Convex Hull 3D Filtering with GPU Ray Tracing and Tensor Cores

TL;DR

Problem: 3D convex hull computation on large point sets under real-time and energy constraints. Approach: a GPU-based preprocessing filter builds a 14-point filtering polyhedron from axis-extreme and Manhattan-extreme points, uses a ray-tracing pipeline with a BVH to label interior points as non-candidates, followed by a Tensor-core–accelerated prefix-sum based compaction to yield a reduced candidate set, then computes the hull from candidates on CPU using ParGeo's Pseudohull. Contributions: end-to-end design and extensive evaluation across GPU architectures showing substantial speedups (up to around two orders of magnitude in filtering and notable hull-time reductions) and energy efficiency compared with a multi-core CPU baseline, across both uniform and sphere distributions. Significance: demonstrates that combining RT and Tensor cores for geometric preprocessing enables real-time, energy-aware convex hull computations in modern GPUs for graphics, robotics, and simulation workloads.

Abstract

In recent years, applications such as real-time simulations, autonomous systems, and video games increasingly demand the processing of complex geometric models under stringent time constraints. Traditional geometric algorithms, including the convex hull, are subject to these challenges. A common approach to improve performance is scaling computational resources, which often results in higher energy consumption. Given the growing global concern regarding sustainable use of energy, this becomes a critical limitation. This work presents a 3D preprocessing filter for the convex hull algorithm using ray tracing and tensor core technologies. The filter builds a delimiter polyhedron based on Manhattan distances that discards points from the original set. The filter is evaluated on two point distributions: uniform and sphere. Experimental results show that the proposed filter, combined with convex hull construction, accelerates the computation of the 3D convex hull by up to $200 \times$ with respect to a CPU parallel implementation. This research demonstrates that geometric algorithms can be accelerated through massive parallelism while maintaining efficient energy utilization. Beyond execution time and speedup evaluation, we also analyze GPU energy consumption, showing that the proposed preprocessing filter not only reduces the computational workload but also achieves performance gains with controlled energy usage. These results highlight the dual benefit of the method in terms of both speed and energy efficiency, reinforcing its applicability in modern high-performance scenarios.

Figures (16)

• Figure 1: Illustration of randomly distributed points (50 points), showcasing the polyhedron formed by the extreme (green) and corner (red) points. This figure summarizes all the phases of the algorithm.
• Figure 2: Randomly distributed points (1000 points) for an uniform and sphere distribution and their convex hulls respectively.
• Figure 3: Randomly sphere distribution points (1000 points) varying the $\rho$ value between $0$ to $1$.
• Figure 4: Filtering time, where y-axis is in logarithmic scale, for the RTX filtering, CUDA filtering, and fastest CPU implementation (Pseudohull with 20 cores) in both distributions.
• Figure 5: Filtering speedup for the RTX, CUDA, over the fastest CPU implementation (Pseudohull with 20 cores) in both distributions.