Simple Methods to Represent Shapes with Sample Spheres

TL;DR

This paper introduces simple, efficient methods for approximating complex shapes with a user-defined number of spheres, balancing accuracy and simplicity for applications in graphics and geometry processing.

Contribution

It proposes novel, easy-to-implement techniques using medial/scale-axis polar balls and k-means for shape approximation with spheres, improving upon existing methods.

Findings

Methods are easy to implement and efficient.

Achieve quality comparable to manual shape approximation.

Allow user-tunable balance between accuracy and simplicity.

Abstract

Representing complex shapes with simple primitives in high accuracy is important for a variety of applications in computer graphics and geometry processing. Existing solutions may produce suboptimal samples or are complex to implement. We present methods to approximate given shapes with user-tunable number of spheres to balance between accuracy and simplicity: touching medial/scale-axis polar balls and k-means smallest enclosing circles. Our methods are easy to implement, run efficiently, and can approach quality similar to manual construction.