/// <inheritdoc />
public override List <Vertex> GenerateVertexList(int resolutionU, int resolutionV)
{
// Generate the vertices of two end caps, and a shaft in between:
List <Vertex> startCapList = startCap.GenerateVertexList(resolutionU, resolutionU / 4);
List <Vertex> endCapList = endCap.GenerateVertexList(resolutionU, resolutionU / 4);
// Using a slice, remove the first and last ring of vertices of the shaft, which overlap with the last
// rings of the startCap and endCap respectively. Later we will stitch the shaft and end caps together with
// triangles between them, during the GenerateIndexList() step.
Slice <Vertex> shaftSlice = new Slice <Vertex>(
shaft.GenerateVertexList(resolutionU, resolutionV),
resolutionU,
Cylinder.CalculateVertexCount(resolutionU, resolutionV) - 2 * resolutionU);
// Recalculate the surface normal between the cylinder and the start cap:
for (int i = 0; i < (resolutionU - 1); i++)
{
dvec3 surfacePosition = startCapList[(resolutionU / 4 - 1) * resolutionU + i + 1].Position;
dvec3 du = surfacePosition - startCapList[(resolutionU / 4 - 1) * resolutionU + i + 1 + 1].Position;
dvec3 dv = surfacePosition - shaftSlice[i].Position;
// Calculate the position of the rings of vertices:
dvec3 surfaceNormal = dvec3.Cross(du.Normalized, dv.Normalized);
startCapList[(resolutionU / 4 - 1) * resolutionU + i + 1] = new Vertex((vec3)surfacePosition, (vec3)surfaceNormal);
}
// Stitch the end of the triangles:
dvec3 surfacePosition2 = startCapList[(resolutionU / 4 - 1) * resolutionU + resolutionU].Position;
dvec3 du2 = surfacePosition2 - startCapList[(resolutionU / 4 - 1) * resolutionU + 1].Position;
dvec3 dv2 = surfacePosition2 - shaftSlice[resolutionU].Position;
// Calculate the position of the rings of vertices:
dvec3 surfaceNormal2 = dvec3.Cross(du2.Normalized, dv2.Normalized);
startCapList[(resolutionU / 4 - 1) * resolutionU + resolutionU] = new Vertex((vec3)surfacePosition2, (vec3)surfaceNormal2);
return(startCapList.Concat(shaftSlice).Concat(endCapList).ToList());
}
/// <summary>
/// Construct a new <c>Capsule</c> around a central curve, the <c>centerCurve</c>.
/// The radius at each point on the central axis is defined by a one-dimensional function <c>radius</c>.
///
/// The surface is parametrized with the coordinates \f$u, \phi\f$, with \f$u\f (along the length of the
/// shaft) and \f$\phi \in [0, 2 \pi]\f$ along the radial coordinate. A <c>Capsule</c> consists of a
/// cylindrical shaft with two hemisphere end caps. $\f$u \in [-\frac{1}{2} \pi, 0]\f$ marks the region
/// in parametrized coordinates of the hemisphere at the start point of the cylinder,
/// $\f$u \in [0, 1]\f$ marks the region in parametrized coordinates of the central shaft,
/// and $\f$u \in [1, 1 + \frac{1}{2} \pi]\f$ marks the region in parametrized coordinates of the hemisphere
/// at the end point of the cylinder. The <c>heightMap</c> is a two-dimensional function defined on these
/// coordinates on the domain given above.
/// </summary>
/// <param name="centerCurve">
/// <inheritdoc cref="Capsule.CenterCurve"/>
/// </param>
/// <param name="heightMap">
/// The radius at each point on the surface. A <c>Capsule</c> is generated around a central curve, with each
/// point on the surface at a certain distance from the curve defined by <c>heightMap</c>. <c>heightMap</c>
/// is therefore a two-dimensional function $h(u, \phi)$ that outputs a distance from the curve at each of
/// the surface's parametric coordinates.
/// </param>
public Capsule(Curve centerCurve, ContinuousMap <Vector2, float> heightMap)
{
Vector3 startTangent = -centerCurve.GetTangentAt(0.0f);
Vector3 startNormal = centerCurve.GetNormalAt(0.0f);
Vector3 endTangent = centerCurve.GetTangentAt(1.0f);
Vector3 endNormal = centerCurve.GetNormalAt(1.0f);
this.shaft = new Cylinder(centerCurve, heightMap);
this.startCap = new Hemisphere(
new ShiftedMap2D <float>(new Vector2(0.0f, -0.5f * (float)Math.PI), heightMap),
centerCurve.GetStartPosition(),
startTangent,
startNormal,
-Vector3.Cross(startTangent, startNormal)
);
this.endCap = new Hemisphere(
new ShiftedMap2D <float>(new Vector2(0.0f, 1.0f + 0.5f * (float)Math.PI), new Vector2(1.0f, -1.0f), heightMap),
centerCurve.GetEndPosition(),
endTangent,
endNormal,
-Vector3.Cross(endTangent, endNormal)
);
}
/// <summary>
/// Construct a new <c>Capsule</c> around a central curve, the <c>centerCurve</c>.
/// The radius at each point on the central axis is defined by a one-dimensional function <c>radius</c>.
///
/// The surface is parametrized with the coordinates \f$u, \phi\f$, with \f$u\f (along the length of the
/// shaft) and \f$\phi \in [0, 2 \pi]\f$ along the radial coordinate. A <c>Capsule</c> consists of a
/// cylindrical shaft with two hemisphere end caps. $\f$u \in [-\frac{1}{2} \pi, 0]\f$ marks the region
/// in parametrized coordinates of the hemisphere at the start point of the cylinder,
/// $\f$u \in [0, 1]\f$ marks the region in parametrized coordinates of the central shaft,
/// and $\f$u \in [1, 1 + \frac{1}{2} \pi]\f$ marks the region in parametrized coordinates of the hemisphere
/// at the end point of the cylinder. The <c>heightMap</c> is a two-dimensional function defined on these
/// coordinates on the domain given above.
/// </summary>
/// <param name="centerCurve">
/// <inheritdoc cref="Capsule.CenterCurve"/>
/// </param>
/// <param name="heightMap">
/// The radius at each point on the surface. A <c>Capsule</c> is generated around a central curve, with each
/// point on the surface at a certain distance from the curve defined by <c>heightMap</c>. <c>heightMap</c>
/// is therefore a two-dimensional function $h(u, \phi)$ that outputs a distance from the curve at each of
/// the surface's parametric coordinates.
/// </param>
public Capsule(Curve centerCurve, ContinuousMap <dvec2, double> heightMap)
{
dvec3 startTangent = -centerCurve.GetTangentAt(0.0);
dvec3 startNormal = centerCurve.GetNormalAt(0.0);
dvec3 endTangent = centerCurve.GetTangentAt(1.0);
dvec3 endNormal = centerCurve.GetNormalAt(1.0);
this.shaft = new Cylinder(centerCurve, heightMap);
this.startCap = new Hemisphere(
new ShiftedMap2D <double>(new dvec2(0.0, -0.5 * Math.PI), heightMap),
centerCurve.GetStartPosition(),
startTangent,
startNormal,
-dvec3.Cross(startTangent, startNormal)
);
this.endCap = new Hemisphere(
new ShiftedMap2D <double>(new dvec2(0.0, 1.0 + 0.5 * Math.PI), new dvec2(1.0, -1.0), heightMap),
centerCurve.GetEndPosition(),
endTangent,
endNormal,
-dvec3.Cross(endTangent, endNormal)
);
}
