private static void SplitEachFacetInFour(KModel model)
{
// Create a new vertex at the midpoint of every edge
var edge2Vertex = new Dictionary<Tuple<int, int>, int>();
foreach (var facet in model.Facets)
{
foreach (var t in new Tuple<int, int>[] {
Tuple.Create(facet.Ve0, facet.Ve1),
Tuple.Create(facet.Ve1, facet.Ve2),
Tuple.Create(facet.Ve2, facet.Ve0)})
{
if (!edge2Vertex.ContainsKey(t))
{
Vector3 midPoint = (model.Vertices[t.Item1].Pt + model.Vertices[t.Item2].Pt) / 2;
int veMidpoint = model.AddVertex(midPoint);
edge2Vertex.Add(t, veMidpoint);
edge2Vertex.Add(Tuple.Create(t.Item2, t.Item1), veMidpoint);
}
}
}
// Split each facet in four
var originalFacetCount = model.Facets.Count;
for (int faId = 0; faId < originalFacetCount; faId++)
{
var f = model.Facets[faId];
// Corners of original facet
int ve0 = f.Ve0;
int ve1 = f.Ve1;
int ve2 = f.Ve2;
// Edge midpoints
int ve01 = edge2Vertex[Tuple.Create(f.Ve0, f.Ve1)];
int ve12 = edge2Vertex[Tuple.Create(f.Ve1, f.Ve2)];
int ve20 = edge2Vertex[Tuple.Create(f.Ve2, f.Ve0)];
// Texture coordinates of corners
var tex0 = f.Tex0;
var tex1 = f.Tex1;
var tex2 = f.Tex2;
// Texture coordinates of midpoints
var tex01 = 0.5f * (tex0 + tex1);
var tex12 = 0.5f * (tex1 + tex2);
var tex20 = 0.5f * (tex2 + tex0);
//
// 2
// / \
// 20---12
// / \ / \
// 0---01--1
// First facet: 0-01-20 (change the original)
f.Ve1 = ve01;
f.Ve2 = ve20;
f.Tex1 = tex01;
f.Tex2 = tex20;
// 01-1-12
f = model.Facets[model.AddFacet(ve01, ve1, ve12)];
f.Tex0 = tex01;
f.Tex1 = tex1;
f.Tex2 = tex12;
// 01-12-20
f = model.Facets[model.AddFacet(ve01, ve12, ve20)];
f.Tex0 = tex01;
f.Tex1 = tex12;
f.Tex2 = tex20;
// 20-12-2
f = model.Facets[model.AddFacet(ve20, ve12, ve2)];
f.Tex0 = tex20;
f.Tex1 = tex12;
f.Tex2 = tex2;
}
}
/// <summary>
/// Creates an icosahedron (regular polyhedron with 20 triangle sides) with vertices on the unit sphere.
/// </summary>
public static KModel CreateIcosahedron(Rectangle texRect)
{
// aka golden ratio
float tao = (float)(1 + Math.Sqrt(5)) / 2;
var model = new KModel();
int v0 = model.AddVertex(new Vector3(1, tao, 0).Normalized());
int v1 = model.AddVertex(new Vector3(-1, tao, 0).Normalized());
int v2 = model.AddVertex(new Vector3(1, -tao, 0).Normalized());
int v3 = model.AddVertex(new Vector3(-1, -tao, 0).Normalized());
int v4 = model.AddVertex(new Vector3(0, 1, tao).Normalized());
int v5 = model.AddVertex(new Vector3(0, -1, tao).Normalized());
int v6 = model.AddVertex(new Vector3(0, 1, -tao).Normalized());
int v7 = model.AddVertex(new Vector3(0, -1, -tao).Normalized());
int v8 = model.AddVertex(new Vector3(tao, 0, 1).Normalized());
int v9 = model.AddVertex(new Vector3(-tao, 0, 1).Normalized());
int vA = model.AddVertex(new Vector3(tao, 0, -1).Normalized());
int vB = model.AddVertex(new Vector3(-tao, 0, -1).Normalized());
model.AddFacet(v0, v6, v1);
model.AddFacet(v0, vA, v6);
model.AddFacet(v0, v8, vA);
model.AddFacet(v0, v4, v8);
model.AddFacet(v0, v1, v4);
model.AddFacet(v3, v5, v9);
model.AddFacet(v3, v2, v5);
model.AddFacet(v3, v7, v2);
model.AddFacet(v3, vB, v7);
model.AddFacet(v3, v9, vB);
model.AddFacet(v1, v6, vB);
model.AddFacet(v1, v9, v4);
model.AddFacet(v1, vB, v9);
model.AddFacet(v2, v7, vA);
model.AddFacet(v2, v8, v5);
model.AddFacet(v2, vA, v8);
model.AddFacet(v4, v5, v8);
model.AddFacet(v4, v9, v5);
model.AddFacet(v6, v7, vB);
model.AddFacet(v6, vA, v7);
// Set texture coordinates on all facets
foreach (var facet in model.Facets)
{
facet.Tex0 = new Vector2(texRect.Left, texRect.Top);
facet.Tex1 = new Vector2((texRect.Left + texRect.Right) / 2f, texRect.Bottom);
facet.Tex2 = new Vector2(texRect.Right, texRect.Top);
}
return model;
}
