Sharp feature lines provide critical structural information in 3D models and are essential for geometric processing. However, the performance of existing algorithms for extracting feature lines from point clouds remains sensitive to the quality of the input data. This paper introduces an algorithm specifically designed to extract feature lines from 3D point clouds. The algorithm calculates the winding number for each point and uses variations in this number within edge regions to identify feature points. These feature points are then mapped onto a cuboid structure to obtain key feature points and capture neighboring relationships. Finally, feature lines are fitted based on the connectivity of key feature points. Extensive experiments demonstrate that this algorithm not only accurately detects feature points on potential sharp edges, but also outperforms existing methods in extracting subtle feature lines and handling complex point clouds.

Vector graphics are widely used in areas such as logo design and digital painting, including both stroked and filled paths as primitives. GPU-based rendering for filled paths already has well-established solutions. Due to the complexity of stroked paths, existing methods often render them by approximating strokes with filled shapes. However, the performance of existing methods still leaves room for improvement. This paper designs a GPU-accelerated rendering algorithm along with a curvature-guided parallel adaptive subdivision method to accurately and efficiently render stroke areas. Additionally, we propose an efficient Newton iteration-based method for arc-length parameterization of quadratic curves, along with an error estimation technique. This enables a parallel rendering approach for dashed stroke styles and arc-length guided texture filling. Experimental results show that our method achieves average speedups of 3 . 4 × for rendering quadratic stroked paths and 2 . 5 × for rendering quadratic dashed strokes, compared to the best existing approaches.

The creation of computational agents capable of generating computer-aided design (CAD) models that rival those produced by professional designers is a pressing challenge in the field of computational design. The key obstacle is the need to generate a large number of realistic and diverse models while maintaining control over the output to a certain degree. Therefore, we propose a novel CAD model generation network called CADTrans which is based on a code tree-guided transformer framework to autoregressively generate CAD construction sequences. Firstly, three regularized discrete codebooks are extracted through vector quantized adversarial learning, with each codebook respectively representing the features of Loop, Profile, and Solid. Secondly, these codebooks are used to normalize a CAD construction sequence into a structured code tree representation which is then used to train a standard transformer network to reconstruct the code tree. Finally, the code tree is used as global information to guide the sketch-and-extrude method to recover the corresponding geometric information, thereby reconstructing the complete CAD model. Extensive experiments demonstrate that CADTrans achieves state-of-the-art performance, generating higher-quality, more varied, and complex models. Meanwhile, it provides more possibilities for CAD applications through its flexible control method, enabling users to quickly experiment with different design schemes, inspiring diverse design ideas and the generation of a wide variety of models or even inspiring models, thereby improving design efficiency and promoting creativity. The code is available at https://effieguoxufei.github.io/CADtrans/ .

Portraits near the periphery of wide-angle photos often suffer conspicuous distortions. With the popularity of wide-angle lenses on mobile phones, portrait correction, which removes portrait distortion in wide-angle photos, has attracted widespread attention as a form of content-aware warping. Existing portrait correction methods for wide-angle photos using uniform quad meshes take a long time to optimize the correction. Most of them focus only on correcting facial distortions, leading to inconsistency between people's heads and bodies after correction. This study proposes an efficient method to remove portrait distortions in wide-angle perspective photos, based on a triangle mesh. We generate an adaptive mesh tailored to the image content with relatively few vertices. According to the characteristics of the triangle mesh, we tailor three smooth and intuitive energy terms for the human area, background area, and boundary to minimize portrait distortions. Our algorithm can easily be extended to allow further geometric constraints, such as line constraints. Experimental results show that our method is robust for photos with various fields of view. Comparisons to the state-of-the-art demonstrate that our method achieves significant improvements in optimization efficiency and consistency of heads and bodies.

We present an efficient approach to generating uniformly distributed resampling points of raw 3D point clouds. A key contribution for making such a resampling method both practical and efficient is the construction of the centroidal Voronoi tessellation on the given point cloud efficiently achieved by applying the proposed Anderson-accelerated Lloyd's method. The calculations involved in the method are mainly carried out over a group of locally approximated quadratic surfaces, instead of directly on the given point cloud, providing us a great advantage in filtering out the affection of distribution of original points on output results. Once the resampling points are initialized, the resampling quality can be improved progressively by optimizing resampling points and updating the local approximated surfaces. In addition, by restricting the movement of resampling points, we can deal with unclosed point clouds without any boundary detection. Our approach outperforms existing resampling methods in generating uniform results, and extensive experiments are conducted to demonstrate its efficacy.

Abstract Image triangulation methods, which decompose an image into a series of triangles, are fundamental in artistic creation and image processing. This paper introduces a novel framework that integrates cubic Bézier curves into image triangulation, enabling the precise reconstruction of curved image features. Our developed framework constructs a well‐structured curved triangle mesh, effectively preventing overlaps between curves. A refined energy function, grounded in differentiable rendering, establishes a direct link between mesh geometry and rendering effects and is instrumental in guiding the curved mesh generation. Additionally, we derive an explicit gradient formula with respect to mesh parameters, facilitating the adaptive and efficient optimization of these parameters to fully leverage the capabilities of cubic Bézier curves. Through experimental and comparative analyses with state‐of‐the‐art methods, our approach demonstrates a significant enhancement in both numerical accuracy and visual quality.

Feature lines play a pivotal role in the reconstruction of CAD models. Currently, there is a lack of a robust explicit reconstruction algorithm capable of achieving sharp feature reconstruction in point clouds with noise and non-uniformity. In this paper, we propose a feature-preserving CAD model surface reconstruction algorithm, named FACE. The algorithm initiates with preprocessing the point cloud through denoising and resampling steps, resulting in a high-quality point cloud that is devoid of noise and uniformly distributed. Then, it employs discrete optimal transport to detect feature regions and subsequently generates dense points along potential feature lines to enhance features. Finally, the advancing-front surface reconstruction method, based on normal vector directions, is applied to reconstruct the enhanced point cloud. Extensive experiments demonstrate that, for contaminated point clouds, this algorithm excels not only in reconstructing straight edges and corner points but also in handling curved edges and surfaces, surpassing existing methods.

Feature-preserving mesh reconstruction from point clouds is challenging. Implicit methods tend to fit smooth surfaces and cannot be used to reconstruct sharp features. Explicit reconstruction methods are sensitive to noise and only interpolate sharp features when points are distributed on feature lines. We propose a watertight surface reconstruction method based on optimal transport that can accurately reconstruct sharp features often present in CAD models. We formalize the surface reconstruction problem by minimizing the optimal transport cost between the point cloud and the reconstructed surface. The algorithm consists of initialization and refinement steps. In the initialization step, the convex hull of the point cloud is deformed under the guidance of a transport plan to obtain an initial approximate surface. Next, the mesh surface was optimized using operations including vertex relocation and edge collapses/flips to obtain feature-preserving results. Experiments demonstrate that our method can preserve sharp features while being robust to noise and missing data.

Style transfer is a popular research topic in the field of computer vision. In 3D stylization, a mesh model is deformed to achieve a specific geometric style. We explore a general neural style transfer framework for 3D meshes that can transfer multiple geometric styles from other meshes to the current mesh. Our stylization network is based on a pre-trained MeshNet model, from which content representation and Gram-based style representation are extracted. By constraining the similarity in content and style representation between the generated mesh and two different meshes, our network can generate a deformed mesh with a specific style while maintaining the content of the original mesh. Experiments verify the robustness of the proposed network and show the effectiveness of stylizing multiple models with one dedicated style mesh. We also conduct ablation experiments to analyze the effectiveness of our network.

Mesh-based image warping techniques typically represent image deformation using linear functions on triangular meshes or bilinear functions on rectangular meshes. This enables simple and efficient implementation, but in turn, restricts the representation capability of the deformation, often leading to unsatisfactory warping results. We present a novel, flexible polygonal finite element (poly-FEM) method for content-aware image warping. Image deformation is represented by high-order poly-FEMs on a content-aware polygonal mesh with a cell distribution adapted to saliency information in the source image. This allows highly adaptive meshes and smoother warping with fewer degrees of freedom, thus significantly extending the flexibility and capability of the warping representation. Benefiting from the continuous formulation of image deformation, our poly-FEM warping method is able to compute the optimal image deformation by minimizing existing or even newly designed warping energies consisting of penalty terms for specific transformations. We demonstrate the versatility of the proposed poly-FEM warping method in representing different deformations and its superiority by comparing it to other existing state-of-the-art methods.

Abstract Image triangulation aims to generate an optimal partition with triangular elements to represent the given image. One bottleneck in ensuring approximation quality between the original image and a piecewise approximation over the triangulation is the inaccurate alignment of straight edges to the curved features. In this paper, we propose a novel variational method called curved optimal triangulation, where not all edges are straight segments, but may also be quadratic Bézier curves. The energy function is defined as the total approximation error determined by vertex locations, connectivity and bending of edges. The gradient formulas of this function are derived explicitly in closed form to optimize the energy function efficiently. We test our method on several models to demonstrate its efficacy and ability in preserving features. We also explore its applications in the automatic generation of stylization and Lowpoly images. With the same number of vertices, our curved optimal triangulation method generates more accurate and visually pleasing results compared with previous methods that only use straight segments.

Vector image representation methods that can faithfully reconstruct objects and color variations in a raster image are desired in many practical applications. This article presents triangular configuration B-spline (referred to as TCB-spline)-based vector graphics for raster image vectorization. Based on this new representation, an automatic raster image vectorization paradigm is proposed. The proposed framework first detects sharp curvilinear features in the image and constructs knot meshes based on the detected feature lines. It iteratively optimizes color and position of control points and updates the knot meshes. By using collinear knots at feature lines, both smooth and discontinuous color variations can be efficiently modeled by the same set of quadratic TCB-splines. A variational knot mesh generation method is designed to adaptively introduce knots and update their connectivity to satisfy the local reconstruction quality. Experiments and comparisons show that our framework outperforms the existing state-of-the-art methods in providing more faithful reconstruction results. In particular, our method is able to model undetected features and subtle or complicated color variations in-between features, which the previous methods cannot handle efficiently. Our vectorization representation also facilitates a variety of editing operations performed directly over vector images.

In this paper, we present a novel geometric method for efficiently and robustly computing intersections between a ray and a triangular Bézier patch defined over a triangular domain, called the hybrid clipping (HC) algorithm. If the ray pierces the patch only once, we locate the parametric value of the intersection to a smaller triangular domain, which is determined by pairs of lines and quadratic curves, by using a multi-degree reduction method. The triangular domain is iteratively clipped into a smaller one by combining a subdivision method, until the domain size reaches a prespecified threshold. When the ray intersects the patch more than once, Descartes’ rule of signs and a split step are required to isolate the intersection points. The algorithm can be proven to clip the triangular domain with a cubic convergence rate after an appropriate preprocessing procedure. The proposed algorithm has many attractive properties, such as the absence of an initial guess and insensitivity to small changes in coefficients of the original problem. Experiments have been conducted to illustrate the efficacy of our method in solving ray-triangular Bézier patch intersection problems.

Abstract We develop a novel isotropic remeshing method based onconstrained centroidal Delaunay mesh(CCDM), a generalization of centroidal patch triangulation from 2D to mesh surface. Our method starts with resampling an input mesh with a vertex distribution according to a user‐defined density function. The initial remeshing result is then progressively optimized by alternatively recovering the Delaunay mesh and moving each vertex to the centroid of its 1‐ring neighborhood. The key to making such simple iterations work is an efficient optimization framework that combines both local and global optimization methods. Our method is parameterization‐free, thus avoiding the metric distortion introduced by parameterization, and generating more well‐shaped triangles. Our method guarantees that the topology of surface is preserved without requiring geodesic information. We conduct various experiments to demonstrate the simplicity, efficacy, and robustness of the presented method.

This paper develops a novel surface fitting scheme for automatically reconstructing a genus-0 object into a continuous parametric spline surface. A key contribution for making such a fitting method both practical and accurate is our spherical generalization of the Delaunay configuration B-spline (DCB-spline), a new non-tensor-product spline. In this framework, we efficiently compute Delaunay configurations on sphere by the union of two planar Delaunay configurations. Also, we develop a hierarchical and adaptive method that progressively improves the fitting quality by new knot-insertion strategies guided by surface geometry and fitting error. Within our framework, a genus-0 model can be converted to a single spherical spline representation whose root mean square error is tightly bounded within a user-specified tolerance. The reconstructed continuous representation has many attractive properties such as global smoothness and no auxiliary knots. We conduct several experiments to demonstrate the efficacy of our new approach for reverse engineering and shape modeling.

We introduce a kind of shape-adjustable spline curves defined over a non-uniform knot sequence. These curves not only have the many valued properties of the usual non-uniform B-spline curves, but also are shape adjustable under fixed control polygons. Our method is based on the degree elevation of B-spline curves, where maximum degrees of freedom are added to a curve parameterized in terms of a non-uniform B-spline. We also discuss the geometric effect of the adjustment of shape parameters and propose practical shape modification algorithms, which are indispensable from the user’s perspective.