private static void ShapewaysPolytopes()
{
VEF loader = new VEF();
loader.Load(@"C:\Users\roice\Documents\projects\vZome\VefProjector\data\24cell-cellFirst.vef");
int divisions = 25;
Shapeways mesh = new Shapeways();
//int count = 0;
foreach (GraphEdge edge in loader.Edges)
{
Segment seg = Segment.Line(
loader.Vertices[edge.V1].ConvertToReal(),
loader.Vertices[edge.V2].ConvertToReal());
Vector3D[] points = seg.Subdivide(divisions);
bool shrink = true;
ProjectAndAddS3Points(mesh, points, shrink);
//if( count++ > 10 )
// break;
}
STL.SaveMeshToSTL(mesh.Mesh, @"D:\p4\R3\sample\out1.stl");
}
public static void EdgesToStl(H3.Cell.Edge[] edges)
{
Shapeways mesh = new Shapeways();
int divisions = 25;
foreach (H3.Cell.Edge edge in edges)
{
Segment seg = Segment.Line(
Sterographic.R3toS3(edge.Start),
Sterographic.R3toS3(edge.End));
Vector3D[] points = seg.Subdivide(divisions);
ProjectAndAddS3Points(mesh, points);
}
for (int i = 0; i < mesh.Mesh.Triangles.Count; i++)
{
mesh.Mesh.Triangles[i] = new Mesh.Triangle(
SphericalModels.StereoToEqualVolume(mesh.Mesh.Triangles[i].a),
SphericalModels.StereoToEqualVolume(mesh.Mesh.Triangles[i].b),
SphericalModels.StereoToEqualVolume(mesh.Mesh.Triangles[i].c));
}
STL.SaveMeshToSTL(mesh.Mesh, @"output.stl");
}
public static Polygon Heart()
{
Polygon newPoly = new Polygon();
double size = 0.12;
double angle = -3 * Math.PI / 2;
Vector3D p1 = new Vector3D(0, -1.5 * size);
Vector3D p2 = new Vector3D(-size, 0);
Vector3D p3 = new Vector3D(-size / 2, size);
Vector3D p4 = new Vector3D(0, size / 2);
Vector3D p5 = new Vector3D(size / 2, size);
Vector3D p6 = new Vector3D(size, 0);
p1.RotateXY(angle);
p2.RotateXY(angle);
p3.RotateXY(angle);
p4.RotateXY(angle);
p5.RotateXY(angle);
p6.RotateXY(angle);
newPoly.Segments.Add(Segment.Line(p1, p2));
newPoly.Segments.Add(Segment.Arc(p2, p3, p4));
newPoly.Segments.Add(Segment.Arc(p4, p5, p6));
newPoly.Segments.Add(Segment.Line(p6, p1));
return(newPoly);
}
/// <summary>
/// Slicing function used for earthquake puzzles.
/// c should be geodesic (orthogonal to the disk boundary).
/// </summary>
public static void SlicePolygonWithHyperbolicGeodesic(Polygon p, CircleNE c, double thickness, out List <Polygon> output)
{
Geometry g = Geometry.Hyperbolic;
Segment seg = null;
if (c.IsLine)
{
Vector3D p1, p2;
Euclidean2D.IntersectionLineCircle(c.P1, c.P2, new Circle(), out p1, out p2);
seg = Segment.Line(p1, p2);
}
else
{
// Setup the two slicing circles.
// These are cuts equidistant from the passed in geodesic.
Vector3D closestToOrigin = H3Models.Ball.ClosestToOrigin(new Circle3D()
{
Center = c.Center, Radius = c.Radius, Normal = new Vector3D(0, 0, 1)
});
Vector3D p1, p2;
Euclidean2D.IntersectionCircleCircle(c, new Circle(), out p1, out p2);
seg = Segment.Arc(p1, closestToOrigin, p2);
}
Circle c1 = H3Models.Ball.EquidistantOffset(g, seg, thickness / 2);
Circle c2 = H3Models.Ball.EquidistantOffset(g, seg, -thickness / 2);
CircleNE c1NE = c.Clone(), c2NE = c.Clone();
c1NE.Center = c1.Center; c2NE.Center = c2.Center;
c1NE.Radius = c1.Radius; c2NE.Radius = c2.Radius;
SlicePolygonHelper(p, c1NE, c2NE, out output);
}
public static Vector3D[] GeodesicPoints(Vector3D v1, Vector3D v2)
{
int div = 4;
Segment seg = Segment.Line(v1, v2);
Vector3D[] result = seg.Subdivide(div);
return(result);
}
/// <summary>
/// Create a new polygon from a set of points.
/// Line segments will be used.
/// </summary>
public static Polygon FromPoints(Vector3D[] points)
{
Polygon result = new Polygon();
for (int i = 0; i < points.Length; i++)
{
int idx1 = i;
int idx2 = i == points.Length - 1 ? 0 : i + 1;
Segment newSeg = Segment.Line(points[idx1], points[idx2]);
result.Segments.Add(newSeg);
}
result.Center = result.CentroidApprox;
return(result);
}
/// <summary>
/// Create a Euclidean polygon from a set of points.
/// NOTE: Do not include starting point twice.
/// </summary>
public void CreateEuclidean(Vector3D[] points)
{
this.Segments.Clear();
for (int i = 0; i < points.Length; i++)
{
int idx1 = i;
int idx2 = i + 1;
if (idx2 == points.Length)
{
idx2 = 0;
}
Segment newSeg = Segment.Line(points[idx1], points[idx2]);
this.Segments.Add(newSeg);
}
Center = this.CentroidApprox;
}
/// <summary>
/// Inputs and Outputs are in R3 (stereographically projected).
/// </summary>
public static Vector3D[] GeodesicPoints(Vector3D v1, Vector3D v2)
{
Vector3D start = Sterographic.R3toS3(v1);
Vector3D end = Sterographic.R3toS3(v2);
AvoidNorthPole(ref start, end);
AvoidNorthPole(ref end, start);
int div = 42;
//int div = 56; // 343
//int div = 50; // 333
Segment seg = Segment.Line(start, end);
Vector3D[] result = seg.Subdivide(div);
for (int i = 0; i < result.Length; i++)
{
result[i].Normalize();
result[i] = Sterographic.S3toR3(result[i]);
}
return(result);
}
private static void AddEuclideanEdge(Shapeways mesh, HashSet <H3.Cell.Edge> completed, Vector3D start, Vector3D end)
{
H3.Cell.Edge edge = new H3.Cell.Edge(start, end);
if (completed.Contains(edge))
{
return;
}
Shapeways tempMesh = new Shapeways();
Segment seg = Segment.Line(start, end);
int div = 20 - (int)(start.Abs() * 4);
if (div < 1)
{
div = 1;
}
tempMesh.AddCurve(seg.Subdivide(div), .05);
Transform(tempMesh.Mesh);
mesh.Mesh.Triangles.AddRange(tempMesh.Mesh.Triangles);
completed.Add(edge);
}
private static void AddSymmetryTriangles(Mesh mesh, Tiling tiling, Polygon boundary)
{
// Assume template centered at the origin.
Polygon template = tiling.Tiles.First().Boundary;
List <Triangle> templateTris = new List <Triangle>();
foreach (Segment seg in template.Segments)
{
int num = 1 + (int)(seg.Length * m_divisions);
Vector3D a = new Vector3D();
Vector3D b = seg.P1;
Vector3D c = seg.Midpoint;
Vector3D centroid = (a + b + c) / 3;
Polygon poly = new Polygon();
Segment segA = Segment.Line(new Vector3D(), seg.P1);
Segment segB = seg.Clone();
segB.P2 = seg.Midpoint;
Segment segC = Segment.Line(seg.Midpoint, new Vector3D());
poly.Segments.Add(segA);
poly.Segments.Add(segB);
poly.Segments.Add(segC);
Vector3D[] coords = TextureHelper.TextureCoords(poly, Geometry.Hyperbolic);
int[] elements = TextureHelper.TextureElements(3, LOD: 3);
for (int i = 0; i < elements.Length / 3; i++)
{
int idx1 = i * 3;
int idx2 = i * 3 + 1;
int idx3 = i * 3 + 2;
Vector3D v1 = coords[elements[idx1]];
Vector3D v2 = coords[elements[idx2]];
Vector3D v3 = coords[elements[idx3]];
templateTris.Add(new Triangle(v1, v2, v3));
}
/*
*
* // Need to shrink a little, so we won't
* // get intersections among neighboring faces.
* a = Shrink( a, centroid );
* b = Shrink( b, centroid );
* c = Shrink( c, centroid );
*
* Vector3D[] list = seg.Subdivide( num * 2 );
* list[0] = b;
* list[list.Length / 2] = c;
* for( int i = 0; i < list.Length / 2; i++ )
* templateTris.Add( new Triangle( centroid, list[i], list[i + 1] ) );
*
* for( int i = num - 1; i >= 0; i-- )
* templateTris.Add( new Triangle( centroid, a + (c - a) * (i + 1) / num, a + (c - a) * i / num ) );
*
* for( int i = 0; i < num; i++ )
* templateTris.Add( new Triangle( centroid, a + (b - a) * i / num, a + (b - a) * (i + 1) / num ) );
*/
}
foreach (Tile tile in tiling.Tiles)
{
Vector3D a = tile.Boundary.Segments[0].P1;
Vector3D b = tile.Boundary.Segments[1].P1;
Vector3D c = tile.Boundary.Segments[2].P1;
Mobius m = new Mobius();
if (tile.Isometry.Reflected)
{
m.MapPoints(template.Segments[0].P1, template.Segments[1].P1, template.Segments[2].P1, c, b, a);
}
else
{
m.MapPoints(template.Segments[0].P1, template.Segments[1].P1, template.Segments[2].P1, a, b, c);
}
foreach (Triangle tri in templateTris)
{
Triangle transformed = new Triangle(
m.Apply(tri.a),
m.Apply(tri.b),
m.Apply(tri.c));
CheckAndAdd(mesh, transformed, boundary);
}
}
}