/// <inheritdoc />
public override Vector3 GetPositionAt(Vector2 uv)
{
float v = uv.Y;
Vector3 translation = CenterCurve.GetPositionAt(v);
float radius = Radius.GetValueAt(uv);
return(translation + radius * GetNormalAt(uv));
}
/// <inheritdoc />
public override dvec3 GetPositionAt(dvec2 uv)
{
DebugUtil.AssertAllFinite(uv, nameof(uv));
double v = uv.y;
dvec3 translation = CenterCurve.GetPositionAt(v);
double radius = Radius.GetValueAt(uv);
return(translation + radius * GetNormalAt(uv));
}
/// <inheritdoc />
public override Vector3 GetNormalAt(Vector2 uv)
{
float u = uv.X;
float v = uv.Y;
Vector3 curveTangent = Vector3.Normalize(CenterCurve.GetTangentAt(v));
Vector3 curveNormal = Vector3.Normalize(CenterCurve.GetNormalAt(v));
Vector3 curveBinormal = Vector3.Cross(curveTangent, curveNormal);
float startAngle = StartAngle.GetValueAt(v);
float endAngle = EndAngle.GetValueAt(v);
return((float)Math.Cos(u) * curveNormal + (float)Math.Sin(u) * curveBinormal);
}
/// <inheritdoc />
public override dvec3 GetNormalAt(dvec2 uv)
{
DebugUtil.AssertAllFinite(uv, nameof(uv));
double u = uv.x;
double v = uv.y;
dvec3 curveTangent = CenterCurve.GetTangentAt(v).Normalized;
dvec3 curveNormal = CenterCurve.GetNormalAt(v).Normalized;
dvec3 curveBinormal = dvec3.Cross(curveTangent, curveNormal);
double startAngle = StartAngle.GetValueAt(v);
double endAngle = EndAngle.GetValueAt(v);
return(Math.Cos(u) * curveNormal + Math.Sin(u) * curveBinormal);
}
/// <inheritdoc />
public override List <Vertex> GenerateVertexList(int resolutionU, int resolutionV)
{
// If asked to sample at zero points, return an empty list.
if (resolutionU <= 0 || resolutionV <= 0)
{
return(new List <Vertex>());
}
var roughs = ParallelEnumerable.Range(0, resolutionV + 1).AsOrdered().SelectMany((j =>
{
double v = (double)j / (double)resolutionV;
// Find the values at each ring:
dvec3 curveTangent = CenterCurve.GetTangentAt(v).Normalized;
dvec3 curveNormal = CenterCurve.GetNormalAt(v).Normalized;
dvec3 curveBinormal = dvec3.Cross(curveTangent, curveNormal);
dvec3 translation = CenterCurve.GetPositionAt(v);
double startAngle = StartAngle.GetValueAt(v);
double endAngle = EndAngle.GetValueAt(v);
return(Enumerable.Range(0, resolutionU).Select((i) =>
{
double u = startAngle + (endAngle - startAngle) * (double)i / (double)resolutionU;
double radius = Radius.GetValueAt(new dvec2(u, v));
// Calculate the position of the rings of vertices:
dvec3 surfaceNormal = (double)Math.Cos(u) * curveNormal + (double)Math.Sin(u) * curveBinormal;
dvec3 surfacePosition = translation + radius * surfaceNormal;
return new Vertex((vec3)surfacePosition, (vec3)surfaceNormal);
}));
}));
List <Vertex> output = roughs.ToList();
// Recalculate the surface normal after deformation:
for (int j = 1; j < resolutionV; j++)
{
for (int i = 0; i < (resolutionU - 1); i++)
{
dvec3 surfacePosition = output[(j - 1) * resolutionU + i].Position;
dvec3 du = surfacePosition - output[(j - 1) * resolutionU + i + 1].Position;
dvec3 dv = surfacePosition - output[(j) * resolutionU + i].Position;
// Calculate the position of the rings of vertices:
dvec3 surfaceNormal = dvec3.Cross(du.Normalized, dv.Normalized);
output[(j - 1) * resolutionU + i] = new Vertex((vec3)surfacePosition, (vec3)surfaceNormal);
}
// Stitch the end of the triangles:
dvec3 surfacePosition2 = output[(j - 1) * resolutionU + resolutionU - 1].Position;
dvec3 du2 = surfacePosition2 - output[(j - 1) * resolutionU].Position;
dvec3 dv2 = surfacePosition2 - output[(j) * resolutionU + resolutionU - 1].Position;
// Calculate the position of the rings of vertices:
dvec3 surfaceNormal2 = dvec3.Cross(du2.Normalized, dv2.Normalized);
output[(j - 1) * resolutionU + resolutionU - 1] = new Vertex((vec3)surfacePosition2, (vec3)surfaceNormal2);
}
return(output);
}
/// <inheritdoc />
public override List <Vertex> GenerateVertexList(int resolutionU, int resolutionV)
{
List <Vertex> output = new List <Vertex>(CalculateVertexCount(resolutionU, resolutionV));
for (int j = 0; j < (resolutionV + 1); j++)
{
float v = (float)j / (float)resolutionV;
// Find the values at each ring:
Vector3 curveTangent = Vector3.Normalize(CenterCurve.GetTangentAt(v));
Vector3 curveNormal = Vector3.Normalize(CenterCurve.GetNormalAt(v));
Vector3 curveBinormal = Vector3.Cross(curveTangent, curveNormal);
Vector3 translation = CenterCurve.GetPositionAt(v);
float startAngle = StartAngle.GetValueAt(v);
float endAngle = EndAngle.GetValueAt(v);
for (int i = 0; i < resolutionU; i++)
{
// First find the normalized uv-coordinates, u = [0, 2pi], v = [0, 1]:
float u = startAngle + (endAngle - startAngle) * (float)i / (float)resolutionU;
float radius = Radius.GetValueAt(new Vector2(u, v));
// Calculate the position of the rings of vertices:
Vector3 surfaceNormal = (float)Math.Cos(u) * curveNormal + (float)Math.Sin(u) * curveBinormal;
Vector3 surfacePosition = translation + radius * surfaceNormal;
output.Add(new Vertex(surfacePosition, surfaceNormal));
}
}
// Recalculate the surface normal after deformation:
for (int j = 1; j < resolutionV; j++)
{
for (int i = 0; i < (resolutionU - 1); i++)
{
Vector3 surfacePosition = output[(j - 1) * resolutionU + i].Position;
Vector3 du = surfacePosition - output[(j - 1) * resolutionU + i + 1].Position;
Vector3 dv = surfacePosition - output[(j) * resolutionU + i].Position;
// Calculate the position of the rings of vertices:
Vector3 surfaceNormal = Vector3.Cross(Vector3.Normalize(du), Vector3.Normalize(dv));
output[(j - 1) * resolutionU + i] = new Vertex(surfacePosition, surfaceNormal);
}
// Stitch the end of the triangles:
Vector3 surfacePosition2 = output[(j - 1) * resolutionU + resolutionU - 1].Position;
Vector3 du2 = surfacePosition2 - output[(j - 1) * resolutionU].Position;
Vector3 dv2 = surfacePosition2 - output[(j) * resolutionU + resolutionU - 1].Position;
// Calculate the position of the rings of vertices:
Vector3 surfaceNormal2 = Vector3.Cross(Vector3.Normalize(du2), Vector3.Normalize(dv2));
output[(j - 1) * resolutionU + resolutionU - 1] = new Vertex(surfacePosition2, surfaceNormal2);
}
return(output);
}