Top-Down Shape Abstraction Based on Greedy Pole Selection

TL;DR

This paper introduces a top-down method for shape abstraction using greedy pole selection to efficiently approximate shapes with medial balls, enabling applications in modeling and porous structure generation.

Contribution

It proposes a novel greedy pole selection strategy for shape approximation, improving efficiency and enabling practical modeling and porous structure applications.

Findings

Efficient shape approximation with fewer medial balls.

A speedup technique based on medial ball intersections.

Applications in shape modeling and porous structure design.

Abstract

Motivated by the fact that the medial axis transform is able to encode nearly the complete shape, we propose to use as few medial balls as possible to approximate the original enclosed volume by the boundary surface. We progressively select new medial balls, in a top-down style, to enlarge the region spanned by the existing medial balls. The key spirit of the selection strategy is to encourage large medial balls while imposing given geometric constraints. We further propose a speedup technique based on a provable observation that the intersection of medial balls implies the adjacency of power cells (in the sense of the power crust). We further elaborate the selection rules in combination with two closely related applications. One application is to develop an easy-to-use ball-stick modeling system that helps non-professional users to quickly build a shape with only balls and wires, but any penetration between two medial balls must be suppressed. The other application is to generate porous structures with convex, compact (with a high isoperimetric quotient) and shape-aware pores where two adjacent spherical pores may have penetration as long as the mechanical rigidity can be well preserved.