Approximate Convex Decomposition for 3D Meshes with Collision-Aware Concavity and Tree Search (2205.02961v1)

Abstract: Approximate convex decomposition aims to decompose a 3D shape into a set of almost convex components, whose convex hulls can then be used to represent the input shape. It thus enables efficient geometry processing algorithms specifically designed for convex shapes and has been widely used in game engines, physics simulations, and animation. While prior works can capture the global structure of input shapes, they may fail to preserve fine-grained details (e.g., filling a toaster's slots), which are critical for retaining the functionality of objects in interactive environments. In this paper, we propose a novel method that addresses the limitations of existing approaches from three perspectives: (a) We introduce a novel collision-aware concavity metric that examines the distance between a shape and its convex hull from both the boundary and the interior. The proposed concavity preserves collision conditions and is more robust to detect various approximation errors. (b) We decompose shapes by directly cutting meshes with 3D planes. It ensures generated convex hulls are intersection-free and avoids voxelization errors. (c) Instead of using a one-step greedy strategy, we propose employing a multi-step tree search to determine the cutting planes, which leads to a globally better solution and avoids unnecessary cuttings. Through extensive evaluation on a large-scale articulated object dataset, we show that our method generates decompositions closer to the original shape with fewer components. It thus supports delicate and efficient object interaction in downstream applications. We will release our implementation to facilitate future research.

• The paper introduces a novel collision-aware concavity metric that accurately captures fine details for improved mesh decomposition.
• It employs direct mesh cutting to eliminate voxelization artifacts while achieving up to 100x speed improvements.
• A multi-step Monte Carlo tree search optimizes plane selection, reducing component counts and enhancing simulation fidelity.

Approximate Convex Decomposition for 3D Meshes: An Analytical Perspective

This paper addresses the task of approximate convex decomposition (ACD) for 3D shapes, essential for applications in game engines, physics simulations, and animation. It aims to decompose a 3D shape into nearly convex components, increasing the efficiency of algorithms that cater specifically to convex geometries.

The authors introduce several innovations to enhance traditional methods of convex decomposition. These innovations span three principal areas: collision-aware concavity, direct mesh cutting, and multi-step tree search.

Key Contributions

1. Collision-Aware Concavity Metric: The paper proposes a novel concavity metric that accounts for the collision properties of shapes. Traditional metrics often neglect the interior structure or focus solely on volume differences, which can lead to inappropriate decompositions that compromise object functionalities in interactive environments. The authors overcome this limitation by measuring concavity through a combination of boundary and interior sampling, specifically targeting Hausdorff distances. This approach effectively captures fine-grained details, crucial for maintaining object functionality.
2. Direct Mesh Cutting: Unlike methods that rely on voxelization, which can introduce artifacts and fail to recognize convex structures, the authors suggest directly cutting 3D solid meshes with planes. This approach ensures flat boundaries and avoids voxelization errors, retaining the integrity of already convex shapes. The implementation, touted to be 100x faster than conventional libraries, highlights the emphasis on computational efficiency.
3. Multi-Step Tree Search: Previous works often employ a one-step greedy strategy for plane selection, resulting in suboptimal decompositions. This paper introduces a multi-step Monte Carlo Tree Search (MCTS), simulating and optimizing multiple future actions to achieve globally superior decompositions. This methodology not only reduces the number of necessary components but also eliminates the need for heuristic workarounds common in greedy approaches.

Numerical Results

The extensive evaluation on datasets such as V-HACD and PartNet Mobility demonstrates significant improvements. The proposed method shows a reduction in the number of components compared to existing techniques while maintaining or lowering concavity scores. For example, the proposed approach achieves fewer components and better concavity on both major datasets, emphasizing its effectiveness.

Implications and Future Directions

The advancements presented yield immediate benefits for fields requiring reliable and efficient mesh decomposition, such as robotics and virtual simulation environments. The application of collision-aware metrics ensures that functional aspects of 3D models are preserved, which is critical for real-world simulations.

Moving forward, this approach opens pathways for further optimization in decomposition algorithms, potentially involving adaptive thresholds or machine learning-based evaluation mechanisms. Moreover, the integration of such methods into real-time systems could significantly enhance the fidelity and performance of interactive applications.

In summary, this paper provides a rigorous and effective methodology for approximate convex decomposition, addressing long-standing issues in capturing fine-grained details and optimizing decomposition processes. It sets a robust foundation for future research in improving geometric processing for 3D modeling and simulation tasks.