CrossGen: Learning and Generating Cross Fields for Quad Meshing

ACM Transactions on Graphics, vol. 44, pp. 1–15

Abstract

Cross fields play a critical role in various geometry processing tasks, especially for quad mesh generation. Existing methods for cross field generation often struggle to balance computational efficiency with generation quality, using slow per-shape optimization. We introduce CrossGen , a novel framework that supports both feed-forward prediction and latent generative modeling of cross fields for quad meshing by unifying geometry and cross field representations within a joint latent space. Our method enables extremely fast computation of high-quality cross fields of general input shapes, typically within one second without per-shape optimization. Our method assumes a point-sampled surface, also called a point-cloud surface , as input, so we can accommodate various surface representations by a straightforward point sampling process. Using an auto-encoder network architecture, we encode input point-cloud surfaces into a sparse voxel grid with fine-grained latent spaces, which are decoded into both SDF-based surface geometry and cross fields (see the teaser figure). We also contribute a dataset of models with both high-quality signed distance fields (SDFs) representations and their corresponding cross fields, and use it to train our network. Once trained, the network is capable of computing a cross field of an input surface in a feed-forward manner, ensuring high geometric fidelity, noise resilience, and rapid inference. Furthermore, leveraging the same unified latent representation, we incorporate a diffusion model for computing cross fields of new shapes generated from partial input, such as sketches. To demonstrate its practical applications, we validate CrossGen on the quad mesh generation task for a large variety of surface shapes. Experimental results demonstrate that CrossGen generalizes well across diverse shapes and consistently yields high-fidelity cross fields, thus facilitating the generation of high-quality quad meshes.

Authors 13

1. Qiujie Dong

   Shandong University · University of Hong Kong

   Affiliation as printed

   Shandong University, Qingdao, China

   University of Hong Kong, Hong Kong, China

2. Jiepeng Wang

   University of Hong Kong

   Affiliation as printed

   University of Hong Kong, Hong Kong, China

3. Rui Xu

   University of Hong Kong

   Affiliation as printed

   University of Hong Kong, Hong Kong, China

4. Cheng Lin

   Macau University of Science and Technology

   Affiliation as printed

   Macau University of Science and Technology, Macau, China

5. Yuan Liu

   Hong Kong University of Science and Technology

   Affiliation as printed

   Hong Kong University of Science and Technology, Hong Kong, China

6. Shiqing Xin

   Shandong University

   Affiliation as printed

   Shandong University, Qingdao, China

7. Zichun Zhong

   Wayne State University

   Affiliation as printed

   Wayne State University, Detroit, USA

8. Xin Shane Li

   Texas A&M University

   Affiliation as printed

   Texas A&M University, Texas, USA

9. Changhe Tu

   Shandong University

   Affiliation as printed

   Shandong University, Qingdao, China

10. Taku Komura

    University of Hong Kong

    Affiliation as printed

    University of Hong Kong, Hong Kong, China

11. Leif P. Kobbelt Aachen

    RWTH Aachen University

    Affiliation as printed

    RWTH Aachen University, Aachen, Germany

12. Scott Schaefer

    Texas A&M University

    Affiliation as printed

    Texas A&M University, Texas, USA

13. Wenping Wang

    Texas A&M University

    Affiliation as printed

    Texas A&M University, Texas, USA