Computer Aided Geometric Design最新文献

The conventional wisdom in point cloud analysis predominantly explores 3D geometries. It is often achieved through the introduction of intricate learnable geometric extractors in the encoder or by deepening networks with repeated blocks. However, these methods contain a significant number of learnable parameters, resulting in substantial computational costs and imposing memory burdens on CPU/GPU. Moreover, they are primarily tailored for object-level point cloud classification and segmentation tasks, with limited extensions to crucial scene-level applications, such as autonomous driving. To this end, we introduce PointeNet, an efficient network designed specifically for point cloud analysis. PointeNet distinguishes itself with its lightweight architecture, low training cost, and plug-and-play capability, while also effectively capturing representative features. The network consists of a Multivariate Geometric Encoding (MGE) module and an optional Distance-aware Semantic Enhancement (DSE) module. MGE employs operations of sampling, grouping, pooling, and multivariate geometric aggregation to lightweightly capture and adaptively aggregate multivariate geometric features, providing a comprehensive depiction of 3D geometries. DSE, designed for real-world autonomous driving scenarios, enhances the semantic perception of point clouds, particularly for distant points. Our method demonstrates flexibility by seamlessly integrating with a classification/segmentation head or embedding into off-the-shelf 3D object detection networks, achieving notable performance improvements at a minimal cost. Extensive experiments on object-level datasets, including ModelNet40, ScanObjectNN, ShapeNetPart, and the scene-level dataset KITTI, demonstrate the superior performance of PointeNet over state-of-the-art methods in point cloud analysis. Notably, PointeNet outperforms PointMLP with significantly fewer parameters on ModelNet40, ScanObjectNN, and ShapeNetPart, and achieves a substantial improvement of over 2% in $3DA{P}_{R40}$ for PointRCNN on KITTI with a minimal parameter cost of 1.4 million. Code is publicly available at https://github.com/lipeng-gu/PointeNet.

Computer-Aided Design (CAD) software remains a pivotal tool in modern engineering and manufacturing, driving the design of a diverse range of products. In this work, we introduce VQ-CAD, the first CAD generation model based on Denoising Diffusion Probabilistic Models. This model utilizes a vector quantized diffusion model, employing multiple hierarchical codebooks generated through VQ-VAE. This integration not only offers a novel perspective on CAD model generation but also achieves state-of-the-art performance in 3D CAD model creation in a fully automatic fashion. Our model is able to recognize and incorporate implicit design constraints by simply forgoing traditional data augmentation. Furthermore, by melding our approach with CLIP, we significantly simplify the existing design process, directly generate CAD command sequences from initial design concepts represented by text or sketches, capture design intentions, and ensure designs adhere to implicit constraints.

Although significant advances have been made in the field of multi-view 3D reconstruction using implicit neural field-based methods, existing reconstruction methods overlook the estimation of the material information (e.g. the base color, albedo, roughness, and metallic) during the learning process. In this paper, we propose a novel differentiable rendering framework, named as material NueS (M-NeuS), for simultaneously achieving precise surface reconstruction and competitive material estimation. For surface reconstruction, we perform multi-view geometry optimization by proposing an enhanced-low-to-high frequency encoding registration strategy (EFERS) and a second-order interpolated signed distance function (SI-SDF) for precise details and outline reconstruction. For material estimation, inspired by the NeuS, we first propose a volume-rendering-based material estimation strategy (VMES) to estimate the base color, albedo, roughness, and metallic accurately. And then, different from most material estimation methods that need ground-truth geometric priors, we use the geometry information reconstructed in the surface reconstruction stage and the directions of incidence from different viewpoints to model a neural light field, which can extract the lighting information from image observations. Next, the extracted lighting and the estimated base color, albedo, roughness, and metallic are optimized by the physics-based rendering equation. Extensive experiments demonstrate that our M-NeuS can not only reconstruct more precise geometry surface than existing state-of-the-art (SOTA) reconstruction methods but also can estimate competitive material information: the base color, albedo, roughness, and metallic.

One of the main challenges of indoor scene synthesis is preserving the functionality of synthesized scenes to create practical and usable indoor environments. Function groups exhibit the capability of balancing the global structure and local scenes of an indoor space. In this paper, we propose a function-centric indoor scene synthesis framework, named FuncScene. Our key idea is to use function groups as an intermedium to connect the local scenes and the global structure, thus achieving a coarse-to-fine indoor scene synthesis while maintaining the functionality and practicality of synthesized scenes. Indoor scenes are synthesized by first generating function groups using generative models and then instantiating by searching and matching the specific function groups from a dataset. The proposed framework also makes it easier to achieve multi-level generation control of scene synthesis, which was challenging for previous works. Extensive experiments on various indoor scene synthesis tasks demonstrate the validity of our method. Qualitative and quantitative evaluations show the proposed framework outperforms the existing state-of-the-art.

The generalization of barycentric coordinates to arbitrary simple polygons with more than three vertices has been a subject of study for a long time. Among the different constructions proposed, mean value coordinates have emerged as a popular choice, particularly due to their suitability for the non-convex setting. Since their introduction, they have found applications in numerous fields, and several equivalent formulas for their evaluation have been presented in the literature. However, so far, there has been no study regarding their numerical stability. In this paper, we aim to investigate the numerical stability of the algorithms that compute mean value coordinates. We show that all the known methods exhibit instability in some regions of the domain. To address this problem, we introduce a new formula for computing mean value coordinates, explain how to implement it, and formally prove that our new algorithm provides a stable evaluation of mean value coordinates. We validate our results through numerical experiments.

In motion planning, two-dimensional (2D) splinegons are typically used to represent the contours of 2D objects. In general, a 2D splinegon must be pre-decomposed to support rapid queries of the shortest paths or visibility. Herein, we propose a new region decomposition strategy, known as the Voronoi-based decomposition (VBD), based on the Voronoi diagram of curved boundary-segment generators (either convex or concave). The number of regions in the VBD is O(n+$c_1$). Compared with the well-established horizontal visibility decomposition (HVD), whose complexity is O(n+$c_2$), the VBD decomposition generally contains less regions because $c_1$≤$c_2$, where n is the number of the vertices of the input splinegon, and $c_1$ and $c_2$ are the number of inserted vertices at the boundary. We systematically discuss the usage of VBD. Based on the VBD, the shortest path tree (SPT) can be computed in linear time. Statistics show that the VBD performs faster than HVD in SPT computations. Additionally, based on the SPT, we design algorithms that can rapidly compute the visibility between two points, the visible area of a point/line-segment, and the shortest path between two points.

In recent years, with the rapid development of the computer aided design and computer graphics, a large number of 3D models have emerged, making it a challenge to quickly find models of interest. As a concise and informative representation of 3D models, shape descriptors are a key factor in achieving effective retrieval. In this paper, we propose a novel global descriptor for 3D models that incorporates both geometric and topological information. We refer to this descriptor as the persistent heat kernel signature descriptor (PHKS). Constructed by concatenating our isometry-invariant geometric descriptor with topological descriptor, PHKS possesses high recognition ability, while remaining insensitive to noise and can be efficiently calculated. Retrieval experiments of 3D models on the benchmark datasets show considerable performance gains of the proposed method compared to other descriptors based on HKS and advanced topological descriptors.

In this paper, we propose a novel surface reconstruction method for unoriented points by establishing and solving a nonlinear equation system. By treating normals as unknown parameters and imposing the conditions that the implicit field is constant and its gradients parallel to the normals on the input point cloud, we establish a nonlinear equation system involving the oriented normals. To simplify the system, we transform it into a 0-1 integer programming problem solely focusing on orientation by incorporating inconsistent oriented normal information through PCA. We solve the simplified problem using flipping-based iterative algorithms and propose two novel criteria for flipping based on theoretical analysis.

Extensive experiments on renowned datasets demonstrate that our flipping-based method with wavelet surface reconstruction achieves state-of-the-art results in orientation and reconstruction. Furthermore, it exhibits linear computational and storage complexity by leveraging the orthogonality and compact support properties of wavelet bases. The source code is available at https://github.com/mayueji/FISR_code.

Compared to triangular meshes, high-quality quadrilateral meshes offer significant advantages in the field of simulation. However, generating high-quality quadrilateral meshes has always been a challenging task. By synthesizing high-quality quadrilateral meshes based on existing ones through Boolean operations such as mesh intersection, union, and difference, the automation level of quadrilateral mesh modeling can be improved. This significantly reduces modeling time. We propose a feature-preserving quadrilateral mesh Boolean operation method that can generate high-quality all-quadrilateral meshes through Boolean operations while preserving the geometric features and shape of the original mesh. Our method, guided by cross-field techniques, aligns mesh faces with geometric features of the model and maximally preserves the original mesh's geometric shape and layout. Compared to traditional quadrilateral mesh generation methods, our approach demonstrates higher efficiency, offering a substantial improvement to the pipeline of mesh-based modeling tools.

One prominent step in isogeometric analysis (IGA) is known as domain parameterization, that is, finding a parametric spline representation for a computational domain. Typically, domain parameterization is divided into two separate steps: identifying an appropriate boundary correspondence and then parameterizing the interior region. However, this separation significantly degrades the quality of the parameterization. To attain high-quality parameterization, it is necessary to optimize both the boundary correspondence and the interior mapping simultaneously, referred to as integral parameterization. In a prior research, an integral parameterization approach for planar domains based on neural networks was introduced. One limitation of this approach is that the neural network has no ability of generalization, that is, a network has to be trained to obtain a parameterization for each specific computational domain. In this article, we propose an efficient enhancement over this work, and we train a network which has the capacity of generalization—once the network is trained, a parameterization can be immediately obtained for each specific computational via evaluating the network. The new network greatly speeds up the parameterization process by two orders of magnitudes. We evaluate the performance of the new network on the MPEG data set and a self-design data set, and experimental results demonstrate the superiority of our algorithm compared to state-of-the-art parameterization methods.