private static void OneHoneycombGoursat( int[] active, string baseName, int baseHue )
{
CalcThickness( active );
// Create the simplex.
Simplex simplex = new Simplex();
simplex.InitializeGoursat();
// Map of labels for mirrors consistent with input scheme to Goursat function.
// Map is from wikipedia labeling scheme to the indices our function generates.
//
// wiki == our index
// 0100 == 0
// 0001 == 1
// 1000 == 2
// 0010 == 3
Func<int, int> mapMirror = i =>
{
switch( i )
{
case 0: return 2;
case 1: return 0;
case 2: return 3;
case 3: return 1;
}
throw new System.ArgumentException();
};
// We need to set this up before converting the mirrors.
string mirrorsString = ActiveMirrorsString( active );
string suffix = "-" + mirrorsString;
// Convert our active mirrors into the Goursat tet indices.
int[] polyMirrors = new int[] { 1, 2, 3 };
active = active.Select( i => mapMirror( i ) ).OrderBy( i => i ).ToArray();
polyMirrors = polyMirrors.Select( i => mapMirror( i ) ).OrderBy( i => i ).ToArray();
Vector3D startingPoint = IterateToStartingPoint( active, simplex );
List<H3.Cell.Edge> startingEdges = new List<H3.Cell.Edge>();
foreach( int a in active )
{
Vector3D reflected = simplex.ReflectInFacet( startingPoint, a );
startingEdges.Add( new H3.Cell.Edge( startingPoint, reflected ) );
}
bool doEdges = true;
bool doCells = false;
// Generate the honeycomb.
H3.Cell.Edge[] edges = null;
if( doEdges )
edges = Recurse.CalcEdgesSmart( simplex.Facets, startingEdges.ToArray() );
// Highlighted cells.
H3.Cell[] cellsToHighlight = null;
if( doCells )
{
H3.Cell startingCell = PolyhedronToHighlight( Geometry.Hyperbolic, polyMirrors, simplex, startingPoint );
cellsToHighlight = Recurse.CalcCells( simplex.Facets, new H3.Cell[] { startingCell } );
//cellsToHighlight = new H3.Cell[] { startingCell };
}
// plugin Wendy's nonuniform calcs here...
//Nonuniform.Wendy( simplex, edges );
// Trim out half the edges (the ones we won't see in our Pov-Ray view).
Vector3D lookFrom = new Vector3D( 1, 1, 1 ) * 0.7;
Vector3D lookAt = new Vector3D( ); // pov-ray lookat
double thresh = -.01;
if( doEdges )
edges = edges.Where( e => e.Start.Dot( lookAt ) > thresh || e.End.Dot( lookAt ) > thresh ).ToArray();
//if( doCells )
// cellsToHighlight = cellsToHighlight.Where( c => c.Center.Dot( lookAt ) > thresh ).ToArray(); // I don't think this works right
// Setup Pov-ray stuff.
// We have 16 possible mirror states. We'll calculate the hue by converting the binary state to decimal, and doubling.
// So for a given family, the hue will range over 32 numbers.
int hue = baseHue + 2 * Convert.ToInt32( mirrorsString, 2 );
string fileName = baseName + suffix;
using( StreamWriter sw = File.CreateText( fileName + ".pov" ) )
{
sw.WriteLine( string.Format( "#declare lookFrom = <{0},{1},{2}>;", lookFrom.X, lookFrom.Y, lookFrom.Z ) );
sw.WriteLine( string.Format( "#declare lookAt = <{0},{1},{2}>;", lookAt.X, lookAt.Y, lookAt.Z ) );
sw.WriteLine( "#include \"C:\\Users\\hrn\\Documents\\roice\\povray\\H3_uniform_faces\\H3_uniform_faces.pov\"" );
//sw.WriteLine( string.Format( "background {{ CHSL2RGB( <{0}, 1, .3> ) }}", hue ) );
//sw.WriteLine( string.Format( "background {{ rgb <.13,.37,.31> }}" ) );
sw.WriteLine( string.Format( "background {{ rgb 1 }}" ) );
}
if( doEdges )
H3.SaveToFile( fileName, edges, finite: true, append: true );
if( doCells )
{
HashSet<H3.Cell.Edge> cellEdges = new HashSet<H3.Cell.Edge>( new H3.Cell.EdgeEqualityComparer() );
foreach( H3.Cell cell in cellsToHighlight )
cell.AppendAllEdges( cellEdges );
edges = cellEdges.ToArray();
H3.SaveToFile( fileName, edges, finite: true, append: true );
H3.AppendFacets( fileName, cellsToHighlight );
}
}
private static H3.Cell PolyhedronToHighlight( Geometry g, int[] mirrors, Simplex simplex, Vector3D startingPoint )
{
if( mirrors.Length != 3 )
throw new System.Exception( "We need exactly three mirrors to generate a polyhedron." );
// In the general case, we can have 3 types of polygons, each being generated by choosing 2 of the 3 mirrors.
// When fewer polygon types exist, GenFacet will return null, so we need to check that.
List<H3.Cell.Facet> polyFacets = new List<H3.Cell.Facet>();
polyFacets.Add( GenFacet( g, mirrors[0], mirrors[1], simplex, startingPoint ) );
polyFacets.Add( GenFacet( g, mirrors[1], mirrors[2], simplex, startingPoint ) );
polyFacets.Add( GenFacet( g, mirrors[0], mirrors[2], simplex, startingPoint ) );
polyFacets.RemoveAll( f => f == null );
HashSet<Vector3D> completedFacetIds = new HashSet<Vector3D>();
foreach( H3.Cell.Facet f in polyFacets )
completedFacetIds.Add( f.ID );
Recurse.GenPolyhedron( mirrors.Select( m => simplex.Facets[m] ).ToArray(),
polyFacets.ToArray(), polyFacets, completedFacetIds );
H3.Cell cell = new H3.Cell( polyFacets.ToArray() );
// Calc a center. XXX - totally wrong.
Vector3D center = new Vector3D();
foreach( Vector3D v in cell.Verts )
center += v;
center /= cell.Verts.Count();
cell.Center = center;
// Calc the spheres.
foreach( H3.Cell.Facet f in cell.Facets )
f.CalcSphereFromVerts( g );
return cell;
}
// CHEAT! (would be better to do a geometrical construction)
// We are going to iterate to the starting point that will make all edge lengths the same.
private static Vector3D IterateToStartingPoint( int[] activeMirrors, Simplex simplex )
{
if( activeMirrors.Length == 1 )
return simplex.Verts[activeMirrors[0]];
// We are minimizing the output of this function,
// because we want all edge lengths to be as close as possible.
// Input vector should be in the Ball Model.
Func<Vector3D, double> diffFunc = v =>
{
List<double> lengths = new List<double>();
for( int i = 0; i < activeMirrors.Length; i++ )
{
Vector3D reflected = simplex.ReflectInFacet( v, activeMirrors[i] );
lengths.Add( H3Models.Ball.HDist( v, reflected ) );
}
double result = 0;
double average = lengths.Average();
foreach( double length in lengths )
result += Math.Abs( length - average );
return result;
};
// So that we can leverage Euclidean barycentric coordinates, we will first convert our simplex to the Klein model.
// We will need to take care to properly convert back to the Ball as needed.
Vector3D[] kleinVerts = simplex.Verts.Select( v => HyperbolicModels.PoincareToKlein( v ) ).ToArray();
// Normalizing barycentric coords amounts to making sure the 4 coords add to 1.
Func<Vector3D, Vector3D> baryNormalize = b =>
{
return b / ( b.X + b.Y + b.Z + b.W );
};
// Bary Coords to Euclidean
Func<Vector3D[], Vector3D, Vector3D> baryToEuclidean = ( kv, b ) =>
{
Vector3D result =
kv[0] * b.X + kv[1] * b.Y + kv[2] * b.Z + kv[3] * b.W;
return result;
};
// Our starting barycentric coords (halfway between all active mirrors).
Vector3D bary = new Vector3D();
foreach( int a in activeMirrors )
bary[a] = 0.5;
bary = baryNormalize( bary );
// For each iteration, we'll shrink this search offset.
// NOTE: The starting offset and decrease factor I'm using don't guarantee convergence,
// but it seems to be working pretty well (even when varying these parameters).
//double searchOffset = 1.0 - bary[activeMirrors[0]];
//double searchOffset = bary[activeMirrors[0]];
double factor = 1.5; // Adjusting this helps get some to converge, e.g. 4353-1111
double searchOffset = bary[activeMirrors[0]] / factor;
double min = double.MaxValue;
int iterations = 1000;
for( int i = 0; i < iterations; i++ )
{
min = diffFunc( HyperbolicModels.KleinToPoincare( baryToEuclidean( kleinVerts, bary ) ) );
foreach( int a in activeMirrors )
{
Vector3D baryTest1 = bary, baryTest2 = bary;
baryTest1[a] += searchOffset;
baryTest2[a] -= searchOffset;
baryTest1 = baryNormalize( baryTest1 );
baryTest2 = baryNormalize( baryTest2 );
double t1 = diffFunc( HyperbolicModels.KleinToPoincare( baryToEuclidean( kleinVerts, baryTest1 ) ) );
double t2 = diffFunc( HyperbolicModels.KleinToPoincare( baryToEuclidean( kleinVerts, baryTest2 ) ) );
if( t1 < min )
{
min = t1;
bary = baryTest1;
}
if( t2 < min )
{
min = t2;
bary = baryTest2;
}
}
if( Tolerance.Equal( min, 0.0, 1e-14 ) )
{
System.Console.WriteLine( string.Format( "Converged in {0} iterations.", i ) );
break;
}
searchOffset /= factor;
}
if( !Tolerance.Equal( min, 0.0, 1e-14 ) )
{
System.Console.WriteLine( "Did not converge: " + min );
// Be a little looser before thrown an exception.
if( !Tolerance.Equal( min, 0.0, 1e-12 ) )
{
System.Console.ReadKey( true );
//throw new System.Exception( "Boo. We did not converge." );
return Vector3D.DneVector();
}
}
return HyperbolicModels.KleinToPoincare( baryToEuclidean( kleinVerts, bary ) );
}
private static H3.Cell.Facet GenFacet( Geometry g, int mirror1, int mirror2, Simplex simplex, Vector3D startingPoint )
{
List<Sphere> mirrors = new List<Sphere>();
mirrors.Add( simplex.Facets[mirror1] );
mirrors.Add( simplex.Facets[mirror2] );
List<H3.Cell.Edge> startingEdges = new List<H3.Cell.Edge>();
Vector3D reflected = simplex.ReflectInFacet( startingPoint, mirror1 );
startingEdges.Add( new H3.Cell.Edge( startingPoint, reflected ) );
reflected = simplex.ReflectInFacet( startingPoint, mirror2 );
startingEdges.Add( new H3.Cell.Edge( startingPoint, reflected ) );
startingEdges.RemoveAll( e => e.Start == e.End );
if( startingEdges.Count == 0 )
return null;
H3.Cell.Edge[] completedEdges = Recurse.CalcEdges( mirrors.ToArray(), startingEdges.ToArray(), new Recurse.Settings() { G = g } );
if( completedEdges.Length == 1 )
return null;
List<Vector3D> facetVerts = new List<Vector3D>();
H3.Cell.Edge edge = completedEdges.First();
Vector3D start = edge.Start;
Vector3D current = edge.End;
facetVerts.Add( edge.End );
while( current != start )
{
edge = completedEdges.First( e => e != edge && ( e.Start == current || e.End == current ) );
current = edge.Start == current ? edge.End : edge.Start;
facetVerts.Add( current );
}
return new H3.Cell.Facet( facetVerts.ToArray() );
}
public static void Paracompact( HoneycombDef def, int[] active, int baseHue )
{
string baseName = BaseName( def );
string mirrorsString = ActiveMirrorsString( active );
string suffix = "-" + mirrorsString;
string fileName = baseName + suffix;
if( File.Exists( fileName + ".pov" ) )
{
Console.WriteLine( string.Format( "Skipping {0}", fileName ) );
return;
}
Console.WriteLine( string.Format( "Building {0}", fileName ) );
CalcThickness( active );
// The wiki mirrors are labeled in the reverse of ours.
Func<int, int> mapMirror = i => 3 - i;
active = active.Select( i => mapMirror( i ) ).OrderBy( i => i ).ToArray();
Simplex simplex = new Simplex();
simplex.Facets = SimplexCalcs.Mirrors( def.P, def.Q, def.R );
simplex.Verts = SimplexCalcs.VertsBall( def.P, def.Q, def.R );
Vector3D startingPoint = IterateToStartingPoint( active, simplex );
if( startingPoint.DNE )
return;
List<H3.Cell.Edge> startingEdges = new List<H3.Cell.Edge>();
foreach( int a in active )
{
Vector3D reflected = simplex.ReflectInFacet( startingPoint, a );
startingEdges.Add( new H3.Cell.Edge( startingPoint, reflected ) );
}
SetupBaseHue( fileName, mirrorsString, baseHue );
Recurse.m_background = new Vector3D( baseHue, 1, .1 );
H3.Cell.Edge[] edges = Recurse.CalcEdgesSmart2( simplex.Facets, startingEdges.ToArray() );
H3.SaveToFile( fileName, edges, finite: true, append: true );
}
/// <summary>
/// This generates a honeycomb by reflecting in 4 mirrors of the fundamental simplex.
/// </summary>
public static void OneHoneycombNew( HoneycombDef imageData )
{
int p = imageData.P;
int q = imageData.Q;
int r = imageData.R;
double thickness = 0.1;
double thicknessSpherical = Spherical2D.s2eNorm( thickness );
double thicknessHyperbolic = R3.Math.DonHatch.h2eNorm( thickness );
double threshold = 1;
H3.Cell.Edge[] edges = null;
H3.Cell[] cellsToHighlight = null;
Sphere[] simplex = null;
Vector3D vertex = new Vector3D();
Geometry g = Util.GetGeometry( p, q, r );
if( g == Geometry.Spherical )
{
thickness = thicknessSpherical /*.07 for 333*/ /* 0.05for 433*/ /*.025 for 533,335*/;
threshold = 10000;
simplex = SimplexCalcs.MirrorsSpherical( p, q, r );
vertex = SimplexCalcs.VertexSpherical( p, q, r );
// Ugly special casing for 333, since it has a vertex project to infinity.
if( p == 3 && q == 3 && r == 3 )
SpecialCase333();
}
else if( g == Geometry.Euclidean )
{
thickness = thickness / 2;
threshold = 5/*20*/;
SimplexCalcs.CalcEScale();
simplex = SimplexCalcs.MirrorsEuclidean();
Vector3D[] verts = SimplexCalcs.VertsEuclidean();
vertex = verts[2];
}
else
{
thickness = thicknessHyperbolic;
threshold = 0.01;
simplex = SimplexCalcs.Mirrors( p, q, r );
Vector3D[] verts = SimplexCalcs.VertsBall( p, q, r );
vertex = verts[2];
//Vector3D[] simplexVerts = SimplexCalcs.VertsBall( p, q, r );
//H3.Cell.Edge edge = new H3.Cell.Edge( simplexVerts[2], simplexVerts[3] );
//H3.Cell.Edge edge = SimplexCalcs.HoneycombEdgeBall( p, q, r );
//H3.Cell.Edge[] startingEdges = new H3.Cell.Edge[] { edge };
//H3.Cell.Edge[] edges = Recurse.CalcEdgesSmart2( simplex, startingEdges );
// Vertex Centered.
bool vertexCentered = false;
if( vertexCentered )
{
Vector3D v = SimplexCalcs.VertexPointBall( p, q, r );
v = H3Models.BallToUHS( v );
double scale = 1.0 / v.Abs();
edges = edges.Select( e =>
{
Vector3D start = H3Models.UHSToBall( H3Models.BallToUHS( e.Start ) * scale );
Vector3D end = H3Models.UHSToBall( H3Models.BallToUHS( e.End ) * scale );
return new H3.Cell.Edge( start, end );
} ).ToArray();
}
// Code to show endpoints of 535
/*using( StreamWriter sw = File.CreateText( "535_points.pov" ) )
{
HashSet<Vector3D> verts = new HashSet<Vector3D>();
foreach( H3.Cell.Edge e in edges )
{
verts.Add( Sterographic.SphereToPlane( e.Start ) );
verts.Add( Sterographic.SphereToPlane( e.End ) );
}
foreach( Vector3D vert in verts )
if( !Infinity.IsInfinite( vert ) )
sw.WriteLine( PovRay.Sphere( new Sphere() { Center = vert, Radius = 0.01 } ) );
}*/
}
// Recurse
bool dual = false;
{
H3.Cell.Edge[] startingEdges = null;
if( dual )
startingEdges = new H3.Cell.Edge[] { SimplexCalcs.DualEdgeBall( simplex ) };
else
startingEdges = new H3.Cell.Edge[] { SimplexCalcs.HoneycombEdgeBall( simplex, vertex ) };
edges = Recurse.CalcEdges( simplex, startingEdges, new Recurse.Settings() { G = g, Threshold = threshold } );
//CullHalfOfEdges( ref edges );
// No need to cull edges in spherical case.
// This was just to generate some images for 350-cell paper.
//edges = Cull120Cell( edges );
Simplex tet = new Simplex();
tet.Facets = simplex;
if( dual )
{
H3.Cell.Edge[] oneDualCell = edges.Where( e => e.Depths[2] == 0 ).ToArray();
simplex = simplex.Skip( 1 ).ToArray();
edges = Recurse.CalcEdges( simplex, oneDualCell, new Recurse.Settings() { G = g, Threshold = threshold } );
int[] polyMirrors = new int[] { 0, 1, 3 };
H3.Cell startingCell = PolyhedronToHighlight( g, polyMirrors, tet, new Vector3D() );
cellsToHighlight = Recurse.CalcCells( simplex, new H3.Cell[] { startingCell } );
//cellsToHighlight = new H3.Cell[] { startingCell };
//cellsToHighlight = cellsToHighlight.Skip( 7 ).ToArray();
}
else
{
int[] polyMirrors = new int[] { 1, 2, 3 };
H3.Cell startingCell = PolyhedronToHighlight( g, polyMirrors, tet, vertex );
//cellsToHighlight = Recurse.CalcCells( simplex, new H3.Cell[] { startingCell } );
cellsToHighlight = new H3.Cell[] { startingCell };
}
// Include just one cell?
bool includeOne = false;
if( includeOne )
{
edges = edges.Where( e => e.Depths[0] == 0 ).ToArray();
//cellsToHighlight = cellsToHighlight.Where( c => c.Depths[0] == 0 ).ToArray();
}
}
// Write the file
bool pov = false;
if( pov )
{
string filename = string.Format( "{0}{1}{2}.pov", p, q, r );
PovRay.WriteEdges( new PovRay.Parameters() { AngularThickness = thickness }, g, edges,
filename, append: false );
//File.Delete( filename );
//PovRay.AppendFacets( cellsToHighlight, filename );
HashSet<Vector3D> verts = new HashSet<Vector3D>();
foreach( H3.Cell.Edge e in edges )
{
verts.Add( e.Start );
verts.Add( e.End );
}
foreach( Vector3D v in verts )
{
Vector3D t = v;
t.Normalize();
t *= 0.9;
System.Diagnostics.Trace.WriteLine( string.Format( "light_source {{ <{0},{1},{2}> White*.2 }}", t.X, t.Y, t.Z ) );
}
/*
// Include the standard pov stuff, so we can batch this.
string fileName = imageData.FormatFilename( string.Empty );
using( StreamWriter sw = File.CreateText( fileName + ".pov" ) )
{
sw.WriteLine( "#include \"C:\\Users\\hrn\\Documents\\roice\\povray\\paper\\H3.pov\"" );
}
bool dummy = true; // Doesn't matter for Pov-Ray, just Shapeways meshes.
H3.SaveToFile( fileName, edges, dummy, append: true );
*/
}
else
{
if( g == Geometry.Spherical )
{
edges = edges.Where( e => e.Start.Valid() && e.End.Valid() && !Infinity.IsInfinite( e.Start ) && !Infinity.IsInfinite( e.End ) ).ToArray();
S3.EdgesToStl( edges );
}
else
throw new System.NotImplementedException();
}
}
/// <summary>
/// Wendy's 77
/// </summary>
public static void Wendy( Simplex simplex, H3.Cell.Edge[] edges )
{
H3.Cell startingCell = null;
Vector3D start = startingCell.Verts.First();
Func<Vector3D, Vector3D> findAntipode = input =>
{
Vector3D antipode = new Vector3D();
double max = double.MinValue;
foreach( Vector3D v in startingCell.Verts )
{
double d = H3Models.Ball.HDist( v, input );
if( d > max )
{
max = d;
antipode = v;
}
}
return antipode;
};
H3.Cell.Edge[] diagonals = new H3.Cell.Edge[] { new H3.Cell.Edge( start, findAntipode( start ) ) };
diagonals = Recurse.CalcEdges( simplex.Facets, diagonals, new Recurse.Settings() { Threshold = 0.9983 } );
// diagonals includes too much at this point (it includes all icosahedra diagonals, but we only want one diagonal from each cell).
// We need to begin at 4 start points, and branch out from each to find the ones we want.
var vertsToDiagonals = FindConnectedEdges( diagonals );
var connectedEdges = FindConnectedEdges( edges );
// Get all edges (not diagonals) connected to start.
List<H3.Cell.Edge> connectedToStart = connectedEdges[start];
Vector3D startOpp = connectedToStart[0].Opp( start );
List<H3.Cell.Edge> connectedToStartOpp = connectedEdges[startOpp];
// We need to pick 4 of these edges, arranged in a tetrahedron for our starting points.
List<Vector3D> startingPoints = new List<Vector3D>();
List<double> distances = new List<double>();
// View1
//startingPoints.Add( start );
//foreach( Vector3D v in connectedToStartOpp.Select( e => e.Opp( startOpp ) ) )
// distances.Add( H3Models.Ball.HDist( startingPoints.First(), v ) );
//startingPoints.Add( connectedToStartOpp[10].Opp( startOpp ) );
//startingPoints.Add( connectedToStartOpp[13].Opp( startOpp ) );
//startingPoints.Add( connectedToStartOpp[14].Opp( startOpp ) );
// View2
startingPoints.Add( startOpp );
foreach( Vector3D v in connectedToStart.Select( e => e.Opp( start ) ) )
distances.Add( H3Models.Ball.HDist( startingPoints.First(), v ) );
startingPoints.Add( connectedToStart[10].Opp( start ) );
startingPoints.Add( connectedToStart[13].Opp( start ) );
startingPoints.Add( connectedToStart[14].Opp( start ) );
distances.Clear();
distances.Add( H3Models.Ball.HDist( startingPoints[1], startingPoints[2] ) );
distances.Add( H3Models.Ball.HDist( startingPoints[1], startingPoints[3] ) );
distances.Add( H3Models.Ball.HDist( startingPoints[2], startingPoints[3] ) );
distances.Add( H3Models.Ball.HDist( startingPoints[0], startingPoints[1] ) );
distances.Add( H3Models.Ball.HDist( startingPoints[0], startingPoints[2] ) );
distances.Add( H3Models.Ball.HDist( startingPoints[0], startingPoints[3] ) );
double dist = 3.097167;
Func<Vector3D[], H3.Cell.Edge[]> RemoveVerts = starting =>
{
List<H3.Cell.Edge> keepers = new List<H3.Cell.Edge>();
HashSet<Vector3D> removedVerts = new HashSet<Vector3D>();
Recurse.BranchAlongVerts( starting.ToArray(), vertsToDiagonals, removedVerts );
foreach( H3.Cell.Edge e in edges )
{
if( removedVerts.Contains( e.Start ) || removedVerts.Contains( e.End ) )
continue;
keepers.Add( e );
}
return keepers.ToArray();
};
edges = RemoveVerts( startingPoints.ToArray() );
bool done = false;
while( !done )
{
done = true;
var newConnectedEdges = FindConnectedEdges( edges );
foreach( Vector3D v in newConnectedEdges.Keys )
{
List<H3.Cell.Edge> oldEdgeList = connectedEdges[v];
List<H3.Cell.Edge> newEdgeList = newConnectedEdges[v];
// Only work edges that were full originally.
if( oldEdgeList.Count != 20 )
continue;
// We need at least two to find the rest.
int newCount = newEdgeList.Count;
if( newCount > 16 && newCount < 19 )
{
List<H3.Cell.Edge> removed = oldEdgeList.Except( newEdgeList, new H3.Cell.EdgeEqualityComparer() ).ToList();
H3.Cell.Edge[] toTrim = newEdgeList.FindAll( e =>
{
foreach( H3.Cell.Edge alreadyRemoved in removed )
{
double d = H3Models.Ball.HDist( alreadyRemoved.Opp( v ), e.Opp( v ) );
if( !Tolerance.Equal( dist, d, 0.00001 ) )
return false;
}
return true;
} ).ToArray();
edges = RemoveVerts( toTrim.Select( e => e.Opp( v ) ).ToArray() );
done = false;
}
if( newCount == 20 )
done = false;
}
}
}