/// <summary>
/// Creates a manifold, consisting of a topology and vertex positions, in the shape of a cube.
/// </summary>
/// <param name="surface">The spherical surface describing the overall shape of the manifold.</param>
/// <param name="topology">The topology created.</param>
/// <param name="vertexPositions">The vertex positions created.</param>
public static void CreateCube(SphericalSurface surface, out Topology topology, out Vector3[] vertexPositions)
{
var a = surface.radius / Mathf.Sqrt(3f);
vertexPositions = new Vector3[8];
vertexPositions[0] = new Vector3(+a, +a, +a);
vertexPositions[1] = new Vector3(+a, +a, -a);
vertexPositions[2] = new Vector3(-a, +a, -a);
vertexPositions[3] = new Vector3(-a, +a, +a);
vertexPositions[4] = new Vector3(+a, -a, +a);
vertexPositions[5] = new Vector3(+a, -a, -a);
vertexPositions[6] = new Vector3(-a, -a, -a);
vertexPositions[7] = new Vector3(-a, -a, +a);
var orientation = surface.orientation;
for (int i = 0; i < vertexPositions.Length; ++i)
{
vertexPositions[i] = orientation * vertexPositions[i];
}
var indexer = new ManualFaceNeighborIndexer(8, 24, 6);
if (!surface.isInverted)
{
indexer.AddFace(0, 1, 2, 3);
indexer.AddFace(0, 4, 5, 1);
indexer.AddFace(1, 5, 6, 2);
indexer.AddFace(2, 6, 7, 3);
indexer.AddFace(3, 7, 4, 0);
indexer.AddFace(7, 6, 5, 4);
}
else
{
indexer.AddFace(3, 2, 1, 0);
indexer.AddFace(1, 5, 4, 0);
indexer.AddFace(2, 6, 5, 1);
indexer.AddFace(3, 7, 6, 2);
indexer.AddFace(0, 4, 7, 3);
indexer.AddFace(4, 5, 6, 7);
}
topology = TopologyUtility.BuildTopology(indexer);
}
/// <summary>
/// Creates a manifold, consisting of a topology and vertex positions, in the shape of an octahedron.
/// </summary>
/// <param name="surface">The spherical surface describing the overall shape of the manifold.</param>
/// <param name="topology">The topology created.</param>
/// <param name="vertexPositions">The vertex positions created.</param>
public static void CreateOctahedron(SphericalSurface surface, out Topology topology, out Vector3[] vertexPositions)
{
vertexPositions = new Vector3[6];
vertexPositions[0] = new Vector3(0, +surface.radius, 0);
vertexPositions[1] = new Vector3(+surface.radius, 0, 0);
vertexPositions[2] = new Vector3(0, 0, -surface.radius);
vertexPositions[3] = new Vector3(-surface.radius, 0, 0);
vertexPositions[4] = new Vector3(0, 0, +surface.radius);
vertexPositions[5] = new Vector3(0, -surface.radius, 0);
var orientation = surface.orientation;
for (int i = 0; i < vertexPositions.Length; ++i)
{
vertexPositions[i] = orientation * vertexPositions[i];
}
var indexer = new ManualFaceNeighborIndexer(6, 24, 8);
if (!surface.isInverted)
{
indexer.AddFace(0, 1, 2);
indexer.AddFace(0, 2, 3);
indexer.AddFace(0, 3, 4);
indexer.AddFace(0, 4, 1);
indexer.AddFace(2, 1, 5);
indexer.AddFace(3, 2, 5);
indexer.AddFace(4, 3, 5);
indexer.AddFace(1, 4, 5);
}
else
{
indexer.AddFace(2, 1, 0);
indexer.AddFace(3, 2, 0);
indexer.AddFace(4, 3, 0);
indexer.AddFace(1, 4, 0);
indexer.AddFace(5, 1, 2);
indexer.AddFace(5, 2, 3);
indexer.AddFace(5, 3, 4);
indexer.AddFace(5, 4, 1);
}
topology = TopologyUtility.BuildTopology(indexer);
}
/// <summary>
/// Creates a manifold, consisting of a topology and vertex positions, in the shape of a tetrahedron.
/// </summary>
/// <param name="surface">The spherical surface describing the overall shape of the manifold.</param>
/// <param name="topology">The topology created.</param>
/// <param name="vertexPositions">The vertex positions created.</param>
public static void CreateTetrahedron(SphericalSurface surface, out Topology topology, out Vector3[] vertexPositions)
{
var y = surface.radius * -1f / 3f;
var z0 = surface.radius * 2f / 3f * Mathf.Sqrt(2f);
var z1 = surface.radius * -Mathf.Sqrt(2f / 9f);
var x = surface.radius * Mathf.Sqrt(2f / 3f);
vertexPositions = new Vector3[4];
vertexPositions[0] = new Vector3(0, surface.radius, 0);
vertexPositions[1] = new Vector3(0, y, z0);
vertexPositions[2] = new Vector3(+x, y, z1);
vertexPositions[3] = new Vector3(-x, y, z1);
var orientation = surface.orientation;
for (int i = 0; i < vertexPositions.Length; ++i)
{
vertexPositions[i] = orientation * vertexPositions[i];
}
var indexer = new ManualFaceNeighborIndexer(4, 12, 4);
if (!surface.isInverted)
{
indexer.AddFace(0, 1, 2);
indexer.AddFace(0, 2, 3);
indexer.AddFace(0, 3, 1);
indexer.AddFace(3, 2, 1);
}
else
{
indexer.AddFace(2, 1, 0);
indexer.AddFace(3, 2, 0);
indexer.AddFace(1, 3, 0);
indexer.AddFace(1, 2, 3);
}
topology = TopologyUtility.BuildTopology(indexer);
}
/// <summary>
/// Creates a new topology based on the one provided, subdividing each face into multiple smaller faces, and adding extra vertices and edges accordingly.
/// </summary>
/// <param name="topology">The original topology to be subdivided. Cannot contain internal faces with neighbor counts of any value other than 3 or 4.</param>
/// <param name="vertexPositions">The positions of the original topology's vertices.</param>
/// <param name="degree">The degree of subdivision, equivalent to the number of additional vertices that will be added along each original edge. Must be non-negative, and a value of zero will result in an exact duplicate with no subdivision.</param>
/// <param name="interpolator">The function that interpolates between two vertex positions along an edge for determining the positions of new vertices. Particularly useful for curved surfaces.</param>
/// <param name="subdividedTopology">The copied and subdivided topology.</param>
/// <param name="subdividedVertexPositions">The positions of the subdivided vertices.</param>
public static void Subdivide(Topology topology, IVertexAttribute <Vector3> vertexPositions, int degree, Func <Vector3, Vector3, float, Vector3> interpolator, out Topology subdividedTopology, out Vector3[] subdividedVertexPositions)
{
if (degree < 0)
{
throw new ArgumentOutOfRangeException("degree", degree, "Topology subdivision degree cannot be negative.");
}
if (degree == 0)
{
subdividedTopology = (Topology)topology.Clone();
var subdividedVertexPositionsArray = new Vector3[topology.vertices.Count];
vertexPositions.CopyTo(subdividedVertexPositionsArray, 0);
subdividedVertexPositions = subdividedVertexPositionsArray;
return;
}
int vertexCount = 0;
int edgeCount = 0;
int internalFaceCount = 0;
vertexCount += topology.vertices.Count + (topology.halfEdges.Count / 2) * degree;
foreach (var face in topology.internalFaces)
{
switch (face.neighborCount)
{
case 3:
vertexCount += (degree * (degree - 1)) / 2;
edgeCount += (degree + 1) * (degree + 1) * 3;
internalFaceCount += (degree + 1) * (degree + 1);
break;
case 4:
vertexCount += degree * degree;
edgeCount += (degree + 1) * (degree + 1) * 4;
internalFaceCount += (degree + 1) * (degree + 1);
break;
default:
throw new InvalidOperationException("Cannot subdivide a face with anything other than 3 or 4 sides.");
}
}
foreach (var face in topology.externalFaces)
{
edgeCount += face.neighborCount * (degree + 1);
}
var indexer = new ManualFaceNeighborIndexer(vertexCount, edgeCount, internalFaceCount, topology.externalFaces.Count);
var subdividedVertexPositionsList = new List <Vector3>();
foreach (var vertex in topology.vertices)
{
subdividedVertexPositionsList.Add(vertexPositions[vertex]);
}
var currentVertexCount = topology.vertices.Count;
var dt = 1f / (degree + 1);
var tEnd = 1f - dt * 0.5f;
var subdividedEdgeVertices = new int[topology.halfEdges.Count * degree];
foreach (var edge in topology.vertexEdges)
{
if (edge.isFirstTwin)
{
var p0 = vertexPositions[edge.nearVertex];
var p1 = vertexPositions[edge.farVertex];
var t = dt;
var subdividedEdgeVertexIndex = edge.index * degree;
while (t < tEnd)
{
subdividedEdgeVertices[subdividedEdgeVertexIndex++] = currentVertexCount++;
subdividedVertexPositionsList.Add(interpolator(p0, p1, t));
t += dt;
}
}
else
{
var subdividedEdgeVertexIndex = edge.index * degree;
var subdividedTwinEdgeVertexIndex = (edge.twinIndex + 1) * degree - 1;
for (int i = 0; i < degree; ++i)
{
subdividedEdgeVertices[subdividedEdgeVertexIndex + i] = subdividedEdgeVertices[subdividedTwinEdgeVertexIndex - i];
}
}
}
foreach (var face in topology.internalFaces)
{
switch (face.neighborCount)
{
case 3:
SubdivideTriangle(indexer, face, degree, interpolator, subdividedVertexPositionsList, subdividedEdgeVertices, ref currentVertexCount);
break;
case 4:
SubdivideQuadrilateral(indexer, face, degree, interpolator, subdividedVertexPositionsList, subdividedEdgeVertices, ref currentVertexCount);
break;
default:
throw new InvalidOperationException("Cannot subdivide a face with anything other than 3 or 4 sides.");
}
}
subdividedTopology = TopologyUtility.BuildTopology(indexer);
subdividedVertexPositions = subdividedVertexPositionsList.ToArray();
}
/// <summary>
/// Creates a topology from the grid specifications of the current surface.
/// </summary>
/// <returns>A topology corresponding to the grid specifications of the surface.</returns>
public Topology CreateTopology()
{
return(TopologyUtility.BuildTopology(this));
}
/// <summary>
/// Creates a manifold, consisting of a topology and vertex positions, in the shape of an icosahedron.
/// </summary>
/// <param name="surface">The spherical surface describing the overall shape of the manifold.</param>
/// <param name="topology">The topology created.</param>
/// <param name="vertexPositions">The vertex positions created.</param>
public static void CreateIcosahedron(SphericalSurface surface, out Topology topology, out Vector3[] vertexPositions)
{
var latitude = Mathf.Atan2(1, 2);
var longitude = Mathf.PI * 0.2f;
var cosLat = Mathf.Cos(latitude);
var scaledCosLat = surface.radius * cosLat;
var x0 = 0.0f;
var x1 = scaledCosLat * Mathf.Sin(longitude);
var x2 = scaledCosLat * Mathf.Sin(longitude * 2.0f);
var y0 = +surface.radius;
var y1 = surface.radius * Mathf.Sin(latitude);
var y2 = -surface.radius;
var z0 = scaledCosLat;
var z1 = scaledCosLat * Mathf.Cos(longitude);
var z2 = scaledCosLat * Mathf.Cos(longitude * 2.0f);
vertexPositions = new Vector3[12];
vertexPositions[0] = new Vector3(x0, y0, 0f);
vertexPositions[1] = new Vector3(x0, +y1, -z0);
vertexPositions[2] = new Vector3(-x2, +y1, -z2);
vertexPositions[3] = new Vector3(-x1, +y1, +z1);
vertexPositions[4] = new Vector3(+x1, +y1, +z1);
vertexPositions[5] = new Vector3(+x2, +y1, -z2);
vertexPositions[6] = new Vector3(x0, -y1, +z0);
vertexPositions[7] = new Vector3(-x2, -y1, +z2);
vertexPositions[8] = new Vector3(-x1, -y1, -z1);
vertexPositions[9] = new Vector3(+x1, -y1, -z1);
vertexPositions[10] = new Vector3(+x2, -y1, +z2);
vertexPositions[11] = new Vector3(x0, y2, 0f);
var orientation = surface.orientation;
for (int i = 0; i < vertexPositions.Length; ++i)
{
vertexPositions[i] = orientation * vertexPositions[i];
}
var indexer = new ManualFaceNeighborIndexer(12, 60, 20);
if (!surface.isInverted)
{
indexer.AddFace(0, 1, 2);
indexer.AddFace(0, 2, 3);
indexer.AddFace(0, 3, 4);
indexer.AddFace(0, 4, 5);
indexer.AddFace(0, 5, 1);
indexer.AddFace(1, 8, 2);
indexer.AddFace(2, 8, 7);
indexer.AddFace(2, 7, 3);
indexer.AddFace(3, 7, 6);
indexer.AddFace(3, 6, 4);
indexer.AddFace(4, 6, 10);
indexer.AddFace(4, 10, 5);
indexer.AddFace(5, 10, 9);
indexer.AddFace(5, 9, 1);
indexer.AddFace(1, 9, 8);
indexer.AddFace(11, 6, 7);
indexer.AddFace(11, 7, 8);
indexer.AddFace(11, 8, 9);
indexer.AddFace(11, 9, 10);
indexer.AddFace(11, 10, 6);
}
else
{
indexer.AddFace(2, 1, 0);
indexer.AddFace(3, 2, 0);
indexer.AddFace(4, 3, 0);
indexer.AddFace(5, 4, 0);
indexer.AddFace(1, 5, 0);
indexer.AddFace(2, 8, 1);
indexer.AddFace(7, 8, 2);
indexer.AddFace(3, 7, 2);
indexer.AddFace(6, 7, 3);
indexer.AddFace(4, 6, 3);
indexer.AddFace(10, 6, 4);
indexer.AddFace(5, 10, 4);
indexer.AddFace(9, 10, 5);
indexer.AddFace(1, 9, 5);
indexer.AddFace(8, 9, 1);
indexer.AddFace(7, 6, 11);
indexer.AddFace(8, 7, 11);
indexer.AddFace(9, 8, 11);
indexer.AddFace(10, 9, 11);
indexer.AddFace(6, 10, 11);
}
topology = TopologyUtility.BuildTopology(indexer);
}
