/// <summary>
/// Creates a convex hull mesh for a set of points.
/// </summary>
/// <param name="points">The points.</param>
/// <param name="vertexLimit">
/// The vertex limit. Must be greater than 0. Common values are 32 or 64.
/// </param>
/// <param name="skinWidth">
/// The skin width. Common values are 0.01 or 0.001.
/// </param>
/// <returns>
/// The mesh of the convex hull or <see langword="null"/> if the point list is
/// <see langword="null"/> or empty.
/// </returns>
/// <remarks>
/// <para>
/// The returned mesh describes the convex hull. All faces are convex polygons.
/// </para>
/// <para>
/// If the created convex hull has more vertices than <paramref name="vertexLimit"/>, the hull
/// will be simplified. The simplified hull is conservative, which means it contains all given
/// <paramref name="points"/> and is less "tight" than the exact hull. It is possible that the
/// simplified hull contains slightly more vertices than <paramref name="vertexLimit"/> (e.g. it
/// is possible that for a vertex limit of 32 a hull with 34 vertices is returned).
/// </para>
/// <para>
/// All planes of the convex hull are extruded by the <paramref name="skinWidth"/>. This can be
/// used to increase or decrease the size of the convex hull.
/// </para>
/// </remarks>
public static DcelMesh CreateConvexHull(IEnumerable<Vector3F> points, int vertexLimit, float skinWidth)
{
// Nothing to do for empty input.
if (points == null)
return null;
ConvexHullBuilder builder = new ConvexHullBuilder();
builder.Grow(points, vertexLimit, skinWidth);
if (builder.Type == ConvexHullType.Empty)
return null;
return builder.Mesh;
}
private float GetConcavity(int vertexLimit, bool sampleVertices, bool sampleCenters)
{
// Initially we assume that the new vertices are simply the union of the islands' vertices.
Vertices = IslandA.Vertices.Union(IslandB.Vertices).ToArray();
try
{
// Create hull mesh.
// Incremental hull building.
// Note: Commented out because this building the hull this way is less stable.
//bool rebuild = true;
//try
//{
// if (IslandA.ConvexHullBuilder != null)
// {
// if (IslandB.ConvexHullBuilder == null || IslandA.Vertices.Length > IslandB.Vertices.Length)
// {
// ConvexHullBuilder = IslandA.ConvexHullBuilder.Clone();
// ConvexHullBuilder.Grow(IslandB.Vertices, vertexLimit, 0);
// }
// else
// {
// ConvexHullBuilder = IslandB.ConvexHullBuilder.Clone();
// ConvexHullBuilder.Grow(IslandA.Vertices, vertexLimit, 0);
// }
// rebuild = false;
// }
// else if (IslandB.ConvexHullBuilder != null)
// {
// ConvexHullBuilder = IslandB.ConvexHullBuilder.Clone();
// ConvexHullBuilder.Grow(IslandA.Vertices, vertexLimit, 0);
// rebuild = false;
// }
//}
//catch (GeometryException)
//{
// rebuild = true;
//}
//if (rebuild)
{
try
{
ConvexHullBuilder = new ConvexHullBuilder();
ConvexHullBuilder.Grow(Vertices, vertexLimit, 0);
}
catch (GeometryException)
{
// Hull building failed. Try again with a randomized order.
var random = new Random(1234567);
// Fisher-Yates shuffle:
for (int i = Vertices.Length - 1; i >= 1; i--)
{
var v = Vertices[i];
var j = random.NextInteger(0, i);
Vertices[i] = Vertices[j];
Vertices[j] = v;
}
}
}
var hullMesh = ConvexHullBuilder.Mesh.ToTriangleMesh();
// Now, we have a reduced set of vertices.
Vertices = hullMesh.Vertices.ToArray();
// For larger meshes we create an AabbTree as acceleration structure.
AabbTree<int> partition = null;
if (hullMesh.NumberOfTriangles > 12)
{
partition = new AabbTree<int>
{
GetAabbForItem = i => hullMesh.GetTriangle(i).Aabb,
BottomUpBuildThreshold = 0,
};
for (int i = 0; i < hullMesh.NumberOfTriangles; i++)
partition.Add(i);
partition.Update(true);
}
Aabb aabb = Aabb;
float aabbExtent = aabb.Extent.Length;
// Note: For a speed-up we could skip some ray tests in the next loop and only sample
// a few vertices if there would be a lot of tests.
// The next loop performs ray casts against the hull mesh to determine the maximum
// concavity. We ensure that we make only one ray cast per vertex even if a vertex
// is shared by many triangles.
float maxConcavity = 0;
foreach (var triangle in IslandA.Triangles.Union(IslandB.Triangles))
{
if (sampleVertices)
{
for (int i = 0; i < triangle.Vertices.Length; i++)
{
// Each vertex can be shared by several triangles of the current islands.
// Therefore, we check the edges that contain this vertex. If an edge neighbor
// is in the same island, we make sure that the vertex concavity is computed only once
// in the triangle with the smallest Id.
var neighbor0 = triangle.Neighbors[(i + 1) % 3];
var neighbor1 = triangle.Neighbors[(i + 2) % 3];
if (neighbor0 != null
&& (neighbor0.Island == IslandA || neighbor0.Island == IslandB)
&& triangle.Id > neighbor0.Id)
{
// No need to test: The neighbor is in the same islands and this triangle Id is larger.
continue;
}
if (neighbor1 != null
&& (neighbor1.Island == IslandA || neighbor1.Island == IslandB)
&& triangle.Id > neighbor1.Id)
{
// No need to test: The neighbor is in the same islands and this triangle Id is larger.
continue;
}
var position = triangle.Vertices[i];
var normal = triangle.VertexNormals[i];
// Degenerate triangles are ignored.
if (normal.IsNumericallyZero)
continue;
// Shoot a ray from outside the hull mesh to the vertex.
float hitDistance;
Vector3F rayOrigin = position + normal * aabbExtent;
float rayLength = (position - rayOrigin).Length;
var ray = new Ray(rayOrigin, -normal, rayLength);
if (partition != null)
{
// Use AABB tree for better performance.
foreach (var triangleIndex in partition.GetOverlaps(ray))
{
var candidateTriangle = hullMesh.GetTriangle(triangleIndex);
var hit = GeometryHelper.GetContact(ray, candidateTriangle, false, out hitDistance);
if (hit)
{
// The concavity is the distance from the hull to the vertex.
float concavity = rayLength - hitDistance;
maxConcavity = Math.Max(maxConcavity, concavity);
break;
}
}
}
else
{
// No AABB tree.
var hit = GeometryHelper.GetContact(hullMesh, ray, out hitDistance);
if (hit)
{
float concavity = rayLength - hitDistance;
maxConcavity = Math.Max(maxConcavity, concavity);
}
}
}
}
if (sampleCenters)
{
// Test: Also shoot from the triangle centers.
var center = (triangle.Vertices[0] + triangle.Vertices[1] + triangle.Vertices[2]) / 3;
var normal = triangle.Normal;
// Degenerate triangles are ignored.
if (normal.IsNumericallyZero)
continue;
// Shoot a ray from outside the hull mesh to the vertex.
float hitDistance;
Vector3F rayOrigin = center + normal * aabbExtent;
float rayLength = (center - rayOrigin).Length;
var ray = new Ray(rayOrigin, -normal, rayLength);
if (partition != null)
{
// Use AABBTree for better performance.
foreach (var triangleIndex in partition.GetOverlaps(ray))
{
var candidateTriangle = hullMesh.GetTriangle(triangleIndex);
var hit = GeometryHelper.GetContact(ray, candidateTriangle, false, out hitDistance);
if (hit)
{
// The concavity is the distance from the hull to the vertex.
float concavity = rayLength - hitDistance;
maxConcavity = Math.Max(maxConcavity, concavity);
break;
}
}
}
else
{
// No AABBTree.
var hit = GeometryHelper.GetContact(hullMesh, ray, out hitDistance);
if (hit)
{
float concavity = rayLength - hitDistance;
maxConcavity = Math.Max(maxConcavity, concavity);
}
}
}
}
return maxConcavity;
}
catch (GeometryException)
{
// Ouch, the convex hull generation failed. This can happen for degenerate inputs
// and numerical problems in the convex hull builder.
ConvexHullBuilder = null;
return 0;
}
}
public ConvexHullBuilder Clone()
{
var clone = new ConvexHullBuilder
{
_isPlanar = _isPlanar,
_type = _type,
_mesh = new DcelMesh(_mesh),
};
return clone;
}