Hair cards remain a widely used representation for hair modeling in real-time applications, offering a practical trade-off between visual fidelity, memory usage, and performance. However, generating high-quality hair card models remains a challenging and labor-intensive task. This work presents an automated pipeline for converting strand-based hair models into hair card models with a limited number of cards and textures while preserving the hairstyle appearance. Our key idea is a novel differentiable representation where each strand is encoded as a projected 2D curve in the texture space, which enables end-to-end optimization with differentiable rendering while respecting the structures of the hair geometry. Based on this representation, we develop a novel algorithm pipeline, where we first cluster hair strands into initial hair cards and project the strands into the texture space. We then conduct a two-stage optimization, where our first stage optimizes the orientation of each hair card separately, and after strand projection, our second stage conducts joint optimization over the entire hair card model for fine-tuning. Our method is evaluated on a range of hairstyles, including straight, wavy, curly, and coily hair. To capture the appearance of short or coily hair, our method comes with support for hair caps and cross-card.

The discrete Laplacian operator holds a crucial role in 3D geometry processing, yet it is still challenging to define it on point clouds. Previous works mainly focused on constructing a local triangulation around each point to approximate the underlying manifold for defining the Laplacian operator, which may not be robust or accurate. In contrast, we simply use the K- nearest neighbors (KNN) graph constructed from the input point cloud and learn the Laplacian operator on the KNN graph with graph neural networks (GNNs). However, the ground-truth Laplacian operator is defined on a manifold mesh with a different connectivity from the KNN graph and thus cannot be directly used for training. To train the GNN, we propose a novel training scheme by imitating the behavior of the ground-truth Laplacian operator on a set of probe functions so that the learned Laplacian operator behaves similarly to the ground-truth Laplacian operator. We train our network on a subset of ShapeNet and evaluate it across a variety of point clouds. Compared with previous methods, our method reduces the error by an order of magnitude and excels in handling sparse point clouds with thin structures or sharp features. Our method also demonstrates a strong generalization ability to unseen shapes. With our learned Laplacian operator, we further apply a series of Laplacian-based geometry processing algorithms directly to point clouds and achieve accurate results, enabling many exciting possibilities for geometry processing on point clouds. The code and trained models are available at https://github.com/IntelligentGeometry/NeLo.

Simulating high-resolution cloth poses computational challenges in real-time applications. In the gaming industry, the proxy mesh technique offers an alternative, simulating a simplified low-resolution cloth geometry, proxy mesh. This proxy mesh's dynamics drive the detailed high-resolution geometry, visual mesh , through Linear Blended Skinning (LBS). However, generating a suitable proxy mesh with appropriate skinning weights from a given visual mesh is non-trivial, often requiring skilled artists several days for fine-tuning. This paper presents an automatic pipeline to convert an ill-conditioned highresolution visual mesh into a single-layer low-poly proxy mesh. Given that the input visual mesh may not be simulation-ready, our approach then simulates the proxy mesh based on specific use scenarios and optimizes the skinning weights, relying on differential skinning with several well-designed loss functions to ensure the skinned visual mesh appears plausible in the final simulation. We have tested our method on various challenging cloth models, demonstrating its robustness and effectiveness.

Mesh repair is a long-standing challenge in computer graphics and related fields. Converting defective meshes into watertight manifold meshes can greatly benefit downstream applications such as geometric processing, simulation, fabrication, learning, and synthesis. In this work, by assuming the model is visually correct, we first introduce three visual measures for visibility, orientation, and openness, based on ray-tracing. We then present a novel mesh repair framework incorporating visual measures with several critical steps, i.e., open surface closing, face reorientation, and global optimization, to effectively repair meshes with defects (e.g., gaps, holes, self-intersections, degenerate elements, and inconsistent orientations) and preserve visual appearances. Our method reduces unnecessary mesh complexity without compromising geometric accuracy or visual quality while preserving input attributes such as UV coordinates for rendering. We evaluate our approach on hundreds of models randomly selected from ShapeNet and Thingi10K, demonstrating its effectiveness and robustness compared to existing approaches.

We present GEGNN, a learning-based method for computing the approximate geodesic distance between two arbitrary points on discrete polyhedra surfaces with constant time complexity after fast precomputation. Previous relevant methods either focus on computing the geodesic distance between a single source and all destinations, which has linear complexity at least or require a long precomputation time. Our key idea is to train a graph neural network to embed an input mesh into a high-dimensional embedding space and compute the geodesic distance between a pair of points using the corresponding embedding vectors and a lightweight decoding function. To facilitate the learning of the embedding, we propose novel graph convolution and graph pooling modules that incorporate local geodesic information and are verified to be much more effective than previous designs. After training, our method requires only one forward pass of the network per mesh as precomputation. Then, we can compute the geodesic distance between a pair of points using our decoding function, which requires only several matrix multiplications and can be massively parallelized on GPUs. We verify the efficiency and effectiveness of our method on ShapeNet and demonstrate that our method is faster than existing methods by orders of magnitude while achieving comparable or better accuracy. Additionally, our method exhibits robustness on noisy and incomplete meshes and strong generalization ability on out-of-distribution meshes. The code and pretrained model can be found on https://github.com/IntelligentGeometry/GeGnn.