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private AddCurve ( List |
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| disks | List |
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| points | Vector3D | |
| start | Vector3D | |
| end | Vector3D | |
| return | void | |
/// <summary>
/// Add a finite (truncated) banana to our mesh. Passed in edge should be in Ball model.
/// </summary>
public static void AddBanana( Shapeways mesh, Vector3D e1, Vector3D e2, H3.Settings settings )
{
Vector3D e1UHS = H3Models.BallToUHS( e1 );
Vector3D e2UHS = H3Models.BallToUHS( e2 );
// Endpoints of the goedesic on the z=0 plane.
Vector3D z1, z2;
H3Models.UHS.GeodesicIdealEndpoints( e1UHS, e2UHS, out z1, out z2 );
// XXX - Do we want to do a better job worrying about rotation here?
// (multiply by complex number with certain imaginary part as well)
//Vector3D z3 = ( z1 + z2 ) / 2;
//if( Infinity.IsInfinite( z3 ) )
// z3 = new Vector3D( 1, 0 );
Vector3D z3 = new Vector3D( Math.E, Math.PI ); // This should vary the rotations a bunch.
// Find the Mobius we need.
// We'll do this in two steps.
// (1) Find a mobius taking z1,z2 to origin,inf
// (2) Deal with scaling e1 to a height of 1.
Mobius m1 = new Mobius( z1, z3, z2 );
Vector3D e1UHS_transformed = m1.ApplyToQuaternion( e1UHS );
double scale = 1.0 / e1UHS_transformed.Z;
Mobius m2 = Mobius.Scale( scale );
Mobius m = m2 * m1; // Compose them (multiply in reverse order).
Vector3D e2UHS_transformed = m.ApplyToQuaternion( e2UHS );
// Make our truncated cone.
// For regular tilings, we really would only need to do this once for a given LOD.
List<Vector3D> points = new List<Vector3D>();
double logHeight = Math.Log( e2UHS_transformed.Z );
if( logHeight < 0 )
throw new System.Exception( "impl issue" );
int div1, div2;
H3Models.Ball.LOD_Finite( e1, e2, out div1, out div2, settings );
double increment = logHeight / div1;
for( int i=0; i<=div1; i++ )
{
double h = increment * i;
// This is to keep different bananas from sharing exactly coincident vertices.
double tinyOffset = 0.001;
if( i == 0 )
h -= tinyOffset;
if( i == div1 )
h += tinyOffset;
Vector3D point = new Vector3D( 0, 0, Math.Exp( h ) );
points.Add( point );
}
Shapeways tempMesh = new Shapeways();
tempMesh.Div = div2;
tempMesh.AddCurve( points.ToArray(), v => H3Models.UHS.SizeFunc( v, settings.AngularThickness ) );
// Unwind the transforms.
TakePointsBack( tempMesh.Mesh, m.Inverse(), settings );
mesh.Mesh.Triangles.AddRange( tempMesh.Mesh.Triangles );
}
/// <summary>
/// Helper to project points from S3 -> S2, then add an associated curve.
/// </summary>
private static void ProjectAndAddS3Points(Shapeways mesh, Vector3D[] pointsS3, bool shrink)
{
// Project to S3, then to R3.
List <Vector3D> projected = new List <Vector3D>();
foreach (Vector3D v in pointsS3)
{
v.Normalize();
Vector3D c = v.ProjectTo3DSafe(1.0);
// Pull R3 into a smaller open disk.
if (shrink)
{
double mag = Math.Atan(c.Abs());
c.Normalize();
c *= mag;
}
projected.Add(c);
}
System.Func <Vector3D, double> sizeFunc = v =>
{
// Constant thickness.
// return 0.08;
double sphericalThickness = 0.002;
double abs = v.Abs();
if (shrink)
{
abs = Math.Tan(abs); // The unshrunk abs.
}
// The thickness at this vector location.
double result = Spherical2D.s2eNorm(Spherical2D.e2sNorm(abs) + sphericalThickness) - abs;
if (shrink)
{
result *= Math.Atan(abs) / abs; // shrink it back down.
}
return(result);
};
mesh.AddCurve(projected.ToArray(), sizeFunc);
}
public static void GenPolyhedron()
{
Tiling tiling;
int p = 3;
int q = 6;
GetAssociatedTiling(p, q, 5000, out tiling);
double overallScale = 12.5; // 2.5 cm = 1 in diameter
Shapeways mesh = new Shapeways();
foreach (Tile tile in tiling.Tiles)
{
foreach (Segment seg in tile.Boundary.Segments)
{
double tilingScale = 0.75;
seg.Scale(new Vector3D(), tilingScale);
Vector3D v1 = Sterographic.PlaneToSphereSafe(seg.P1);
Vector3D v2 = Sterographic.PlaneToSphereSafe(seg.P2);
//if( v1.Dist( v2 ) < 0.01 )
// continue;
if (SphericalCoords.CartesianToSpherical(v1).Y < Math.PI / 12 &&
SphericalCoords.CartesianToSpherical(v2).Y < Math.PI / 12)
{
continue;
}
double dist = v1.Dist(v2);
int divisions = 2 + (int)(dist * 20);
Vector3D[] points = seg.Subdivide(divisions);
points = points.Select(v => Sterographic.PlaneToSphereSafe(v)).ToArray();
mesh.AddCurve(points, v => SizeFunc(v, overallScale));
}
}
mesh.Mesh.Scale(overallScale);
string outputFileName = @"d:\temp\" + p + q + ".stl";
STL.SaveMeshToSTL(mesh.Mesh, outputFileName);
}
private static void ProjectAndAddS3Points(Shapeways mesh, Vector3D[] pointsS3)
{
double r = 0.02;
List <Vector3D> projected = new List <Vector3D>();
List <double> radii = new List <double>();
foreach (Vector3D v in pointsS3)
{
v.Normalize();
Vector3D c = v.ProjectTo3DSafe(1.0);
Vector3D p;
double d;
H3Models.Ball.DupinCyclideSphere(c, r, Geometry.Spherical, out p, out d);
projected.Add(p);
radii.Add(d);
}
mesh.AddCurve(projected.ToArray(), radii.ToArray());
}
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);
}
/// <summary>
/// Helper to project points from S3 -> S2, then add an associated curve.
/// XXX - Not completely correct.
/// </summary>
private static void ProjectAndAddS3Points( Shapeways mesh, Vector3D[] pointsS3, bool shrink )
{
List<Vector3D> projected = new List<Vector3D>();
foreach( Vector3D v in pointsS3 )
{
v.Normalize();
Vector3D c = v.ProjectTo3DSafe( 1.0 );
// Pull R3 into a smaller open disk.
if( shrink )
{
double mag = Math.Atan( c.Abs() );
c.Normalize();
c *= mag;
}
projected.Add( c );
}
System.Func<Vector3D, double> sizeFunc = v =>
{
// Constant thickness.
// return 0.08;
double sphericalThickness = 0.05;
double abs = v.Abs();
if( shrink )
abs = Math.Tan( abs ); // The unshrunk abs.
// The thickness at this vector location.
double result = Spherical2D.s2eNorm( Spherical2D.e2sNorm( abs ) + sphericalThickness ) - abs;
if( shrink )
result *= Math.Atan( abs ) / abs; // shrink it back down.
return result;
};
mesh.AddCurve( projected.ToArray(), sizeFunc );
}
private static void ProjectAndAddS3Points( Shapeways mesh, Vector3D[] pointsS3 )
{
double r = 0.02;
List<Vector3D> projected = new List<Vector3D>();
List<double> radii = new List<double>();
foreach( Vector3D v in pointsS3 )
{
v.Normalize();
Vector3D c = v.ProjectTo3DSafe( 1.0 );
Vector3D p;
double d;
H3Models.Ball.DupinCyclideSphere( c, r, Geometry.Spherical, out p, out d );
projected.Add( p );
radii.Add( d );
}
mesh.AddCurve( projected.ToArray(), radii.ToArray() );
}
/// <summary>
/// Add an ideal banana to our mesh. Passed in edge should be in Ball model.
/// </summary>
public static void AddIdealBanana( Shapeways mesh, Vector3D e1, Vector3D e2, H3.Settings settings )
{
Vector3D z1 = H3Models.BallToUHS( e1 );
Vector3D z2 = H3Models.BallToUHS( e2 );
// Mobius taking z1,z2 to origin,inf
Complex dummy = new Complex( Math.E, Math.PI );
Mobius m = new Mobius( z1, dummy, z2 );
// Make our truncated cone. We need to deal with the two ideal endpoints specially.
List<Vector3D> points = new List<Vector3D>();
double logHeight = 2; // XXX - magic number, and going to cause problems for infinity checks if too big.
int div1, div2;
H3Models.Ball.LOD_Ideal( e1, e2, out div1, out div2, settings );
double increment = logHeight / div1;
for( int i=-div1; i<=div1; i+=2 )
points.Add( new Vector3D( 0, 0, Math.Exp( increment * i ) ) );
Shapeways tempMesh = new Shapeways();
tempMesh.Div = div2;
System.Func<Vector3D, double> sizeFunc = v => H3Models.UHS.SizeFunc( v, settings.AngularThickness );
//Mesh.OpenCylinder... pass in two ideal endpoints?
tempMesh.AddCurve( points.ToArray(), sizeFunc, new Vector3D(), Infinity.InfinityVector );
// Unwind the transforms.
TakePointsBack( tempMesh.Mesh, m.Inverse(), settings );
mesh.Mesh.Triangles.AddRange( tempMesh.Mesh.Triangles );
}
