Related papers: Algorithms for geometrical operations with NURBS s…
In this paper, we present the geodesic-like algorithm for the computation of the shortest path between two objects on NURBS surfaces and periodic surfaces. This method can improve the distance problem not only on surfaces but in…
Currently, the area of geometric modeling and the construction of 3D models based on point clouds from laser sensors is actively developing. One of the basic tasks of geometric modeling is the reconstruction of a surface from a cloud of…
Unit disk graphs are intersection graphs of circles of unit radius in the plane. We present simple and provably good heuristics for a number of classical NP-hard optimization problems on unit disk graphs. The problems considered include…
Boolean operations of geometric models is an essential issue in computational geometry. In this paper, we develop a simple and robust approach to perform Boolean operations on closed and open triangulated surfaces. Our method mainly has two…
Geometric rounding of a mesh is the task of approximating its vertex coordinates by floating point numbers while preserving mesh structure. Geometric rounding allows algorithms of computational geometry to interface with numerical…
Maps are arguably one of the most fundamental concepts used to define and operate on manifold surfaces in differentiable geometry. Accordingly, in geometry processing, maps are ubiquitous and are used in many core applications, such as…
Quadratic surfaces gain more and more attention among the Geometric Algebra community and some frameworks were proposed in order to represent, transform, and intersect these quadratic surfaces. As far as the authors know, none of these…
Geometry processing presents a variety of difficult numerical problems, each seeming to require its own tailored solution. This breadth is largely due to the expansive list of geometric primitives, e.g., splines, triangles, and hexahedra,…
In this paper, we study the computation of curvatures at the singular points of algebraic curves and surfaces. The idea is to convert the problem to compute the curvatures of the corresponding regular parametric curves and surfaces, which…
By employing the closest point method, we extend the applicability of minimizing movements to the surface PDE setting. The corresponding approximation methods are created, and their convergence is observed. The numerical methods are then…
In well-studied graph modification problems, adding and deleting vertices and edges are used as graph editing operations. We propose a model for graph modification on geometric intersection graphs called Geometric Graph Edit Distance that…
This draft summarizes some basics about geometric computer vision needed to implement efficient computer vision algorithms for applications that use measurements from at least one digital camera mounted on a moving platform with a special…
Modeling, simulation and visualization of three-dimension complex bodies widely use mathematical model of curves and surfaces. The most important curves and surfaces for these purposes are curves and surfaces in Hermite and Bezier forms,…
We propose a space-efficient algorithm for hidden surface removal that combines one of the fastest previous algorithms for that problem with techniques based on bit manipulation. Such techniques had been successfully used in other settings,…
This article presents original work combining a NURBS-based inverse analysis with both kinematic and constitutive nonlinearities to recover the applied loads and deformations of thin shell structures. The inverse formulation is tackled by…
This paper designs an alogrithm to compute the minimal combinations of finite sets in Euclidean spaces, and applys the algorithm of study the moment maps and geometric invariant stability of hypersurfaces. The classical example of cubic…
Global Route-Planning Algorithms (GRPA) are required to compute paths between several points located on Earth's surface. A geodesic algorithm is employed as an auxiliary tool, increasing the precision of distance calculations. This work…
We describe a simple geometric transformation of triangles which leads to an efficient and effective algorithm to smooth triangle and tetrahedral meshes. Our focus lies on the convergence properties of this algorithm: we prove the…
Manipulation of granular materials such as sand or rice remains an unsolved problem due to challenges such as the difficulty of defining their configuration or modeling the materials and their particles interactions. Current approaches tend…
We introduce an algorithm which can be directly used to feasible and optimum search in linear programming. Starting from an initial point the algorithm iteratively moves a point in a direction to resolve the violated constraints. At the…