Approximate convex decomposition (ACD) is a technique that partitions an input object into approximately convex components.
Decomposition into approximately convex pieces is both more efficient to compute than exact convex decomposition and can also
generate a more manageable number of components. It can be used as a basis of divide-and-conquer algorithms for applications such
as collision detection, skeleton extraction and mesh generation. In this paper, we propose a new method called Fast Approximate
Convex Decomposition (FACD) that improves the quality of the decomposition and reduces the cost of computing it for both 2D and
3D models. In particular, we propose a new strategy for evaluating potential cuts that aims to reduce the relative concavity, rather
than absolute concavity. As shown in our results, this leads to more natural and smaller decompositions that include components
for small but important features such as toes or fingers while not decomposing larger components, such as the torso, that may have
concavities due to surface texture. Second, instead of decomposing a component into two pieces at each step, as in the original
ACD, we propose a new strategy that uses a dynamic programming approach to select a set of nc non-crossing (independent) cuts
that can be simultaneously applied to decompose the component into nc + 1 components. This reduces the depth of recursion and,
together with a more efficient method for computing the concavity measure, leads to significant gains in efficiency. We provide
comparitive results for 2D and 3D models illustrating the improvements obtained by FACD over ACD and we compare with the
segmentation methods in the Princeton Shape Benchmark.