A Surface-Based Approach for 3D Approximate Convex Decomposition

Approximate convex decomposition simplifies complex shapes into manageable convex components. In this work, we propose a novel surface-based method that achieves efficient computation times and sufficiently convex results while avoiding overapproximation of the input model. We start approximation using mesh simplification. Then we iterate over the surface polygons of the mesh and divide 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 level of simplification, we find the planar threshold that leads to the decomposition with the least number of pieces while remaining under a certain concavity threshold. Subsequently, we find the simplification level that houses the decomposition with the least concavity, and output that decomposition as our result. We demonstrated experiment results that show the stability of our method as well as compared our work to two convex decomposition algorithms, providing discussion on the shortcomings and advantages of the proposed method. Notably, our main advantage turns out to be on time efficiency as we produce output faster than our competitors which, however, outperform our results for some models from an accuracy perspective.