/// <summary>
/// Calculates a mesh for an RLD surface.
/// </summary>
private static Mesh SurfaceInternal(out RLD_outputs outputs)
{
Mesh mesh = new Mesh();
Func <double, double, double, Vector3D[]> oneCircle = (x, o, scale) =>
{
Vector3D normal = Normal(x, o * scale);
Vector3D cen = new Vector3D(0, 0, normal.Z);
Vector3D radius = new Vector3D(normal.X, 0);
return(Shapeways.Disk(cen, new Vector3D(0, 0, 1), radius, m_params.Res));
};
outputs = RLD_Sphere(m_params.K);
double s = m_params.Scale;
//double s = outputs.scale;
// Add in two bands for each segment along the profile, one for +z coords, and one for -z coords.
Vector3D[] profile = outputs.profile;
for (int i = 0; i < profile.Length - 1; i++)
{
Vector3D p1 = profile[i];
Vector3D p2 = profile[i + 1];
mesh.AddBand(oneCircle(p1.X, p1.Y, s), oneCircle(p2.X, p2.Y, s));
mesh.AddBand(oneCircle(p1.X, -p1.Y, s), oneCircle(p2.X, -p2.Y, s));
}
return(mesh);
}
/// <summary>
/// Calculates a mesh for a standard euclidean catenoid.
/// This will need to be transformed to the various locations later.
/// </summary>
private static Mesh StandardCatenoid(double waist, double height)
{
Mesh mesh = new Mesh();
int res = m_params.Res * 2;
Func <double, Vector3D[]> oneCircle = z =>
{
double r = waist * Math.Cosh(z / waist);
Vector3D cen = new Vector3D(0, 0, z);
Vector3D radius = new Vector3D(r, 0);
return(Shapeways.Disk(cen, new Vector3D(0, 0, 1), radius, res));
};
double inc = height / (res * 2);
for (int i = 0; i < res; i++)
{
double z1 = inc * i;
double z2 = inc * (i + 1);
mesh.AddBand(oneCircle(z1), oneCircle(z2));
mesh.AddBand(oneCircle(-z1), oneCircle(-z2));
}
return(mesh);
}
private static Mesh ThickenBoundary(Vector3D[] edge, System.Func <Vector3D, System.Tuple <Vector3D, Vector3D> > thickenFn)
{
List <Vector3D> side1 = new List <Vector3D>();
List <Vector3D> side2 = new List <Vector3D>();
foreach (Vector3D v in edge)
{
var thickened = thickenFn(v);
side1.Add(thickened.Item1);
side2.Add(thickened.Item2);
}
Mesh m = new Mesh();
m.AddBand(side1.ToArray(), side2.ToArray(), close: false);
return(m);
}
private static void ThinMesh(H3.Cell.Edge[] edges, System.Func <H3.Cell.Edge, Vector3D[]> divider,
out Mesh thinMesh, out List <Vector3D[]> boundaryPoints)
{
thinMesh = new Mesh();
boundaryPoints = new List <Vector3D[]>();
List <Vector3D> starts = new List <Vector3D>();
List <Vector3D> ends = new List <Vector3D>();
for (int i = 0; i < edges.Length - 1; i++)
{
int idx1 = i;
int idx2 = i + 1;
H3.Cell.Edge e1 = edges[idx1];
H3.Cell.Edge e2 = edges[idx2];
Vector3D[] points1 = divider(e1);
Vector3D[] points2 = divider(e2);
thinMesh.AddBand(points1, points2, close: false);
starts.Add(e1.Start);
ends.Add(e1.End);
if (idx1 == 0)
{
boundaryPoints.Add(points1);
}
if (idx2 == edges.Length - 1)
{
boundaryPoints.Add(points2);
starts.Add(e2.Start);
ends.Add(e2.End);
}
}
starts.Reverse();
boundaryPoints.Add(starts.ToArray());
boundaryPoints.Add(ends.ToArray());
}
/// <summary>
/// Calculates a mesh for a standard euclidean catenoid.
/// This will need to be transformed to the various locations later.
///
/// Like above, but we adjust the xy components of the mesh using one of the mappings described here:
/// https://arxiv.org/ftp/arxiv/papers/1509/1509.06344.pdf
/// I found that paper here:
/// https://stackoverflow.com/questions/13211595/how-can-i-convert-coordinates-on-a-circle-to-coordinates-on-a-square
/// This is so we can connect up to the RLD mesh later.
/// </summary>
private static Mesh CatenoidSquared(double waist, double height)
{
Mesh mesh = new Mesh();
int res = m_params.Res * 2;
double diskRad = waist * Math.Cosh(height / 2 / waist);;
// NOTE: A band is *not* a constant height slice,
// so the input z value is the height at the edge midpoints of the square.
Func <double, Vector3D[]> oneCircle = z =>
{
bool neg = z < 0;
z = Math.Abs(z);
// Radius on disk at a starting edge midpoint.
double r = waist * Math.Cosh(z / waist);
Vector3D start = new Vector3D(r, 0);
Vector3D axis = new Vector3D(0, 0, 1);
List <Vector3D> points = new List <Vector3D>();
double angleInc = 2 * Math.PI / res;
double angle = 0;
for (int i = 0; i < res; i++)
{
Vector3D point = start;
point.RotateAboutAxis(axis, angle);
point = DiskToSquare(point, diskRad);
double zi = waist * DonHatch.acosh(point.Abs() / waist);
if (double.IsNaN(zi))
{
zi = 0;
}
if (neg)
{
zi *= -1;
}
Vector3D newPoint = new Vector3D(point.X, point.Y, zi);
if (newPoint.DNE)
{
throw new System.Exception();
}
points.Add(newPoint);
angle += angleInc;
}
return(points.ToArray());
};
double inc = height / (res * 2);
for (int i = 0; i < res; i++)
{
double z1 = inc * i;
double z2 = inc * (i + 1);
mesh.AddBand(oneCircle(z1), oneCircle(z2));
mesh.AddBand(oneCircle(-z1), oneCircle(-z2));
}
return(mesh);
}
