/// <inheritdoc />
public override List <int> GenerateIndexList(int resolutionU, int resolutionV, int indexOffset = 0)
{
// The index list of a model tells the GPU between which vertices to draw triangles. Each three consecutive
// indices constitute a single triangle. Since the Capsule vertex array consists of several lists stitched
// together, the indices of the shaft and endCap will have shifted by some amount. Therefore, calculate
// this index offset for all submodels:
int indexOffset2 = indexOffset + Hemisphere.CalculateVertexCount(resolutionU, resolutionU / 4) - resolutionU;
int indexOffset3 = indexOffset2 + Cylinder.CalculateVertexCount(resolutionU, resolutionV) - resolutionU;
int indexOffset4 = indexOffset3 + Hemisphere.CalculateVertexCount(resolutionU, resolutionU / 4) - resolutionU;
// Generate the startCap indices as normal:
List <int> startCapList = startCap.GenerateIndexList(resolutionU, resolutionU / 4, indexOffset);
// Generate a shaft, using the last ring of the startCap to begin with. This is done by subtracting
// `resolutionU` from indexOffset2. This automatically stitches the gap between the start cap and the shaft:
List <int> shaftList = shaft.GenerateIndexList(resolutionU, resolutionV - 1, indexOffset2);
// Generate the endCap indices as normal:
List <int> endCapList = endCap.GenerateIndexList(resolutionU, resolutionU / 4, indexOffset3);
// The final ring between the endCap and the shaft must be generated manually:
List <int> stitchList = new List <int>(resolutionU);
// Add a ring of triangles:
for (int i = 1; i < resolutionU - 1; i++)
{
int invertedI = resolutionU - i;
stitchList.Add(indexOffset + invertedI + indexOffset4);
stitchList.Add(indexOffset + (i + 1) + indexOffset3 - resolutionU);
stitchList.Add(indexOffset + i + indexOffset3 - resolutionU);
stitchList.Add(indexOffset + (invertedI - 1) + indexOffset4);
stitchList.Add(indexOffset + (i + 1) + indexOffset3 - resolutionU);
stitchList.Add(indexOffset + invertedI + indexOffset4);
}
// Stitch the end of the ring of triangles:
stitchList.Add(indexOffset + 1 + indexOffset4);
stitchList.Add(indexOffset + indexOffset3 - resolutionU);
stitchList.Add(indexOffset + resolutionU - 1 + indexOffset3 - resolutionU);
stitchList.Add(indexOffset + indexOffset4);
stitchList.Add(indexOffset + indexOffset3 - resolutionU);
stitchList.Add(indexOffset + 1 + indexOffset4);
stitchList.Add(indexOffset + resolutionU - 1 + indexOffset4);
stitchList.Add(indexOffset + 1 + indexOffset3 - resolutionU);
stitchList.Add(indexOffset + indexOffset3 - resolutionU);
stitchList.Add(indexOffset + indexOffset4);
stitchList.Add(indexOffset + resolutionU - 1 + indexOffset4);
stitchList.Add(indexOffset + indexOffset3 - resolutionU);
return(startCapList.Concat(shaftList).Concat(endCapList).Concat(stitchList).ToList());
}
public override List <int> GenerateIndexList(int resolutionU, int resolutionV, int indexOffset = 0)
{
int indexOffset2 = indexOffset + Hemisphere.CalculateVertexCount(resolutionU, resolutionU / 4);
int indexOffset3 = indexOffset + indexOffset2 + Cylinder.CalculateVertexCount(resolutionU, resolutionV);
List <int> startCapList = startCap.GenerateIndexList(resolutionU, resolutionU / 4, indexOffset);
List <int> shaftList = shaft.GenerateIndexList(resolutionU, resolutionV, indexOffset2);
List <int> endCapList = endCap.GenerateIndexList(resolutionU, resolutionU / 4, indexOffset3);
return(startCapList.Concat(shaftList).Concat(endCapList).ToList());
}
public Capsule(Cylinder shaft)
{
this.shaft = shaft;
this.startCap = new Hemisphere(
shaft.Radius.GetValueAt(0.0f),
shaft.CenterCurve.GetStartPosition(),
-shaft.CenterCurve.GetTangentAt(0.0f)
);
this.endCap = new Hemisphere(
shaft.Radius.GetValueAt(1.0f),
shaft.CenterCurve.GetEndPosition(),
shaft.CenterCurve.GetTangentAt(1.0f)
);
}
/// <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)
);
}