Approximate convex decomposition is a variant of shape segmentation where a concave mesh is divided into smaller pieces that are all convex and combined to
form an approximate of the original mesh. This enables the simplification of complex shapes into manageable convex components. In this work, we propose a
novel surface-based method to achieve this which leads to efficient computation times and sufficiently convex results without over-approximating the input model. We achieve approximation by using mesh simplification. Then we start iterating over the surface polygons of the mesh and dividing them into convex groups. We utilize planar and angular equations to determine suitable neighboring polygons for inclusion in forming convex groups. To ensure our method outputs a sufficient result for a wide range of input shapes, we run multiple iterations of our algorithm using varying planar thresholds and mesh simplification levels. For each simplification level, we find the planar threshold that leads to the decomposition with the least number of pieces while remaining under a certain concavity threshold. Then, we find the simplification level that houses the decomposition with the least concavity, and output that decomposition as our result. We demonstrate experiment results that show the viability of our method as well as compare our work to an established convex decomposition algorithm, providing discussion on the shortcomings and advantages of the proposed method.
Keywords: Computational Geometry, Convex Decomposition