Perfect Laplacians for Polygon Meshes

Results

We present animated images to demonstrate the behaviour of our algorithm for different types of polygon meshes. Challenging examples, like non-convex polygonal mesh, converge more slowly. Overall our algorithm was able to find solutions in all examples we tested. The spring energy decreased montonically for all examples.
Delaunay Triangulation

Non-Regular Triangulation

Convex Polygonal Mesh

Triangulated Polygonal Mesh

Non-Convex Polygonal Mesh

Energy per iteration

Non-Regular triangle mesh

Non-Regular polygon mesh

Polygon Mesh

Input mesh

Polygon Mesh

Input mesh

Noisy Polygon Mesh

Input mesh