1 - Zhejiang University, Hangzhou, 310007, China

2 - Shenzhen Poisson Software Co., Ltd., Shenzhen, 518129, China

* - Corresponding Author

Abstract

Mid-surface abstraction is essential for finite element analysis of thin-walled CAD models, yet existing face pairing-based methods suffer from quadratic complexity and CPU-bound bottlenecks, limiting scalability for variable-thickness models. We present gMidSurf, a GPU-accelerated pipeline that transforms the two computational bottlenecks in mid-surface abstraction (face pairing and mid-point generation) into massively parallel operations. For face pairing, we introduce a hierarchical filtering strategy that progressively culls candidate pairs through three GPU-optimized gates: normal compatibility, simplified overlap criterion, and LBVH-based distance queries, reducing the search space by 10–100× while maintaining cache coherence. For mid-point generation, we employ parallel distance dilation followed by bracket-and-bisect refinement for precise equidistant point localization. This method handles variable-thickness models with complex surfaces through complete dilation, thereby avoiding gaps and truncations that occur in previous methods. Experimental results on real-world benchmarks demonstrate that gMidSurf achieves 4.2×–18.5× speedups in face pairing and 4.8×–9.8× in mid-point generation compared to CPU implementations, yielding 5×–15× acceleration on a commodity GPU (NVIDIA RTX 5090D) compared to state-of-the-art methods while maintaining geometric accuracy.
 

Overview: The input thin-walled model is first discretized into triangular meshes on the GPU. Then (a) hierarchical GPU-based face pairing applies three progressive filtering gates (normal, overlap, and distance) to prune candidate face pairs by 10–100× and identify the face group pairs (FGPs), abstracting 1-1 face pairs into n-n FGPs through parallel bipartite graph optimization. Next, (b) GPU-based mid-point generation produces initial mid-points via parallel distance dilation and refines them to precise equidistant points through a bracket-and-bisect kernel. Finally, the model undergoes surface fitting and trimming operations to determine the boundaries of the mid-surface, yielding the final output mid-surface.

Pipeline: The gMidSurf pipeline keeps geometry resident on the GPU through both core stages. Two computational bottlenecks — hierarchical GPU-based face pairing and dilation-based precise mid-point generation — are recast as massively parallel operations, while surface fitting and trimming run on the host. This end-to-end design preserves B-Rep modeling intent, supports both 1-1 and n-n face pairs, and handles constant- and variable-thickness regions robustly.

Technical Contributions

• Full GPU-based face pairing with hierarchical culling. Normal, overlap, and distance tests are cast as GPU-friendly gates backed by LBVH traversal, pruning candidates by 10×–100× before fine checks and yielding near-linear scaling with face count.
• Branchless mid-point solver for variable-thickness. A bracket-and-bisect kernel equalizes distances robustly across planes, quadrics, and free-form NURBS while minimizing warp divergence and maximizing throughput.
• End-to-end GPU design that preserves B-Rep intent. Geometry stays resident on device through face pairing and mid-point generation, supports 1-1 and n-n face pairs, and interoperates with trimming on the host to balance robustness and speed.
• Extensive evaluation on industrial-style models. Stage-wise and end-to-end speedups over a tuned multi-core CPU baseline and previous methods, with more accurate results on variable-thickness parts and complex free-form models.

Key Results

• Hierarchical filtering gates reduce the candidate face-pair search space by 10×–100×.
• 4.2×–18.5× speedup for face pairing and 4.8×–9.8× for mid-point generation versus CPU implementations.
• 5×–15× end-to-end acceleration on a single NVIDIA RTX 5090D GPU compared with state-of-the-art methods (MidSurfer, Parasolid, Zhu et al.).
• Complete dilation eliminates the gaps and truncations of prior methods while keeping the maximum positional deviation within 10^-5 (FP32 vs. FP64).

Benchmark: Eight iconic models (M1–M8) selected from the GrabCAD library cover a diverse range of geometric and topological configurations, including constant- and variable-thickness FGPs (C/V-FGPs), high curvature, n-n pairings, and complex free-form surfaces.

• Model 1: An instrument microphone clip, consisting of 30 faces with no constant-thickness FGPs (all 11 FGPs are variable), used to validate the algorithm’s basic capabilities.
• Model 2: A motorcycle winglet with 61 faces, including 15 variable-thickness FGPs (V-FGPs) and 3 constant-thickness FGPs (C-FGPs). This model presents a scenario where both C-FGPs and V-FGPs exist.
• Model 3: A pipe bracket with 74 faces, where most V-FGPs exhibit significant curvature variations (>15° angular variation between paired faces), used to evaluate geometric correctness under challenging dilation conditions.
• Model 4: A car wheel rim from the automotive industry, featuring 121 faces, including 20 V-FGPs and 19 n-n face pairs. Its multi-ring topology, local blends, and diverse variable-thickness scenarios pose significant challenges for face pairing.
• Model 5: A table flower pot with 195 faces, containing the most V-FGPs (24) among all benchmarks. It demonstrates the algorithm’s capability to handle models with great curvature variations.
• Model 6: A multi-port distributor from the mechanical design domain, with 215 faces and 52 C-FGPs — the highest C-FGP count among all benchmarks — demonstrating scenarios where constant-thickness structures predominate.
• Model 7: A rear spoiler with 236 faces, with all FGPs exhibiting highly similar geometric primitives and gentle curvature variations, testing the filtering gates under low-discrimination conditions.
• Model 8: An aircraft model from a real-world aerospace scenario with 286 faces and highly complex topological and geometric structures, used to verify algorithm robustness under the most challenging configurations.

Contents

Related Links

MidSurfer: Efficient Mid-surface Abstraction from Variable Thin-walled Models

gDist: Efficient Distance Computation between 3D Meshes on GPU

CTSN: Predicting Cloth Deformation for Skeleton-based Characters with a Two-stream Skinning Network

D-Cloth: Skinning-based Cloth Dynamic Prediction with a Three-stage Network

N-Cloth: Predicting 3D Cloth Deformation with Mesh-Based Networks

P-Cloth: Interactive Cloth Simulation on Multi-GPU Systems using Dynamic Matrix Assembly and Pipelined Implicit Integrators

I-Cloth: Incremental Collision Handling for GPU-Based Interactive Cloth Simulation

PSCC: Parallel Self-Collision Culling with Spatial Hashing on GPUs

I-Cloth: API for fast and reliable cloth simulation with CUDA

Efficient BVH-based Collision Detection Scheme with Ordering and Restructuring

MCCD: Multi-Core Collision Detection between Deformable Models using Front-Based Decomposition

Interactive Continuous Collision Detection between Deformable Models using Connectivity-Based Culling

TightCCD: Efficient and Robust Continuous Collision Detection using Tight Error Bounds

Fast and Exact Continuous Collision Detection with Bernstein Sign Classification

A GPU-based Streaming Algorithm for High-Resolution Cloth Simulation

Continuous Penalty Forces

UNC dynamic model benchmark repository

Collision-Streams: Fast GPU-based Collision Detection for Deformable Models

Fast Continuous Collision Detection using Deforming Non-Penetration Filters

Fast Collision Detection for Deformable Models using Representative-Triangles

DeformCD: Collision Detection between Deforming Objects

Self-CCD: Continuous Collision Detection for Deforming Objects

Interactive Collision Detection between Deformable Models using Chromatic Decomposition

Fast Proximity Computation Among Deformable Models using Discrete Voronoi Diagrams

CULLIDE: Interactive Collision Detection between Complex Models using Graphics Hardware

RCULLIDE: Fast and Reliable Collision Culling using Graphics Processors

Quick-CULLIDE: Efficient Inter- and Intra-Object Collision Culling using Graphics Hardware

Collision Detection

UNC GAMMA Group

Acknowledgements

This work was funded in part by "Pioneer" and "Leading Goose" R&D Program of Zhejiang Province (No. 2025C01086).

tang_m@zju.edu.cn