Robust and Feature-Preserving Offset Meshing

TL;DR

The results demonstrate the superiority of the approach over current state-of-the-art methods in terms of element count, feature preservation, and non-uniform offset distances of the resulting offset mesh surfaces, marking a significant advancement in the field.

Abstract

We introduce a novel offset meshing approach that can robustly handle a 3D surface mesh with an arbitrary geometry and topology configurations, while nicely capturing the sharp features on the original input for both inward and outward offsets. Compared to the existing approaches focusing on constant-radius offset, to the best of our knowledge, we propose the first-ever solution for mitered offset that can well preserve sharp features. Our method is designed based on several core principals: 1) explicitly generating the offset vertices and triangles with feature-capturing energy and constraints; 2) prioritizing the generation of the offset geometry before establishing its connectivity, 3) employing exact algorithms in critical pipeline steps for robustness, balancing the use of floating-point computations for efficiency, 4) applying various conservative speed up strategies including early reject non-contributing computations to the final output. Our approach further uniquely supports variable offset distances on input surface elements, offering a wider range practical applications compared to conventional methods. We have evaluated our method on a subset of Thinkgi10K, containing models with diverse topological and geometric complexities created by practitioners in various fields. Our results demonstrate the superiority of our approach over current state-of-the-art methods in terms of element count, feature preservation, and non-uniform offset distances of the resulting offset mesh surfaces, marking a significant advancement in the field.

Figures (22)

• Figure 1: Pipeline : starting from a triangle mesh $M_\text{I}$ (left most), our approach first generates its vertices' offset points (second to the left), then builds an offset polyhedron for each of its triangle, edge and vertex (middle). After that, we convert the polyhedra set to an intersection-free triangle soup $M_\text{C}$ by filtering out those triangles not part of $M_\text{O}$ (second to the right), Along with some acceleration measures, this approach involves selecting only a subset of triangles from the polyhedra set for computation, which may result in the creation of some holes. Finally, by detecting the boundaries of the holes, we retrieve the triangles that were excluded in the previous step, Then we construct the connectivity of $M_\text{O}$ (right).
• Figure 2: The two curves respectively demonstrate the computational time required to calculate a point with and without prior classification. It can be observed that when $K$ is particularly large, lacking this classification makes it difficult to compute the offset points within a reasonable timeframe.
• Figure 3: Nine different vertex offset scenarios computed by our approach on a mesh example. Each column corresponds to one scenario, where the top and bottom rows show two different offset direct (outward and inward). It can be observed that in some sharp cases, the points generated by the inward offset of vertices may appear outside the input model. This situation does not pose any issues. The subsequent convex hull and winding number computations will exclude these points and .
• Figure 4: From left to right, the diagrams respectively illustrate the construction of offset volumes from a triangle, a vertex, and an edge.
• Figure 5: This figure shows the results of our algorithm for inward offsets at different distances. From left to right, the images are the input, $0.05\%l$, $0.1\%l$, $0.5\%l$, $1\%l$, and $5\%l$.