Coronary artery segmentation in X-ray angiography is crucial for cardiovascular diagnosis and treatment planning, yet remains challenging due to the inherently low signal-to-noise ratio (SNR) and low contrast of the images, which degrade obscure vascular structures and fine details. Although the Segment Anything Model (SAM) has demonstrated strong potential in various vision tasks, its capabilities for coronary artery segmentation in X-ray angiography have yet to be fully explored. To overcome these challenges, we propose CoroSAM, a novel promptfree SAM fine-tuning framework tailored for coronary artery segmentation in X-ray angiography. CoroSAM introduces two key innovations: (1) Gated Spatial-Frequency Adapter (GSFA) designed to fine-tune SAM's image encoder by dynamically integrating both spatial- and frequency-domain information to better capture vascular structures under noisy conditions; and (2) Orientation-Guided Adapter (OGA), the first to our knowledge to incorporate orientation maps for refining structural details in SAM predictions, enhancing structural awareness and improving robustness under low-contrast conditions. Extensive experiments on four public datasets demonstrate that CoroSAM consistently outperforms state-of-the-art methods. The code is available at https://github.com/HITZhengGW/CoroSAM

Tool shape selection and path planning are critical for 5-axis CNC flank milling of freeform surfaces, typically addressed using optimization algorithms where initialization plays a pivotal role. Existing approaches rely on user-specified initialization of either tool shapes or motion paths, often resulting in suboptimal outcomes. This paper introduces a fully automated method that simultaneously initializes both tool shapes and motion paths, achieving high-precision machining with efficient surface coverage. Our approach explores a solution space of potential tool axes represented by line segments near the design surface. To efficiently manage the vast number of lines, we integrate space voxelization with a discrete distance field for effective line sampling. A graph-based algorithm generates feasible line sequences for motion paths, while path optimization refines a single tool shape across multiple paths simultaneously. The method identifies optimal tool shapes of various sizes, each paired with corresponding motion paths for multi-pass machining. Experiments on industrial benchmark models and freeform surfaces validate the effectiveness and practicality of the proposed approach.

We introduce a progressive and iterative method for B-spline curve and surface approximation, incorporating parameter correction based on the Newton iterative method. While parameter corrections have been used in existing Geometric Approximation (GA) methods to enhance approximation quality, they suffer from low computational efficiency. Our approach unifies control point updates and parameter corrections in a progressive and iterative procedure, employing a one-step strategy for parameter correction. We provide a theoretical proof of convergence for the algorithm, demonstrating its superior computational efficiency compared to current GA methods. Furthermore, the provided convergence proof offers a methodology for proving the convergence of existing GA methods with location parameter correction.

Voronoi diagrams on triangulated surfaces based on the geodesic metric play a key role in many applications of computer graphics. Previous methods of constructing such Voronoi diagrams generally depended on having an exact geodesic metric. However, exact geodesic computation is time-consuming and has high memory usage, limiting wider application of geodesic Voronoi diagrams (GVDs). In order to overcome this issue, instead of using exact methods, we reformulate a graph method based on Steiner point insertion, as an effective way to obtain geodesic distances. Further, since a bisector comprises hyperbolic and line segments, we utilize Apollonius diagrams to encode complicated structures, enabling Voronoi diagrams to encode a medial-axis surface for a dense set of boundary samples. Based on these strategies, we present an approximation algorithm for efficient Voronoi diagram construction on triangulated surfaces. We also suggest a measure for evaluating similarity of our results to the exact GVD. Although our GVD results are constructed using approximate geodesic distances, we can get GVD results similar to exact results by inserting Steiner points on triangle edges. Experimental results on many 3D models indicate the improved speed and memory requirements compared to previous leading methods.

Abstract Freeform surfaces whose principal curvature line network is regularly distributed, are essential to many real applications like CAD modeling, architecture design, and industrial fabrication. However, most designed surfaces do not hold this nice property because it is hard to enforce such constraints in the design process. In this paper, we present a novel method for surface fairing which takes a regular distribution of the principal curvature line network on a surface as an objective. Our method first removes the high‐frequency signals from the curvature tensor field of an input freeform surface by a novel rolling guidance tensor filter, which results in a more regular and smooth curvature tensor field, then deforms the input surface to match the smoothed field as much as possible. As an application, we solve the problem of approximating freeform surfaces with regular principal curvature line networks, discretized by quadrilateral meshes. By introducing the circular or conical conditions on the quadrilateral mesh to guarantee the existence of discrete principal curvature line networks, and minimizing the approximate error to the original surface and improving the fairness of the quad mesh, we obtain a regular discrete principal curvature line network that approximates the original surface. We evaluate the efficacy of our method on various freeform surfaces and demonstrate the superiority of the rolling guidance tensor filter over other tensor smoothing techniques. We also utilize our method to generate high‐quality circular/conical meshes for architecture design and cyclide spline surfaces for CAD modeling.

We present a new approach to geometric modeling with developable surfaces and the design of curved-creased origami. We represent developables as splines and express the nonlinear conditions relating to developability and curved folds as quadratic equations. This allows us to utilize a constraint solver, which may be described as energy-guided projection onto the constraint manifold, and which is fast enough for interactive modeling. Further, a combined primal-dual surface representation enables us to robustly and quickly solve approximation problems.

Abstract We present a heuristic approach to tetrahedral mesh generation for implicit closed surfaces. It consists of a surface sampling step and a volume sampling step that both work in a unified optimization framework. First, high‐quality isotropic samplings as well as a triangular mesh on the surface are generated. Then uniform volume samplings are determined by optimizing the point distribution inside the closed surface domain. Finally, the tetrahedral mesh is easily obtained by constrained Delaunay triangulation. Experimental results show that the new method can generate ideal tetrahedral meshes for closed implicit surfaces efficiently that are Delaunay based. Our method has the advantage of high efficiency and nice performance at surface boundaries. Copyright © 2015 John Wiley & Sons, Ltd.

We present an automatic method for fitting multiple B-spline curves to unorganized planar points. The method works on point clouds which have complicated topological structures and a single curve is insufficient for fitting the shape. A divide-and-merge algorithm is developed for dividing the unorganized data points into several groups while each group represents a smooth curve. Each point group is then fitted with a B-spline curve by the SDM method. Our algorithm also sets up automatically the control polygon of initial B-spline curves. Experiments demonstrate the capability of the presented algorithm in accurate reconstruction of topological structures of point clouds.

The most important guiding principle in computational methods for freeform architecture is the balance between cost efficiency on the one hand, and adherence to the design intent on the other. Key issues are the simplicity of supporting and connecting elements as well as repetition of costly parts. This paper proposes so-called circular arc structures as a means to faithfully realize freeform designs without giving up smooth appearance. In contrast to non-smooth meshes with straight edges where geometric complexity is concentrated in the nodes, we stay with smooth surfaces and rather distribute complexity in a uniform way by allowing edges in the shape of circular arcs. We are able to achieve the simplest possible shape of nodes without interfering with known panel optimization algorithms. We study remarkable special cases of circular arc structures which possess simple supporting elements or repetitive edges, we present the first global approximation method for principal patches, and we show an extension to volumetric structures for truly three-dimensional designs.

Motivated by applications in architecture and manufacturing, we discuss the problem of covering a freeform surface by single curved panels. This leads to the new concept of semi-discrete surface representation, which constitutes a link between smooth and discrete surfaces. The basic entity we are working with is the developable strip model. It is the semi-discrete equivalent of a quad mesh with planar faces, or a conjugate parametrization of a smooth surface. We present a B-spline based optimization framework for efficient computing with D-strip models. In particular we study conical and circular models, which semi-discretize the network of principal curvature lines, and which enjoy elegant geometric properties. Together with geodesic models and cylindrical models they offer a rich source of solutions for surface panelization problems.

Abstract We present a novel and effective method for modeling a developable surface to simulate paper bending in interactive and animation applications. The method exploits the representation of a developable surface as the envelope of rectifying planes of a curve in 3D, which is therefore necessarily a geodesic on the surface. We manipulate the geodesic to provide intuitive shape control for modeling paper bending. Our method ensures a natural continuous isometric deformation from a piece of bent paper to its flat state without any stretching. Test examples show that the new scheme is fast, accurate, and easy to use, thus providing an effective approach to interactive paper bending. We also show how to handle non‐convex piecewise smooth developable surfaces.