Yuxuan Yu

Yuxuan Yu, Jiashuo Liu, Hua Tong et al.

Polycube structures provide parametric domains for all-hexahedral (all-hex) mesh generation and analysis-suitable volumetric spline construction in isogeometric analysis (IGA). Recent learning-based polycube pipelines have improved automation, yet several challenges remain when handling complex CAD geometries. These challenges include the limited diversity of primitive geometries, restricted grid configurations, and the increasing cost of genus-guided context search during inference as both the primitive set and the grid size grow. In this paper, we present {Scalable DDPM-Polycube}, an extended diffusion-based polycube construction method that addresses these limitations. First, we expand the primitive set from two primitive geometries to three by introducing a blind-hole cube primitive, thereby improving the representation of local hole-like features that do not change the global genus. Second, we extend the grid configuration from the previous $2\times 1$ setting to an enlarged three-dimensional grid configuration, which increases representational capacity and reduces mapping distortion for complex geometries. Third, we develop a genus-guided context generation strategy together with a hierarchical verification procedure, enabling robust context generation in both user-guided and automated modes. Once a valid polycube structure is generated, it is used for parametric mapping, all-hex control mesh generation, and volumetric spline construction. Experimental results demonstrate that scalable DDPM-Polycube improves the generality, scalability, and automation of diffusion-based polycube generation, and supports hex mesh generation and volumetric spline construction for IGA applications on complex geometries.

Yuxuan Yu, Yuzhuo Fang, Hua Tong et al.

In this paper, we present a novel algorithm that integrates deep learning with the polycube method (DL-Polycube) to generate high-quality hexahedral (hex) meshes, which are then used to construct volumetric splines for isogeometric analysis. Our DL-Polycube algorithm begins by establishing a connection between surface triangular meshes and polycube structures. We employ deep neural network to classify surface triangular meshes into their corresponding polycube structures. Following this, we combine the acquired polycube structural information with unsupervised learning to perform surface segmentation of triangular meshes. This step addresses the issue of segmentation not corresponding to a polycube while reducing manual intervention. Quality hex meshes are then generated from the polycube structures, with employing octree subdivision, parametric mapping and quality improvement techniques. The incorporation of deep learning for creating polycube structures, combined with unsupervised learning for segmentation of surface triangular meshes, substantially accelerates hex mesh generation. Finally, truncated hierarchical B-splines are constructed on the generated hex meshes. We extract trivariate Bézier elements from these splines and apply them directly in isogeometric analysis. We offer several examples to demonstrate the robustness of our DL-Polycube algorithm.

Humphrey Yang, Kuanren Qian, Haolin Liu et al.

Morphing materials allow us to create new modalities of interaction and fabrication by leveraging dynamic behaviors of materials. Yet, despite the ongoing rapid growth of computational tools within this realm, current developments are bottlenecked by the lack of an effective simulation method. As a result, existing design tools must trade-off between speed and accuracy to support a real-time interactive design scenario. In response, we introduce SimuLearn, a data-driven method that combines finite element analysis and machine learning to create real-time (0.61 seconds) and truthful (97% accuracy) morphing material simulators. We use mesh-like 4D printed structures to contextualize this method and prototype design tools to exemplify the design workflows and spaces enabled by a fast and accurate simulation method. Situating this work among existing literature, we believe SimuLearn is a timely addition to the HCI CAD toolbox that can enable the proliferation of morphing materials.