In this paper two approaches for the computation of the, shape diameter function (SDF) on the GPU are outlined and compared. The SDF is a scalar function describing the local thickness of an object. It can be used for consistent mesh partitioning and skeletonization. In the first approach, we have reorganized the tracing of the rays to be well suited for the rasterization hardware. To the best of our knowledge, this is the first method to show how to compute the SDF using only the rasterization hardware and without the need of any acceleration data structures. The second approach uses parallel ray casting and an octree traversal using OpenCL. We demonstrate that the first method achieves similar results as the ray casting using OpenCL. In addition, it is faster for large meshes and it is simpler to implement. Furthermore, we extend the SDF computation by fast post-processing using texture-space diffusion. The fast SDF computation can be used in many applications such as the automatic skeleton extraction as we demonstrate in the article. (C) 2016 Elsevier Ltd. All rights reserved.