///<summary>
/// Computes the center, volume, and surface triangles of a convex hull defined by a point set.
///</summary>
///<param name="vertices">Point set defining the convex hull.</param>
///<param name="volume">Volume of the convex hull.</param>
///<param name="outputSurfaceTriangles">Indices of surface triangles of the convex hull.</param>
///<param name="outputLocalSurfaceVertices">Local positions of vertices on the convex hull.</param>
///<returns>Center of the convex hull.</returns>
public static Vector3 ComputeCenter(IList <Vector3> vertices, out float volume, IList <int> outputSurfaceTriangles, IList <Vector3> outputLocalSurfaceVertices)
{
Vector3 centroid = Toolbox.ZeroVector;
for (int k = 0; k < vertices.Count; k++)
{
centroid += vertices[k];
}
centroid /= vertices.Count;
//Toolbox.GetConvexHull(vertices, outputSurfaceTriangles, outputLocalSurfaceVertices);
ConvexHullHelper.GetConvexHull(vertices, outputSurfaceTriangles, outputLocalSurfaceVertices);
volume = 0;
var volumes = CommonResources.GetFloatList();
var centroids = CommonResources.GetVectorList();
for (int k = 0; k < outputSurfaceTriangles.Count; k += 3)
{
volumes.Add(Vector3.Dot(
Vector3.Cross(vertices[outputSurfaceTriangles[k + 1]] - vertices[outputSurfaceTriangles[k]],
vertices[outputSurfaceTriangles[k + 2]] - vertices[outputSurfaceTriangles[k]]),
centroid - vertices[outputSurfaceTriangles[k]]));
volume += volumes[k / 3];
centroids.Add((vertices[outputSurfaceTriangles[k]] + vertices[outputSurfaceTriangles[k + 1]] + vertices[outputSurfaceTriangles[k + 2]] + centroid) / 4);
}
Vector3 center = Toolbox.ZeroVector;
for (int k = 0; k < centroids.Count; k++)
{
center += centroids[k] * (volumes[k] / volume);
}
volume /= 6;
for (int k = 0; k < outputLocalSurfaceVertices.Count; k++)
{
outputLocalSurfaceVertices[k] -= center;
}
CommonResources.GiveBack(centroids);
CommonResources.GiveBack(volumes);
return(center);
}