/// <summary>
/// Triangulates a list of vertices, interpreted as the vertices of a planar polygon in clockwise order.
/// </summary>
/// <param name="vertices">The vertices.</param>
/// <param name="normal">The normal of the polygon, if not know, use the overload without normal.</param>
/// <param name="triangles">The output in which the resulting triangles will be written.</param>
public static void Triangulate(this IList <Vector3> vertices, Vector3 normal, List <int> triangles)
{
if (vertices.Count == 3)
{
triangles.AddRange(new[] { 0, 1, 2 });
return;
}
if (vertices.Count == 4)
{
var d1 = Vector3.SqrMagnitude(vertices[0] - vertices[2]);
var d2 = Vector3.SqrMagnitude(vertices[1] - vertices[3]);
if (d1 > d2)
{
triangles.AddRange(new[] { 0, 1, 3, 1, 2, 3 });
return;
}
triangles.AddRange(new[] { 0, 1, 2, 0, 2, 3 });
return;
}
var vertexReferences = new LinkedList <(Vector3 v, float a, int i)>();
for (var i = 0; i < vertices.Count; i++)
{
var prev = vertices[Nums.Mod(i - 1, vertices.Count)];
var current = vertices[i];
var next = vertices[(i + 1) % vertices.Count];
vertexReferences.AddLast((current, Math3D.InnerAngle(prev, current, next, normal), i));
}
while (vertexReferences.Count > 3)
{
var prevCount = vertexReferences.Count;
var currentNode = vertexReferences.First;
// The inner angle when all inner angles are equal, used to exclude inner angles larger than this, as a smaller angle must exist then. (incl. epsilon)
var minAngle = 180f - (360f / vertexReferences.Count) + 1e-5f;
while (currentNode != null)
{
var prevNode = currentNode.Previous ?? vertexReferences.Last;
var nextNode = currentNode.Next ?? vertexReferences.First;
var current = currentNode.Value;
var angle = current.a;
// Test whether the three points are nearly collinear.
if (Mathf.Abs((angle - 0.001f) % 180) <= 0.001f)
{
// Don't create invalid triangles.
continue;
}
// If the inner angle of this vertex is pointy enough
if (angle <= minAngle)
{
var v0 = prevNode.Value.v;
var v1 = current.v;
var v2 = nextNode.Value.v;
var collision = false;
// Test whether any other vertex intersects with the triangle that we want as ear
foreach (var vr in vertexReferences)
{
if (vr.i == prevNode.Value.i || vr.i == current.i || vr.i == nextNode.Value.i)
{
continue;
}
if (Math3D.IsPointInTriangle(v0, v1, v2, vr.v))
{
collision = true;
break;
}
}
// Extract the triangle, update the data structure.
if (!collision)
{
vertexReferences.Remove(currentNode);
triangles.Add(prevNode.Value.i);
triangles.Add(current.i);
triangles.Add(nextNode.Value.i);
// Update angles for prev and next
var pPrevVertex = (prevNode.Previous ?? vertexReferences.Last).Value.v;
var nNextVertex = (nextNode.Next ?? vertexReferences.First).Value.v;
var prevValue = prevNode.Value;
var nextValue = nextNode.Value;
prevNode.Value = (prevValue.v, Math3D.InnerAngle(pPrevVertex, prevValue.v, nextValue.v, normal), prevValue.i);
nextNode.Value = (nextValue.v, Math3D.InnerAngle(prevValue.v, nextValue.v, nNextVertex, normal), nextValue.i);
break;
}
}
currentNode = currentNode.Next;
}
// Prevents endless loops in case the provided polygon somehow breaks the algorithm.
if (vertexReferences.Count >= prevCount)
{
throw new ArgumentException("This polygon cannot be triangulated.");
}
}
if (vertexReferences.Count == 3)
{
foreach (var value in vertexReferences)
{
triangles.Add(value.i);
}
}
}
/// <summary>
/// Triangulates a list of vertices, interpreted as the vertices of a planar polygon in clockwise order.
/// </summary>
/// <param name="vertices">The vertices.</param>
/// <param name="triangles">The output in which the resulting triangles will be written.</param>
public static void Triangulate(this IList <Vector3> vertices, List <int> triangles)
{
Triangulate(vertices, Math3D.PlanarPolygonNormal(vertices), triangles);
}