, A);
scratchMesh.insertEdgeBefore(BC, B);
scratchMesh.insertEdgeBefore(CA, C);
scratchMesh.insertEdgeBefore(AB.opposite(), B.opposite().next());
scratchMesh.insertEdgeBefore(BC.opposite(), C.opposite().next());
scratchMesh.insertEdgeBefore(CA.opposite(), A.opposite().next());
scratchMesh.sanityCheckTopology();
Mesh.Vertex vert = A.finalVertex();
CHECK_EQ(vert.arity, 3);
scratchMesh.deleteEdge(A);
CHECK_EQ(vert.arity, 2);
scratchMesh.deleteEdge(B);
CHECK_EQ(vert.arity, 1);
scratchMesh.deleteEdge(C);
CHECK_EQ(vert.arity, 0);
scratchMesh.deleteVertex(vert, null, null);
scratchMesh.sanityCheckTopology();
continue;
}
}
break; // didn't find any of the constructs
}
if (verboseLevel >= 1) OUT(" out messAroundWithDeltaWye");
} // messAroundWithDeltaWye
// Simpler mesh data structure, suitable for running
// the algorithm from David Bruce Wilson
// "Generating Random Spanning Trees More Quickly than the Cover Time".
//
// Subtleties:
// - Depending on how original mesh was constructed,
// it might have edges leading nowhere or coming from nowhere.
// In this case, the "nowhere" gets made into an extra vertex (the "infinite vertex").
// - We might or might not want to consider all inside-out vertices
// (i.e. those with weight < 0) to be part of the infinite vertex.
// This is a param to the constructor.
// If true, such vertices get merged into the infinite vertex (which gets created if necessary),
// and the original entries of v2e end up empty.
// CBB: tell me again why I need the param? doesn't true always work? I'm confused.
// Let's get it straight:
// Calc underside = false (the usual case I work with):
// - primal mesh (mostly triangulated) has standard topology, nVerts is unambiguous, all verts rightside out
// mergeInsideOutVertsIntoInfiniteVert=false: gives the mesh, unambiguous
// mergeInsideOutVertsIntoInfiniteVert=true: gives the mesh, unambiguous
// - dual has some edges to nowhere, so converting to standard topology requires adding a vert. all other verts rightside out
// mergeInsideOutVertsIntoInfiniteVert=false: gives the mesh with one vertex added
// mergeInsideOutVertsIntoInfiniteVert=true: gives the mesh with one vertex added
// Calc underside = true:
// - primal mesh straightforward, as before (except fully triangulated)
// - dual mesh has standard topology, but some verts are inside out.
// mergeInsideOutVertsIntoInfiniteVert=false: gives the mesh
// mergeInsideOutVertsIntoInfiniteVert=true: adds a vertex (since there was at least one inside out), transfers all edges incident
// on inside out verts to the added vertex instead, leaving empty entries in v2e.
// Note that the resulting structure is not dual to that for the primal mesh!
// TL;DR: mergeInsideOutVertsIntoInfiniteVert is never relevant for primal,
// it's relevant only for dual, and then only when "calc underside" is on.
public static class SimplerMeshDataStructure
{
public int v2e[/*nVerts*/][]; // vert to edges out, CCW if next pointers go CW around face, and vice versa.
public int e2v[/*nEdges*/][/*2*/]; // edge to verts
// Note, we allow multigraphs and loops
public static void sanityCheck(int v2e[][], int e2v[][])
{
int nVerts = v2e.length;
int nEdges = e2v.length;
CHECK_EQ(nEdges % 2, 0);
FORI (iEdge, nEdges)
{
CHECK_EQ(e2v[iEdge][0], e2v[iEdge^1][1]); // other gets checked on the other one
}
FORI (iEdge, nEdges)
{
int iVert = e2v[iEdge][0];
int jVert = e2v[iEdge][1];
CHECK_LE_LT(0, iVert, nVerts);
CHECK_LE_LT(0, jVert, nVerts);
}
int sumOfArities = 0;
FORI (iVert, nVerts)
{
FORI (j, v2e[iVert].length)
{
int iEdge = v2e[iVert][j];
CHECK_LE_LT(0, iEdge, nEdges);
CHECK_EQ(e2v[iEdge][0], iVert);
}
sumOfArities += v2e[iVert].length;
}
CHECK_EQ(sumOfArities, nEdges);
} // sanityCheck
public SimplerMeshDataStructure(Mesh mesh, boolean mergeInsideOutVertsIntoInfiniteVert)
{
int nVerts = mesh.verts.size(); // may add 1 though
int nEdges = mesh.edges.size();
this.e2v = new int[nEdges][2];
int e2next[] = new int[nEdges];
boolean infiniteVertUsed = false; // until proven otherwise
FORI (iEdge, nEdges)
{
Mesh.Edge edge = mesh.getEdge(iEdge);
CHECK_EQ(edge.myIndex(), iEdge);
CHECK_EQ(edge.opposite().myIndex(), (iEdge^1));
Mesh.Vertex v0 = edge.initialVertex();
Mesh.Vertex v1 = edge.finalVertex();
if (v0 == null || v1 == null)
infiniteVertUsed = true;
int i0 = v0==null ? nVerts : v0.myIndex();
int i1 = v1==null ? nVerts : v1.myIndex();
e2v[iEdge][0] = i0;
e2v[iEdge][1] = i1;
Mesh.Edge next = edge.next();
if (next == null)
{
// final vertex is the infinite one; to find next, need to walk backwards around the face
next = edge;
while (next.prev() != null)
next = next.prev();
}
e2next[iEdge] = next.myIndex();
}
if (mergeInsideOutVertsIntoInfiniteVert)
{
boolean isInsideOut[] = new boolean[nVerts+1];
FORI (iVert, nVerts)
isInsideOut[iVert] = (mesh.getVert(iVert).weight < 0);
isInsideOut[nVerts] = true; // the infinite one, if any
//PRINTVEC(isInsideOut);
FORI (iEdge, nEdges)
FORI (iVertThisEdge, 2)
{
if (isInsideOut[e2v[iEdge][iVertThisEdge]])
{
e2v[iEdge][iVertThisEdge] = nVerts;
infiniteVertUsed = true;
}
}
// Note that it may be that some original verts are now unused in e2v
}
if (infiniteVertUsed)
nVerts++;
this.v2e = new int[nVerts][];
{
int arities[] = new int[nVerts]; // zeros initially
FORI (iEdge, nEdges)
arities[e2v[iEdge][0]]++;
FORI (iVert, nVerts)
{
v2e[iVert] = new int[arities[iVert]];
arities[iVert] = 0;
}
if (false)
{
// Simple way, edges don't come out in any particular order.
FORI (iEdge, nEdges)
{
int iVert = e2v[iEdge][0];
v2e[iVert][arities[iVert]++] = iEdge;
}
}
else
{
// Edges come out in order, following the mesh's ->opp->next pointers.
// I.e. CCW if next pointers go CW around face,
// and vice versa.
// CBB: I don't think I really need this bit array; could instead just clear
// entries in e2next or something. But that would be more complicated.
boolean edgeDone[] = new boolean[nEdges]; // all false initially
FORI(iEdge0, nEdges)
{
for (int iEdge = iEdge0; !edgeDone[iEdge]; iEdge = e2next[iEdge^1])
{
edgeDone[iEdge] = true;
int iVert = e2v[iEdge][0];
v2e[iVert][arities[iVert]++] = iEdge;
}
}
}
// sanity check
FORI (iVert, nVerts)
{
CHECK_EQ(v2e[iVert].length, arities[iVert]);
FORI (iEdgeOut, v2e[iVert].length)
CHECK_EQ(e2v[v2e[iVert][iEdgeOut]][0], iVert);
}
}
} // SimplerMeshDataStructure ctor
// CBB: also have isConnected() above... silly, maybe.
// Isolated here apparently means *no incident edges*
// (not even self-loops).
public boolean isConnectedExceptMaybeForIsolatedVerts()
{
// BFS or DFS is actually faster supposedly but whatever
int nVerts = v2e.length;
int nEdges = e2v.length;
MergeFind mergeFind = new MergeFind(nVerts);
FORI (iEdge, nEdges)
{
int iVert = e2v[iEdge][0];
int jVert = e2v[iEdge][1];
mergeFind.merge(iVert, jVert);
// CBB: if we use a SizeTrackingMergeFind, can notice as soon as there's a single component, and return true. but would have to count number of non-isolated verts first
}
int found = -1;
FORI (iVert, nVerts)
{
if (v2e[iVert].length == 0) continue; // vertex got removed (or was isolated)
if (found == -1)
found = mergeFind.find(iVert);
else if (mergeFind.find(iVert) != found)
return false;
}
return true;
} // isConnectedExceptMaybeForIsolatedVerts
// Do not call this unless connected! (in the sense that isConnectedExceptMaybeForIsolatedVerts returns).
public boolean[/*nEdges/2*/] randomSpanningTree(java.util.Random generator)
{
if (e2v.length == 0)
return new boolean[0];
// Use uniform random spanning tree algorithm, from David Bruce Wilson
// "Generating Random Spanning Trees More Quickly than the Cover Time"
// Must start with random vertex of random edge.
int r = e2v[generator.nextInt(e2v.length)][generator.nextInt(2)];
int nVerts = v2e.length;
boolean inTree[] = new boolean[nVerts]; // false initially
int theEdgeOut[] = new int[nVerts];
theEdgeOut[r] = -1;
inTree[r] = true;
FORI (iVert, nVerts)
{
if (v2e[iVert].length == 0)
continue; // the vertex got removed (probably merged into the infinite vertex)
for (int u = iVert; !inTree[u]; u = e2v[theEdgeOut[u]][1])
theEdgeOut[u] = v2e[u][generator.nextInt(v2e[u].length)];
for (int u = iVert; !inTree[u]; u = e2v[theEdgeOut[u]][1])
inTree[u] = true;
}
boolean answer[] = new boolean[e2v.length/2]; // all false initially
FORI (iVert, nVerts)
{
if (v2e[iVert].length == 0)
continue; // the vertex got removed (probably merged into the infinite vertex)
int iEdge = theEdgeOut[iVert];
CHECK_EQ((iEdge == -1), (iVert==r));
if (iEdge != -1)
{
CHECK_EQ(e2v[iEdge][0], iVert);
answer[iEdge/2] = true;
}
}
return answer;
} // randomSpanningTree
// Given a spanning tree, expressed in undirectedEdgeIsInSpanningTree
// (as returned by randomSpanningTree()), and a root,
// figure out each vertex's "parent" edge, i.e. the edge pointing towards the root.
public int[] getVertToParentEdgeOut(int root,
boolean undirectedEdgeIsInSpanningTree[/*nUndirectedEdges*/])
{
int verboseLevel = 0;
if (verboseLevel >= 1) System.out.println("in getVertToParentEdgeOut");
// TODO: BUG: VecMath.toString messes up on int[][], it omits final closing brace
if (verboseLevel >= 1) System.out.println(" e2v = "+VecMath.toString(e2v));
if (verboseLevel >= 1) System.out.println(" v2e = "+VecMath.toString(v2e));
if (verboseLevel >= 1) System.out.println(" undirectedEdgeIsInSpanningTree = "+VecMath.toString(undirectedEdgeIsInSpanningTree));
int nVerts = this.v2e.length;
int vertToParentEdgeOut[] = VecMath.fillvec(nVerts, -1);
int queue[] = new int[nVerts];
int queueSize = 0;
queue[queueSize++] = root;
while (queueSize > 0)
{
int iVert = queue[--queueSize];
int edgesOut[] = this.v2e[iVert];
FORI (iEdgeOut, edgesOut.length)
{
int iEdge = edgesOut[iEdgeOut];
if (iEdge != vertToParentEdgeOut[iVert] // i.e. if didn't just come from there
&& undirectedEdgeIsInSpanningTree[iEdge/2])
{
CHECK_EQ(this.e2v[iEdge][0], iVert);
int jVert = this.e2v[iEdge][1];
int parentEdgeOut = iEdge ^ 1; // opposite edge, i.e. the edge from jVert to iVert
vertToParentEdgeOut[jVert] = parentEdgeOut;
CHECK_EQ(this.e2v[parentEdgeOut][0], jVert);
CHECK_EQ(this.e2v[parentEdgeOut][1], iVert);
queue[queueSize++] = jVert;
}
}
}
if (verboseLevel >= 1) System.out.println(" vertToParentEdgeOut = "+Arrays.toStringCompact(vertToParentEdgeOut));
if (verboseLevel >= 1) System.out.println("out getVertToParentEdgeOut");
return vertToParentEdgeOut;
} // getVertToParent
} // SimplerMeshDataStructure
// See paper "Generating Random Spanning Trees
// More Quickly than the Cover Time" by David Bruce Wilson.
// But, can't I do it in O(n) time,
// by simply growing the tree and picking a random new edge out of it on every step?
// (answer: no, the next edge out of the spanning tree can't be picked uniformly)
// Verify that Wilson's algorithm gives something uniformly random,
// or that the more well known random walk one does,
// or that a similar one doesn't.
// Note: This doesn't really do anything useful, it just prints stats, with method
// chosen via hard-coded true/false's in the code below.
public static void analyzeRandomSpanningTrees(Mesh mesh)
{
System.out.println(" in analyzeRandomSpanningTrees");
int nEdges = mesh.edges.size();
PRINT(nEdges);
if (nEdges > 26) // i.e. 13 undirected. (takes too long otherwise)
{
System.out.println(" too many edges, bailing");
System.out.println(" out analyzeRandomSpanningTrees");
return;
}
SimplerMeshDataStructure simplerMeshDataStructure = new SimplerMeshDataStructure(mesh, /*mergeInsideOutVertsIntoInfiniteVert=*/false);
if (!simplerMeshDataStructure.isConnectedExceptMaybeForIsolatedVerts())
{
System.out.println(" graph is disconnected; bailing");
System.out.println(" out analyzeRandomSpanningTrees");
return;
}
java.util.Random generator = new java.util.Random();
int counts[] = new int[1<<nEdges];
int nTries = 1000*1000;
FORI (iTry, nTries)
{
// Make a random spanning tree, and increment its count.
int whichTree;
if (true)
{
// Wilson's algorithm.
boolean answer[] = simplerMeshDataStructure.randomSpanningTree(generator);
whichTree = 0;
FORI (iUndirectedEdge, answer.length)
if (answer[iUndirectedEdge])
{
CHECK_LT(iUndirectedEdge, 32);
whichTree |= (1 << iUndirectedEdge);
}
}
else if (false)
{
// random walk from 0,
// keeping *last* edge to each new vertex.
// This apparently isn't uniform!
int e2v[][] = simplerMeshDataStructure.e2v;
int v2e[][] = simplerMeshDataStructure.v2e;
int nVerts = v2e.length; // may be 1 more than mesh.verts.size(). CBB: error prone!
boolean inTree[] = new boolean[nVerts]; // false initially