Smooth surfaces from an arbitrary topological control grid have been widely studied, which are mostly generalized from splines with uniform knot intervals. These methods fail to work well on extraordinary points (EPs) whose edges have varying knot intervals. This article presents a patching solution for arbitrary topological 2-manifold control grid with non-uniform knots that defines one bi-cubic Bézier patch per control grid face except those faces with EPs. Experimental results demonstrate that the new solution can improve the surface quality for non-uniform parameterization. Applications in surface reconstruction, arbitrary sharp features on the complex surface and tool path planning for the new surface representation are also provided in the paper.

Reconstructing a spline surface from a given arbitrary topological triangle mesh is a fundamental and challenging problem in computer-aided design and engineering. This article introduces a novel surface fitting method utilizing G-NURBS capable of handling control meshes with arbitrary topologies. This method employs adaptive control point adjustment, guided by the geometric attributes of the input model, ensuring precise representation of sharp features such as edges and corners. Two primary strategies are employed: A parameter correspondence approach designed for sharp features and a control mesh iterative refinement technique that incorporates geometrical feature information. The proposed method has been tested and evaluated on various CAD models to demonstrate its effectiveness. This method can achieve higher fitting accuracy while faithfully preserving the geometrical features with fewer control points.

We present a novel implicit neural representation to reconstruct CAD models from point clouds with high quality. Our method first extracts edge points from input points by an edge detection network and then recovers implicit surfaces while preserving the sharp features of ground-truth models. The edge detection network uses a U-Net structure for feature encoding, and the attention module is introduced to improve the accuracy in the CAD models. This detection network is light weighted and runs fast. Afterward, we propose an MLP-based network to train an implicit representation from input points with its extracted edge points. A two-stage training process is proposed, and loss functions are designed for each stage to ensure that the sharp features of the input points are learned while the surface details are fitted. Comparing our method with other SOTA methods in the ABC dataset, our method is significantly superior to the existing nonlearning and learning 3D reconstruction methods in terms of surface approximation quality and sharp feature preservation. Moreover, we can gain spline representations from learned shapes for CAM as the application of our method.

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.

This paper develops new refinement rules for non-uniform Catmull-Clark surfaces that produce G 1 extraordinary points whose blending functions have a single local maximum. The method consists of designing an "eigen polyhedron" in R 2 for each extraordinary point, and formulating refinement rules for which refinement of the eigen polyhedron reduces to a scale and translation. These refinement rules, when applied to a non-uniform Catmull-Clark control mesh in R 3 , yield a G 1 extraordinary point.

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.

This paper addresses the long-standing problem of the unavoidable gaps that arise when expressing the intersection of two NURBS surfaces using conventional trimmed-NURBS representation. The solution converts each trimmed NURBS into an untrimmed T-Spline, and then merges the untrimmed T-Splines into a single, watertight model. The solution enables watertight fillets of NURBS models, as well as arbitrary feature curves that do not have to follow iso-parameter curves. The resulting T-Spline representation can be exported without error as a collection of NURBS surfaces.

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.