Computer Aided Geometric Design最新文献

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.

High-order mesh optimization has many goals, such as improving smoothness, reducing approximation error, and improving mesh quality. The previous methods do not optimize these objectives together, resulting in suboptimal results. To this end, we propose a multi-objective optimization method for high-order meshes. Central to our algorithm is using the multi-objective genetic algorithm (MOGA) to adapt to the multiple optimization objectives. Specifically, we optimize each control point one by one, where the MOGA is applied. We demonstrate the feasibility and effectiveness of our method over various models. Compared to other state-of-the-art methods, our method achieves a favorable trade-off between multiple objectives.

Recent advancements in shrink-wrapping-based mesh approximation have shown tremendous advantages for non-manifold defective meshes. However, these methods perform unsatisfactorily when maintaining the regions with sharp features and rich details of the input mesh. We propose an adaptive shrink-wrapping method based on the recent Alpha Wrapping technique, offering improved feature preservation while handling defective inputs. The proposed approach comprises three main steps. First, we compute a new sizing field with the capability to assess the discretization density of non-manifold defective meshes. Then, we generate a mesh feature skeleton by projecting input feature lines onto the offset surface, ensuring the preservation of sharp features. Finally, an adaptive wrapping approach based on normal projection is applied to preserve the regions with sharp features and rich details simultaneously. By conducting experimental tests on various datasets including Thingi10k, ABC, and GrabCAD, we demonstrate that our method exhibits significant improvements in mesh fidelity compared to the Alpha Wrapping method, while maintaining the advantage of manifold property inherited from shrink-wrapping methods.

3D mesh denoising is a crucial pre-processing step in many graphics applications. However, existing data-driven mesh denoising models, primarily trained on synthetic white noise, are less effective when applied to real-world meshes with the noise of complex intensities and distributions. Moreover, how to comprehensively capture information from input meshes and apply suitable denoising models for feature-preserving mesh denoising remains a critical and unresolved challenge. This paper presents a rotation-Equivariant model-based Mesh Denoising (EMD) model and a Realistic Mesh Noise Generation (RMNG) model to address these issues. Our EMD model leverages rotation-equivariant features and self-attention weights of geodesic patches for more effective feature extraction, thereby achieving SOTA denoising results. The RMNG model, based on the Generative Adversarial Networks (GANs) architecture, generates massive amounts of realistic noisy and noiseless mesh pairs data for data-driven mesh denoising model training, significantly benefiting real-world denoising tasks. To address the smooth degradation and loss of sharp edges commonly observed in captured meshes, we further introduce varying levels of Laplacian smoothing to input meshes during the paired training data generation, endowing the trained denoising model with feature recovery capabilities. Experimental results demonstrate the superior performance of our proposed method in preserving fine-grained features while removing noise on real-world captured meshes.

Current infrared and visible image fusion (IVIF) methods lack ground truth and require prior knowledge to guide the feature fusion process. However, in the fusion process, these features have not been placed in an equal and well-defined position, which causes the degradation of image quality. To address this challenge, this study develops a new end-to-end model, termed unpaired high-quality image-guided generative adversarial network (UHG-GAN). Specifically, we introduce the high-quality image as the reference standard of the fused image and employ a global discriminator and a local discriminator to identify the distribution difference between the high-quality image and the fused image. Through adversarial learning, the generator can generate images that are more consistent with high-quality expression. In addition, we also designed the laplacian pyramid augmentation (LPA) module in the generator, which integrates multi-scale features of source images across domains so that the generator can more fully extract the structure and texture information. Extensive experiments demonstrate that our method can effectively preserve the target information in the infrared image and the scene information in the visible image and significantly improve the image quality.

We propose a novel method to generate high-quality triangular meshes with specified anisotropy. Central to our algorithm is to present metric-adapted embeddings for converting the anisotropic meshing problem to an isotropic meshing problem with constant density. Moreover, the orientation of the input Riemannian metric forms a field, enabling us to use field-based meshing techniques to improve regularity and penalize obtuse angles. To achieve such metric-adapted embeddings, we use the cone singularities, which are generated to adapt to the input Riemannian metric. We demonstrate the feasibility and effectiveness of our method over various models. Compared to other state-of-the-art methods, our method achieves higher quality on all metrics in most models.