Integrating artificial intelligence (AI) into computer-aided design (CAD) has shown the potential to transform design and manufacturing processes, enabling more efficient, intuitive, and intelligent workflows. In recent years, the application of AI to 3D CAD model generation tasks has gradually emerged. To better enable researchers to understand the current research status of the AI-based CAD generation field and to inspire them to conduct further research, this survey explores the role of AI in 3D CAD model generation tasks that utilize various representations and conditions, ranging from traditional machine learning to LLM-based approaches. Additionally, AI applications in other extended CAD areas are also touched upon in the survey. Finally, we analyze current progress, identify challenges and limitations faced by this field, and propose possible directions for future work.

Boundary representation (B-rep) of geometric models is a fundamental format in Computer-Aided Design (CAD). However, automatically generating valid and high-quality B-rep models remains challenging due to the complex interdependence between the topology and geometry of the models. Existing methods tend to prioritize geometric representation while giving insufficient attention to topological constraints, making it difficult to maintain structural validity and geometric accuracy. In this paper, we propose DTGBrepGen, a novel topology-geometry decoupled framework for B-rep generation that explicitly addresses both aspects. Our approach first generates valid topological structures through a two-stage process that independently models edge-face and edge-vertex adjacency relationships. Subsequently, we employ Transformer-based diffusion models for sequential geometry generation, progressively generating vertex coordinates, followed by edge geometries and face geometries which are represented as B-splines. Extensive experiments on diverse CAD datasets show that DTGBrepGen significantly outperforms existing methods in both topological validity and geometric accuracy, achieving higher validity rates and producing more diverse and realistic B-reps. Our code is publicly available at https://github.com/jinli99/DTGBrepGen.

Self-intersections of NURBS surfaces are unavoidable during the CAD modeling process, especially in operations such as offset or sweeping. The existence of self-intersections might cause problems in the subsequent simulation and manufacturing process. Therefore, fast detection of self-intersections of NURBS is highly demanded in industrial applications. Self-intersections are essentially singular points on the surface. Although there is a long history of exploring singular points in mathematics community, the fast and robust determination and computation of self-intersections have been a challenging problem in practice. In this article, we construct an algebraic signature whose non-negativity is proven to be sufficient for excluding the existence of self-intersections from a global perspective. An efficient algorithm for determining the existence of self-intersections is provided by recursively using this signature. Once the self-intersection is detected, if necessary, the self-intersection locus can also be computed via a further recursively cross-use of this signature and the surface-surface intersection function. Various experiments and comparisons with existing methods, as well as geometry kernels, including OCCT and ACIS, validate the robustness and efficiency of our algorithm. We also adapt our algorithm to self-intersection elimination, self-intersection trimming, and applications in mesh generation, Boolean operation, and shelling.

Owing to the rapid development in additive manufacturing , the potential to fabricate intricate structures has become a reality, emphasizing the importance of designing structures conducive to additive manufacturing processes . A crucial consideration is the ability to design structures requiring no additional support during manufacturing. This paper employs implicit B-spline representations for self-supporting structure design by integrating a topology optimization model with self-supporting constraints derived analytically from the implicit representation. This analytical derivation for detecting overhang regions enables accurate and efficient calculation of constraints, outperforming other B-spline-based methods. Compared to the traditional voxel-based methods, the implicit B-spline representation significantly expedites the optimization process by reducing the number of design variables. Additionally, several acceleration techniques are implemented to enhance the efficiency of our method, allowing simulations of 3D models with millions of finite elements to be completed within one and half an hour, excelling other B-spline-based methods and voxel-based methods. Various numerical experiments validate its excellent performance, confirming the effectiveness and efficiency of the proposed algorithm.

Abstract Recent advancements in generative models have enabled image editing very effective with impressive results. By extending this progress to 3D geometry models, we introduce iShapEditing, a novel framework for 3D shape editing which is applicable to both generated and real shapes. Users manipulate shapes by dragging handle points to corresponding targets, offering an intuitive and intelligent editing interface. Leveraging the Triplane Diffusion model and robust intermediate feature correspondence, our framework utilizes classifier guidance to adjust noise representations during sampling process, ensuring alignment with user expectations while preserving plausibility. For real shapes, we employ shape predictions at each time step alongside a DDPM‐based inversion algorithm to derive their latent codes, facilitating seamless editing. iShapEditing provides effective and intelligent control over shapes without the need for additional model training or fine‐tuning. Experimental examples demonstrate the effectiveness and superiority of our method in terms of editing accuracy and plausibility.

Singularity computation is a fundamental problem in Computer Graphics and Computer Aided Geometric Design, since it is closely related to topology determination, intersection, mesh generation, rendering, simulation, and modeling of curves and surfaces. In this article, we present an efficient and robust algorithm for computing all the singularities (including their orders) of rational parametric surfaces using the technique of moving planes. The main approach is first to construct a representation matrix whose columns correspond to moving planes following the parametric surface. Then, by substituting the parametric equation of the rational surface into this representation matrix, one can extract the singularity information from the corresponding matrix and return all the singular loci including self-intersection curves, cusp curves, and isolated singular points of the rational surface, together with the order of each singular locus. We present some examples to compare our algorithm with state-of-the-art methods from different perspectives including robustness, efficiency, order computation, and numerical stability, and the experimental results show that our method outperforms existing methods in all these aspects. Furthermore, applications of our algorithm in surface rendering, mesh generation and surface/surface intersections are provided to demonstrate that correctly computing the self-intersection curves of a surface is essential to generate high quality results for these applications.

Abstract Sharp features are important characteristics in surface modelling. However, it is still a significantly difficult task to create complex sharp features for Non‐Uniform Rational B‐Splines compatible subdivision surfaces. Current non‐uniform subdivision methods produce sharp features generally by setting zero knot intervals, and these sharp features may have unpleasant visual effects. In this paper, we construct a non‐uniform subdivision scheme to create complex sharp features by extending the eigen‐polyhedron technique. The new scheme allows arbitrarily specifying sharp edges in the initial mesh and generates non‐uniform cubic B‐spline curves to represent the sharp features. Experimental results demonstrate that the present method can generate visually more pleasant sharp features than other existing approaches.

Mesh segmentation is a process of partitioning a mesh model into meaningful parts - a fundamental problem in various disciplines. This paper introduces a novel mesh segmentation method inspired by sparsity pursuit. Based on the local geometric and topological information of a given mesh, we build a Laplacian matrix whose Fiedler vector is used to characterize the uniformity among elements of the same segment. By analyzing the Fiedler vector, we reformulate the mesh segmentation problem as a ℓ0gradient minimization problem. To solve this problem efficiently, we adopt a coarse-to-fine strategy. A fast heuristic algorithm is first devised to find a rational coarse segmentation, and then an optimization algorithm based on the alternating direction method of multiplier (ADMM) is proposed to refine the segment boundaries within their local regions. To extract the inherent hierarchical structure of the given mesh, our method performs segmentation in a recursive way. Experimental results demonstrate that the presented method outperforms the state-of-the-art segmentation methods when evaluated on the Princeton Segmentation Benchmark, the LIFL/LIRIS Segmentation Benchmark and a number of other complex meshes.

This paper presents a joint head pose and facial landmark regression method with input from depth images for real-time application. Our main contributions are: firstly, a joint optimization method to estimate head pose and facial landmarks, i.e., the pose regression result provides supervised initialization for cascaded facial landmark regression, while the regression result for the facial landmarks can also help to further refine the head pose at each stage. Secondly, we classify the head pose space into 9 sub-spaces, and then use a cascaded random forest with a global shape constraint for training facial landmarks in each specific space. This classification-guided method can effectively handle the problem of large pose changes and occlusion. Lastly, we have built a 3D face database containing 73 subjects, each with 14 expressions in various head poses. Experiments on challenging databases show our method achieves state-of-the-art performance on both head pose estimation and facial landmark regression.

Abstract Shape interpolation is a classical problem in computer graphics and has been widely investigated in the past two decades. Ideal shape interpolation should be natural and smooth which have good properties such as affine and conformal reproduction, bounded distortion, no fold‐overs, etc. In this paper, we present a new approach for planar shape interpolation based on Teichmüller maps ‐ a special type of maps in the class of quasi‐conformal maps. The algorithm consists of two steps. In the first step, a Teichmüller map is computed from the source shape to the target shape, and then the Beltrami coefficient is interpolated such that the conformal distortion is linear with respect to the time variable. In the second step, the intermediate shape is reconstructed by solving the Beltrami equation locally over each triangle and then stitching the mapped triangles by conformal transformations. The new approach preserves all the good properties mentioned above and produces more natural and more uniform intermediate shapes than the start‐of‐the‐art methods. Especially, the conformal distortion changes linearly with respect to the time variable. Experiment results show that our method can produce appealing results regardless of interpolating between the same or different objects.

Manifold is an important technique to model geometric objects with arbitrary topology. In this article, we propose a novel approach for constructing manifolds from discrete meshes based on sparse optimization. The local geometry for each chart is sparsely represented by a set of redundant atom functions, which have the flexibility to represent various geometries with varying smoothness. A global optimization is then proposed to guarantee compatible sparse representations in the overlapping regions of different charts. Our method can construct manifolds of varying smoothness including sharp features (creases, darts, or cusps). As an application, we can easily construct a skinning manifold surface from a given curve network. Examples show that our approach has much flexibility to generate manifold surfaces with good quality.

Box splines are considered as a natural generalization of univariate uniform B-splines. Box splines have local support and are positive in the interior of its support. The translates of box splines form a partition of unity. In this paper we extend the hierarchical paradigm of tensor product B-splines to box splines, which are called hierarchical box splines. We take the application of quartic smooth hierarchical box splines in surface fitting as an example to demonstrate the adaptivity and flexibility of hierarchical box splines.

Many geometry processing applications are sensitive to noise and sharp features. Although there are a number of works on detecting noise and sharp features in the literature, they are heuristic. On one hand, traditional denoising methods use filtering operators to remove noise, however, they may blur sharp features and shrink the object. On the other hand, noise makes detection of features, which relies on computation of differential properties, unreliable and unstable. Therefore, detecting noise and features on discrete surfaces still remains challenging. In this article, we present an approach for decoupling noise and features on 3D shapes. Our approach consists of two phases. In the first phase, a base mesh is estimated from the input noisy data by a global Laplacian regularization denoising scheme. The estimated base mesh is guaranteed to asymptotically converge to the true underlying surface with probability one as the sample size goes to infinity. In the second phase, an ℓ 1 -analysis compressed sensing optimization is proposed to recover sharp features from the residual between base mesh and input mesh. This is based on our discovery that sharp features can be sparsely represented in some coherent dictionary which is constructed by the pseudo-inverse matrix of the Laplacian of the shape. The features are recovered from the residual in a progressive way. Theoretical analysis and experimental results show that our approach can reliably and robustly remove noise and extract sharp features on 3D shapes.

3D printers have become popular in recent years and enable fabrication of custom objects for home users. However, the cost of the material used in printing remains high. In this paper, we present an automatic solution to design a skin-frame structure for the purpose of reducing the material cost in printing a given 3D object. The frame structure is designed by an optimization scheme which significantly reduces material volume and is guaranteed to be physically stable, geometrically approximate, and printable. Furthermore, the number of struts is minimized by solving an l 0 sparsity optimization. We formulate it as a multi-objective programming problem and an iterative extension of the preemptive algorithm is developed to find a compromise solution. We demonstrate the applicability and practicability of our solution by printing various objects using both powder-type and extrusion-type 3D printers. Our method is shown to be more cost-effective than previous works.

We present a novel method to approximate a freeform shape with a planar quadrilateral (PQ) mesh for modeling architectural glass structures. Our method is based on the study of conjugate direction fields (CDF) which allow the presence of ±κ/4(κ ε Z) singularities. Starting with a triangle discretization of a freeform shape, we first compute an as smooth as possible conjugate direction field satisfying the user's directional and angular constraints, then apply mixed-integer quadrangulation and planarization techniques to generate a PQ mesh which approximates the input shape faithfully. We demonstrate that our method is effective and robust on various 3D models.

In this paper, we discuss the singularities of rational space curves. Two methods are provided to compute the singularities of arbitrary degree curves. These methods are a generalization of the paper (Chen, Wang and Liu. Computing singular points of plane rational curves. Journal of Symbolic Computation 43, 92--117, 2008), which are based on the μ-basis of the rational space curve and on random technique. The μ-basis induces a matrix M which contains all the information about the singularities including the parameter values corresponding to the singularities, multiplicities and infinitely near singularities. These information can be obtained by computing the Smith form of the matrix M. We compare our methods with previous approaches such as generalized resultants, and provide some examples to illustrate the effectiveness of our methods.

We present a new shape representation, the implicit PHT-spline, which allows us to efficiently reconstruct surface models from very large sets of points. A PHT-spline is a piece-wise tricubic polynomial over a 3D hierarchical T-mesh, the basis functions of which have good properties such as non-negativity, compact support and partition of unity. Given a point cloud, an implicit PHT-spline surface is constructed by interpolating the Hermitian information at the basis vertices of the T-mesh, and the Hermitian information is obtained by estimating the geometric quantities on the underlying surface of the point cloud. We use the natural hierarchical structure of PHT-splines to reconstruct surfaces adaptively, with simple error-guided local refinements that adapt to the regional geometric details of the target object. Unlike some previous methods that heavily depend on the normal information of the point cloud, our approach only uses it for orientation and is insensitive to the noise of normals. Examples show that our approach can produce high quality reconstruction surfaces very efficiently.

In this paper we propose a new type of splines -biquadratic submesh splines over hierarchical T-meshes. The biquadratic submesh splines are in rational form consisting of some biquadratic B-splines defined over tensor-product submeshes of a hierarchical T-mesh, where every submesh is around a cell in the crossing-vertex relationship graph of the T-mesh. We provide an effective algorithm to locate the valid tensor-product submeshes. A local refinement algorithm is presented and the application of submesh splines in surface fitting is provided.

A trimmed surface is usually represented as a parametric surface with a set of trimming curves. However, many CAD processes and algorithms cannot be applied to trimmed surfaces directly because of the complexity in manipulating trimmed surfaces. Moreover, trimmed surfaces will create gaps between different trimmed surfaces. Thus it is desirable to represent a trimmed surface by a group of regular surfaces, such as NURBS or Bezier surfaces. The present paper provides an algorithm to split a trimmed NURBS surface into several NURBS or Beacutezier surfaces. The surface patches which domains are far away from the trimming curves coincide with the given trimmed NURBS surface and the patches which domains are close to the trimming curves are represented with high degree Beacutezier surface patches (exact) or bi-cubic B-spline surfaces (approximate). The algorithm is simple, efficient and easy to implement. Compared with previous approaches (and), the new algorithm doesn't change the parameterization of most regions and is easy to maintain the continuity. Since our algorithm can keep most of the patches unchanged, most of the surface patches will be C2continuous. Furthermore, the surface patches can be locally merged to be G1in the neighbor of trimming curves which is very difficult for those in and.

The present authors have introduced polynomial splines over T-meshes (PHT-splines) and provided the theories and applications for PHT-splines over hierarchical T-meshes. This paper generalizes PHT-splines to arbitrary topology over general T-meshes with any structures. The general PHT-spline surfaces can be constructed through an unified scheme to interpolate the local geometric information at the basis vertices of the T-mesh. We also discuss the edge insertion and removal algorithms for PHT-splines over general T-meshes. As applications, we present algorithms to construct a spline surface over a T-mesh from a quadrilateral mesh.

Discrete filtering of information over triangulated surfaces has proved very useful in computer graphics applications. This technique is based on diffusion equations and has been extensively applied to image processing, harmonic map regularization and texture generating, etc. [C. L. Bajaj and G. Xu, ACM Trans. Graph., 22 (2003), pp. 4–32], [C. Wu, J. Deng, and F. Chen, IEEE Trans. Vis. Comput. Graph., 14 (2008), pp. 666–679]. However, little has been done on analysis (especially quantitative analysis) of the behavior of these filtering procedures. Since in applications mesh surfaces can be of arbitrary topology and the filtering can be nonlinear and even anisotropic, the analysis of the quantitative behavior is a very difficult issue. In this paper, we first present the discrete linear, nonlinear, and anisotropic filtering schemes via discretizing diffusion equations with appropriately defined differential operators on triangulated surfaces, and then use concepts of discrete scale-spaces to describe these filtering procedures and analyze their properties respectively. Scale-space properties such as existence and uniqueness, continuous dependence on initial value, discrete semigroup property, grey level shift invariance and conservation of total grey level, information reduction (also known as topology simplification), and constant limit behavior have been proved. In particular, the information reduction property is analyzed by eigenvalue and eigenvector analysis of matrices. Different from the direct observation of the local filtering to the diffusion equations and other interpretation methods based on wholly global quantities such as energy and entropy, this viewpoint helps us understand the filtering both globally (information reduction as image components shrink) and locally (how the image component contributes to its shrink rate). With careful consideration of the correspondence between eigenvalues and eigenvectors and their features, differences between linear and nonlinear filtering, as well as between isotropic and anisotropic filtering, are discussed. We also get some stability results of the filtering schemes. Several examples are provided to illustrate the properties.

Complex mesh models of man-made objects often consist of multiple components connected by various types of joints. We propose a joint-aware deformation framework that supports the direct manipulation of an arbitrary mix of rigid and deformable components. First we apply slippable motion analysis to automatically detect multiple types of joint constraints that are implicit in model geometry. For single-component geometry or models with disconnected components, we support user-defined virtual joints. Then we integrate manipulation handle constraints, multiple components, joint constraints, joint limits, and deformation energies into a single volumetric-cell-based space deformation problem. An iterative, parallelized Gauss-Newton solver is used to solve the resulting nonlinear optimization. Interactive deformable manipulation is demonstrated on a variety of geometric models while automatically respecting their multi-component nature and the natural behavior of their joints.

This paper discusses implicitization and parametrization of

In computer graphics, triangular mesh representations of surfaces have become very popular. Compared with parametric and implicit forms of surfaces, triangular mesh surfaces have many advantages, such as easy to render, convenient to store and the ability to model geometric objects with arbitrary topology. In this paper, we are interested in data processing over triangular mesh surfaces through PDEs (partial differential equations). We study several diffusion equations over triangular mesh surfaces, and present corresponding numerical schemes to solve them. Our methods work for triangular mesh surfaces with arbitrary geometry (the angles of each triangle are arbitrary) and topology (open meshes or closed meshes of arbitrary genus). Besides the flexibility, our methods are efficient due to the implicit/semi-implicit time discretization. We finally apply our methods to several filtering and texture applications such as image processing, texture generating and regularization of harmonic maps over triangular mesh surfaces. The results demonstrate the flexibility and effectiveness of our methods.

Computer graphics and computer-aided design communities prefer piecewise spline patches to represent surfaces. But keeping the smoothness between the adjacent patches is a challenging task. In this paper, we present a method for stitching several surface patches, which is a key step in complicated surface modeling, with polynomial splines over hierarchical T-meshes (PHT-spline for short). The method is simple and can be easily applied to complex surface modeling. With the method, spline surfaces can be constructed efficiently and adoptively to fit genus-zero meshes after their spherical parameterization is obtained, where only small sized linear systems of equations are involved.

In the paper we propose a method to determine parameters that appear in algebraic surface blending. By minimizing the surface energy and adding some point restrictions, we can select the free parameters such that a blending surface with reasonable shape is constructed. The method seems to be extensible for other surface blending problems, although we concentrate on algebraic surface blending.

We present a new interpolatory subdivision scheme based on PB-splines (point-based B-splines), over triangular meshes. Using the stencil of the interpolatory /spl radic/3-subdivision scheme, we propose a different refinement strategy by introducing a variable a to each regular vertex (valence = 6). By applying different a (locally or globally), the scheme is suitable for adaptive refinement and can perfectly reach different smoothness conditions (C/sup 0/, C/sup 1/ or C/sup 2/).

The μ-bases of rational curves/surfaces are newly developed tools which play an important role in connecting parametric forms and implicit forms of the rational curves/surfaces. They provide efficient algorithms to implicitize rational curves/surfaces as well as algorithms to compute singular points of rational curves and to reparametrize rational ruled surfaces. In this paper, we present an efficient algorithm to compute the μbasis of a rational curve/surface by using polynomial matrix factorization followed by a technique similar to Gaussian elimination. The algorithm is shown superior than previous algorithms to compute the μ-basis of a rational curve, and it is the only known algorithm that can rigorously compute the μ-basis of a general rational surface. We present some examples to illustrate the algorithm.

In this paper, we present a construction approach to blend the corner of three coordinate planes with G/sup 2/ continuous piecewise algebraic surfaces. For each pair of two coordinate planes, an algebraic surface patch (which is defined in a tetrahedron or a prism) is used to blend the two coordinate planes, and then a center patch is constructed to blend the three algebraic surface patches. The defining region and the shape of the blending surface can be easily adjusted with a few free parameters. Examples are provided to illustrate the blending method. The result can be combined with a potential method to blend three arbitrary algebraic surfaces intersecting transversally at a common point.

This paper provides a physically based model to animate water. A disturbance model is proposed to simulate various kinds of waves. We use a powerful solver called the finite volume method to solve the water fluid equation and give various kinds of disturbance to the solutions according to different disturbance sources such as wind and rain droplets. In this way, we can nicely simulate the movement of waves such as superposition and reflection, and thus easily simulate scenes of a raining pool, windy lake, etc.

In this paper we put forward and study the problem of bounding an interval rational Bezier curve with an interval polynomial Bezier curve. We propose three different methods-hybrid method, perturbation method and linear programming method to solve this problem. Examples are illustrated to compare the three different methods. The empirical results show that the perturbation method and the linear programming method produce much tighter bounds than the hybrid method, though they are computationally several times more expensive.

Given the positions and orientations of several pipe surfaces (cylinders) in 3D space, a scheme for constructing a piecewise algebraic surface to blend the pipe surfaces is presented. The algorithm starts with a suitable partitioning of the 3D space into tetrahedra or prisms in which the algebraic surface patches are defined. Then a smooth piecewise algebraic surface is constructed which meets the pipe surfaces with a certain order of geometric continuity. The proper choice of free parameters is briefly discussed.

This paper presents a radically new approach to the century old problem of computing the implicit equation of a parametric surface. For surfaces without base points, the new method expresses the implicit equation in a determinant which is one fourth the size of the conventional expression based on Dixon's resultant. If base points do exist, previous implicitization methods either fail or become much more complicated, while the new method actually simplifies.