public void PointInsideTriangleInside()
{
Assert.IsTrue(ContainmentTests.PointInsideTriangle(
new Vector2D(0.25, 0.25),
Vector2D.Zero,
new Vector2D(1, 0),
new Vector2D(0, 1)));
}
public void PointInsideTriangleOnEdge()
{
Assert.IsFalse(ContainmentTests.PointInsideTriangle(
new Vector2D(0.5, 0),
Vector2D.Zero,
new Vector2D(1, 0),
new Vector2D(0, 1)));
}
public void PointInsideThreeSidedInfinitePyramidOutside()
{
Assert.IsFalse(ContainmentTests.PointInsideThreeSidedInfinitePyramid(
new Vector3D(2, 0, 0.5),
Vector3D.Zero,
new Vector3D(1, -1, 1),
new Vector3D(1, 1, 1),
new Vector3D(-1, 0, 1)));
}
public static IndicesUnsignedInt Triangulate(IEnumerable <Vector3D> positions)
{
if (positions == null)
{
throw new ArgumentNullException("positions");
}
//
// Doubly linked list. This would be a tad cleaner if it were also circular.
//
LinkedList <IndexedVector <Vector3D> > remainingPositions = new LinkedList <IndexedVector <Vector3D> >();;
int index = 0;
foreach (Vector3D position in positions)
{
remainingPositions.AddLast(new IndexedVector <Vector3D>(position, index++));
}
if (remainingPositions.Count < 3)
{
throw new ArgumentOutOfRangeException("positions", "At least three positions are required.");
}
IndicesUnsignedInt indices = new IndicesUnsignedInt(3 * (remainingPositions.Count - 2));
///////////////////////////////////////////////////////////////////
LinkedListNode <IndexedVector <Vector3D> > previousNode = remainingPositions.First;
LinkedListNode <IndexedVector <Vector3D> > node = previousNode.Next;
LinkedListNode <IndexedVector <Vector3D> > nextNode = node.Next;
int bailCount = remainingPositions.Count * remainingPositions.Count;
while (remainingPositions.Count > 3)
{
Vector3D p0 = previousNode.Value.Vector;
Vector3D p1 = node.Value.Vector;
Vector3D p2 = nextNode.Value.Vector;
if (IsTipConvex(p0, p1, p2))
{
bool isEar = true;
for (LinkedListNode <IndexedVector <Vector3D> > n = ((nextNode.Next != null) ? nextNode.Next : remainingPositions.First);
n != previousNode;
n = ((n.Next != null) ? n.Next : remainingPositions.First))
{
if (ContainmentTests.PointInsideThreeSidedInfinitePyramid(n.Value.Vector, Vector3D.Zero, p0, p1, p2))
{
isEar = false;
break;
}
}
if (isEar)
{
indices.AddTriangle(new TriangleIndicesUnsignedInt(previousNode.Value.Index, node.Value.Index, nextNode.Value.Index));
remainingPositions.Remove(node);
node = nextNode;
nextNode = (nextNode.Next != null) ? nextNode.Next : remainingPositions.First;
continue;
}
}
previousNode = (previousNode.Next != null) ? previousNode.Next : remainingPositions.First;
node = (node.Next != null) ? node.Next : remainingPositions.First;
nextNode = (nextNode.Next != null) ? nextNode.Next : remainingPositions.First;
if (--bailCount == 0)
{
break;
}
}
LinkedListNode <IndexedVector <Vector3D> > n0 = remainingPositions.First;
LinkedListNode <IndexedVector <Vector3D> > n1 = n0.Next;
LinkedListNode <IndexedVector <Vector3D> > n2 = n1.Next;
indices.AddTriangle(new TriangleIndicesUnsignedInt(n0.Value.Index, n1.Value.Index, n2.Value.Index));
return(indices);
}
public static IndicesUnsignedInt Triangulate(IEnumerable <Vector2D> positions)
{
//
// O(n^3)
//
// There are several optimization opportunities:
// * http://www.geometrictools.com/Documentation/TriangulationByEarClipping.pdf
// * http://cgm.cs.mcgill.ca/~godfried/publications/triangulation.held.ps.gz
// * http://blogs.agi.com/insight3d/index.php/2008/03/20/triangulation-rhymes-with-strangulation/
//
if (positions == null)
{
throw new ArgumentNullException("positions");
}
//
// Doubly linked list. This would be a tad cleaner if it were also circular.
//
LinkedList <IndexedVector <Vector2D> > remainingPositions = new LinkedList <IndexedVector <Vector2D> >();;
int index = 0;
foreach (Vector2D position in positions)
{
remainingPositions.AddLast(new IndexedVector <Vector2D>(position, index++));
}
if (remainingPositions.Count < 3)
{
throw new ArgumentOutOfRangeException("positions", "At least three positions are required.");
}
IndicesUnsignedInt indices = new IndicesUnsignedInt(3 * (remainingPositions.Count - 2));
///////////////////////////////////////////////////////////////////
LinkedListNode <IndexedVector <Vector2D> > previousNode = remainingPositions.First;
LinkedListNode <IndexedVector <Vector2D> > node = previousNode.Next;
LinkedListNode <IndexedVector <Vector2D> > nextNode = node.Next;
int bailCount = remainingPositions.Count * remainingPositions.Count;
while (remainingPositions.Count > 3)
{
Vector2D p0 = previousNode.Value.Vector;
Vector2D p1 = node.Value.Vector;
Vector2D p2 = nextNode.Value.Vector;
if (IsTipConvex(p0, p1, p2))
{
bool isEar = true;
for (LinkedListNode <IndexedVector <Vector2D> > n = ((nextNode.Next != null) ? nextNode.Next : remainingPositions.First);
n != previousNode;
n = ((n.Next != null) ? n.Next : remainingPositions.First))
{
if (ContainmentTests.PointInsideTriangle(n.Value.Vector, p0, p1, p2))
{
isEar = false;
break;
}
}
if (isEar)
{
indices.AddTriangle(new TriangleIndicesUnsignedInt(previousNode.Value.Index, node.Value.Index, nextNode.Value.Index));
remainingPositions.Remove(node);
node = nextNode;
nextNode = (nextNode.Next != null) ? nextNode.Next : remainingPositions.First;
continue;
}
}
previousNode = (previousNode.Next != null) ? previousNode.Next : remainingPositions.First;
node = (node.Next != null) ? node.Next : remainingPositions.First;
nextNode = (nextNode.Next != null) ? nextNode.Next : remainingPositions.First;
if (--bailCount == 0)
{
break;
}
}
LinkedListNode <IndexedVector <Vector2D> > n0 = remainingPositions.First;
LinkedListNode <IndexedVector <Vector2D> > n1 = n0.Next;
LinkedListNode <IndexedVector <Vector2D> > n2 = n1.Next;
indices.AddTriangle(new TriangleIndicesUnsignedInt(n0.Value.Index, n1.Value.Index, n2.Value.Index));
return(indices);
}
