C ⁵ D: Sequential Continuous Convex Collision Detection Using Cone Casting

In physics-based simulation of rigid or nearly rigid objects, collisions often become the primary performance bottleneck, particularly when enforcing intersection-free constraints. Previous simulation frameworks rely on primitive-level CCD algorithms. Due to the large number of colliding surface primitives to process, those methods are computationally intensive and heavily dependent on advanced parallel computing resources such as GPUs, which are often inaccessible due to competing tasks or capped threading capacity in applications like policy training for robotics. To address these limitations, we propose a sequential CCD algorithm for convex shapes undergoing constant affine motion. This approach uses the conservative advancement method to iteratively refine a lower-bound estimate of the TOI, exploiting the linearity of affine motion and the efficiency of convex shape distance computation. Our CCD algorithm integrates seamlessly into the ABD framework, achieving a 10-fold speed-up over primitive-level CCD. Its high single-threaded efficiency further enables significant throughput improvements via scene-level parallelism, making it well-suited for resource-constrained environments.