Sampling Superquadric Point Clouds with Normals
This addresses a technical bottleneck in computer graphics, vision, and robotics for modeling shapes, but it is incremental as it builds on prior 2D work.
The paper tackles the problem of uniform sampling of superquadric point clouds with normals, extending a 2D method to 3D superellipsoids and developing a new approach for superparaboloids, providing the first complete framework for close-to-uniform sampling with available code and results.
Superquadrics provide a compact representation of common shapes and have been used both for object/surface modelling in computer graphics and as object-part representation in computer vision and robotics. Superquadrics refer to a family of shapes: here we deal with the superellipsoids and superparaboloids. Due to the strong non-linearities involved in the equations, uniform or close-to-uniform sampling is not attainable through a naive approach of direct sampling from the parametric formulation. This is specially true for more `cubic' superquadrics (with shape parameters close to $0.1$). We extend a previous solution of 2D close-to-uniform uniform sampling of superellipses to the superellipsoid (3D) case and derive our own for the superparaboloid. Additionally, we are able to provide normals for each sampled point. To the best of our knowledge, this is the first complete approach for close-to-uniform sampling of superellipsoids and superparaboloids in one single framework. We present derivations, pseudocode and qualitative and quantitative results using our code, which is available online.