/// <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 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));
// Load all required variables:
dvec3 up = dvec3.UnitZ;
dvec3 pointTangent = Direction;
dvec3 pointNormal = Normal;
dvec3 pointBinormal = Binormal;
dvec3 translation = Center;
// Get the radius at the top of the hemisphere:
double topRadius = Radius.GetValueAt(new dvec2(0.0, 0.5 * Math.PI));
// Generate the first point at the pole of the hemisphere:
output.Add(new Vertex((vec3)(translation + topRadius * pointTangent), (vec3)pointTangent));
// Generate rings of the other points:
for (int j = 1; j < (resolutionV + 1); j++)
{
for (int i = 0; i < resolutionU; i++)
{
// First find the normalized uv-coordinates, u = [0, 2pi], v = [0, 1/2pi]:
double u = i / (double)resolutionU * 2.0 * Math.PI;
double v = j / (double)resolutionV * 0.5 * Math.PI;
// Calculate the position of the rings of vertices:
double x = Math.Sin(v) * Math.Cos(u);
double y = Math.Sin(v) * Math.Sin(u);
double z = Math.Cos(v);
double radius = Radius.GetValueAt(new dvec2(u, v));
dvec3 surfaceNormal = x * pointNormal + y * pointBinormal + z * pointTangent;
dvec3 surfacePosition = translation + radius * surfaceNormal;
output.Add(new Vertex((vec3)surfacePosition, (vec3)surfaceNormal));
}
}
// 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 + 1].Position;
dvec3 du = surfacePosition - output[(j - 1) * resolutionU + i + 1 + 1].Position;
dvec3 dv = surfacePosition - output[(j) * resolutionU + i + 1].Position;
// Calculate the position of the rings of vertices:
dvec3 surfaceNormal = dvec3.Cross(du.Normalized, dv.Normalized);
output[(j - 1) * resolutionU + i + 1] = new Vertex((vec3)surfacePosition, (vec3)surfaceNormal);
}
// Stitch the end of the triangles:
dvec3 surfacePosition2 = output[(j - 1) * resolutionU + resolutionU].Position;
dvec3 du2 = surfacePosition2 - output[(j - 1) * resolutionU + 1].Position;
dvec3 dv2 = surfacePosition2 - output[(j) * resolutionU + resolutionU].Position;
// Calculate the position of the rings of vertices:
dvec3 surfaceNormal2 = dvec3.Cross(du2.Normalized, dv2.Normalized);
output[(j - 1) * resolutionU + resolutionU] = 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);
}
public override List <Vertex> GenerateVertexList(int resolutionU, int resolutionV)
{
List <Vertex> output = new List <Vertex>(CalculateVertexCount(resolutionU, resolutionV));
Console.WriteLine(resolutionV);
for (int j = 0; j < (resolutionV + 1); j++)
{
float v = (float)j / (float)resolutionV;
// Generate a rotation matrix to rotate each circle in the cylinder
// to align with the tangent vector of the center curve. The matrix
// rotates the 'up' vector onto the 'direction' vector, using
// Rodrigues' Rotation Formula:
Vector3 up = new Vector3(0.0f, 0.0f, 1.0f);
// To prevent division by zero, flip the direction if facing the other way:
float sign = 1.0f;
if (Vector3.Dot(up, CenterCurve.GetTangentAt(v)) < 0.0f)
{
sign = -1.0f;
}
Vector3 direction = Vector3.Normalize(CenterCurve.GetTangentAt(v));
Vector3 k = Vector3.Cross(sign * direction, up);
Matrix4x4 identity = new Matrix4x4(1.0f, 0.0f, 0.0f, 0.0f,
0.0f, 1.0f, 0.0f, 0.0f,
0.0f, 0.0f, 1.0f, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f);
Matrix4x4 K = new Matrix4x4(0.0f, -k.Z, k.Y, 0.0f,
k.Z, 0.0f, -k.X, 0.0f,
-k.Y, k.X, 0.0f, 0.0f,
0.0f, 0.0f, 0.0f, 0.0f);
Matrix4x4 rotationMatrix = identity + K + K * K * (1.0f / (1.0f + Vector3.Dot(up, sign * direction)));
Matrix4x4 transformationMatrix = rotationMatrix;
transformationMatrix.Translation = CenterCurve.GetPositionAt(v);
float radius = Radius.GetValueAt(v);
for (int i = 0; i < resolutionU; i++)
{
// First find the normalized uv-coordinates, u = [0, 2pi], v = [0, 1]:
float u = (float)i / (float)resolutionU * 2.0f * (float)Math.PI;
// Calculate the position of the rings of vertices:
float x = sign * (float)Math.Cos(u);
float y = sign * (float)Math.Sin(sign * u);
float z = 0;
Vector3 position = new Vector3(x, y, z);
// Rotate the vector to orient the hemisphere correctly:
Vector3 vertexPosition = Vector3.Transform(sign * radius * position, transformationMatrix);
Vector3 normal = Vector3.Transform(sign * position, rotationMatrix);
output.Add(new Vertex(vertexPosition, normal));
}
}
return(output);
}
