Approximate convex decomposition (ACD) converts triangle meshes into small sets of convex parts and is a standard preprocessing step for physics simulation, collision detection, and large-scale robot learning. The majority of modern ACD methods produce high-quality decompositions through an expensive search over candidate cutting planes, with per-mesh runtimes of tens of seconds that force game pipelines into overnight bakes and keep articulated-object datasets on CPU clusters for days. Prior work has accelerated isolated stages, most recently VisACD's GPU-based visibility metric, yet the dominant costs -- search, mesh cutting, and convex hull construction -- have remained on the CPU because their natural decomposition into many small homogeneous phases trails off in a fading last wave at every kernel boundary, and the variable-sized output of each phase forces a host round trip simply to allocate the next launch's input. We address these obstacles by adopting the warp, rather than the thread or thread block, as the unit of algorithm design, an idea introduced in the graph-processing community for a different pathology and which we adapt here to fuse the many heterogeneous phases of a computational-geometry pipeline into single warp-resident kernels, paired with a device-side heap allocator that lets the buffers between fused phases be sized and allocated on the device. Building on this template, we present CuACD (CUDA ACD), the first fully GPU-resident ACD system, together with a suite of reusable GPU components, released as open-source standalone CUDA modules that drop into any search-based ACD pipeline. On the V-HACD benchmark, PartNet-Mobility, and an Objaverse subset, CuACD achieves more than an order of magnitude of speedup over CoACD at matched or better quality.

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