Digital orthodontics represents a prominent and critical application of computer vision technology in the medical field. So far, the labor-intensive process of collecting clinical data, particularly in acquiring paired 3D orthodontic teeth models, constitutes a crucial bottleneck for developing tooth arrangement neural networks. Although numerous general 3D shape generation methods have been proposed, most of them focus on single-object generation and are insufficient for generating anatomically structured teeth models, each comprising 24-32 segmented teeth. In this paper, we propose TeethGenerator, a novel two-stage framework designed to synthesize paired 3D teeth models pre- and post-orthodontic, aiming to facilitate the training of downstream tooth arrangement networks. Specifically, our approach consists of two key modules: (1) a teeth shape generation module that leverages a diffusion model to learn the distribution of morphological characteristics of teeth, enabling the generation of diverse post-orthodontic teeth models; and (2) a teeth style generation module that synthesizes corresponding pre-orthodontic teeth models by incorporating desired styles as conditional inputs. Extensive qualitative and quantitative experiments demonstrate that our synthetic dataset aligns closely with the distribution of real orthodontic data, and promotes tooth alignment performance significantly when combined with real data for training. The code and dataset are available at https://github.com/lcshhh/teeth_generator.

Delaunay meshes play a critical role in geometry processing for their favorable geometric and numerical properties. However, Delaunay mesh simplification is rather challenging because of the no-differentiable constraint and the two conflicting goals: high geometric fidelity and low mesh complexity. To simultaneously meet these criteria, this paper addresses the Delaunay mesh simplification from an evolutionary multi-objective viewpoint. First, the adaptive segment-specific thresholds replace the previous unique error-bound threshold. Second, we perform constrained simplification by a sequence of edge collapses with Delaunay and error constraints. Finally, the non-dominated sorting genetic algorithm II (NSGA-II) is introduced to search optimal trade-off threshold sequences. Compared with state-of-the-art methods, our method can consistently achieve a satisfactory balance regarding approximation error and the number of vertices.