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We consider the problem of computing the topology and describing the geometry of a parametric curve in $\mathbb{R}^n$. We present an algorithm, PTOPO, that constructs an abstract graph that is isotopic to the curve in the embedding space.…
In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…
This paper presents an end-to-end framework for reconstructing 3D parametric curves directly from multi-view edge maps. Contrasting with existing two-stage methods that follow a sequential ``edge point cloud reconstruction and parametric…
This article represents the computational model for spacial addresation of the sensors in the dynamically changing real-time internet of things system. The model bases on the Voronoi diagrams as a basic data structure. Problem - the correct…
Reconstructing 2D curves from sample points has long been a critical challenge in computer graphics, finding essential applications in vector graphics. The design and editing of curves on surfaces has only recently begun to receive…
Cellular structures manifest their outstanding mechanical properties in many biological systems. One key challenge for designing and optimizing these geometrically complicated structures lies in devising an effective geometric…
Offset surfaces, defined as the Minkowski sum of a base surface and a rolling ball, play a crucial role in geometry processing, with applications ranging from coverage motion planning to brush modeling. While considerable progress has been…
Representing a scanned map of the real environment as a topological structure is an important research topic in robotics. Since topological representations of maps save a huge amount of map storage space and online computing time, they are…
We explore offsets of Cayley ovals, by networking with different kinds of software. Using their specific abilities, algebraic, geometric, dynamic, we conjecture interesting properties of the offsets. For a given progenitor (the given plane…
Deep learning has been used as a powerful tool for various tasks in computer vision, such as image segmentation, object recognition and data generation. A key part of end-to-end training is designing the appropriate encoder to extract…
Reconstruction of geometry based on different input modes, such as images or point clouds, has been instrumental in the development of computer aided design and computer graphics. Optimal implementations of these applications have…
We present some algorithms that provide useful topological information about curves in surfaces. One of the main algorithms computes the geometric intersection number of two properly embedded 1-manifolds $C_1$ and $C_2$ in a compact…
We consider the offset-deconstruction problem: Given a polygonal shape Q with n vertices, can it be expressed, up to a tolerance \eps in Hausdorff distance, as the Minkowski sum of another polygonal shape P with a disk of fixed radius? If…
Marching surfaces is a method for isosurface extraction and approximation based on a $G^1$ multi-sided patch interpolation scheme. Given a 3D grid of scalar values, an underlying curve network is formed using second order information and…
We introduce a novel representation and optimization framework for discrete geodesics on triangle meshes that reduces artifacts of linear methods on uneven and coarse discretizations. Our method computes squared geodesic distances from…
Curves play a fundamental role across computer graphics, physical simulation, and mathematical visualization, yet most tools for curve design do nothing to prevent crossings or self-intersections. This paper develops efficient algorithms…
High-efficient direct numerical methods are currently in demand for optimization procedures in the fields of both conventional diffractive and metasurface optics. With a view of extending the scope of application of the previously proposed…
We introduce a new approach for identifying and characterizing voids within two-dimensional (2D) point distributions through the integration of Delaunay triangulation and Voronoi diagrams, combined with a Minimal Distance Scoring algorithm.…
The advancements in neural rendering have increased the need for techniques that enable intuitive editing of 3D objects represented as neural implicit surfaces. This paper introduces a novel neural algorithm for parameterizing neural…
The point inclusion tests for polygons, in other words the point-in-polygon (PIP) algorithms, are fundamental tools for many scientific fields related to computational geometry, and they have been studied for a long time. The PIP algorithms…