Computing Symmetry Sets from 3D Shapes

In this paper we discuss the implementation of 3D Symmetry Sets. It describes how the Symmetry Set can be derived given a parametrized shape, as well as given an unorganized point cloud. It presents a geometric method to derive the Symmetry Set, that is an extension of the one given in deliverable 10. Just as in the 2D case, level set methods cannot be applied. Although the mathematics are a simple extension of the 2D case, the visualization, numerical computations and their stability are complicated. An example is give by means of a ellipsoid. In this example the Symmetry Set can be computed exactly and results can be compared to the ground truth.