• Home
• Evgeny Lipovetsky

# Evgeny Lipovetsky--

Ph.D.
3D meshes smoothing and simplification

8
Publications
1,154
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
21
Citations

## Publications

Publications (8)
Article
Full-text available
Subdivision is a well-known and established method for generating smooth curves and surfaces from discrete data by repeated refinements. The typical input for such a process is a mesh of vertices. In this work we propose to refine 2D data consisting of vertices of a polygon and a normal at each vertex. Our core refinement procedure is based on a ci...
Article
Full-text available
This article continues the investigation started in [9] on subdivision schemes refining 2D point-normal pairs, obtained by modifying linear subdivision schemes using the circle average. While in [9] the convergence of the Modified Lane-Riesenfeld algorithm and the Modified 4-Point schemes is proved, here we show that the curves generated by these t...
Article
Full-text available
In a previous paper (Lipovetsky and Dyn in Comput Aided Geom Des 48:36–48, 2016), we introduced a weighted binary average of two 2D point-normal pairs, termed circle average, and investigated subdivision schemes based on it. These schemes refine point-normal pairs in 2D and converge to limit curves and limit normals. Such a scheme has the disadvant...
Preprint
Full-text available
In this paper we extend the 2D circle average of [11] to a 3D binary average of point-normal pairs, and study its properties. We modify classical surface-generating linear subdivision schemes with this average obtaining surface-generating schemes refining point-normal pairs. The modified schemes give the possibility to generate more geometries by e...
Article
In this paper we extend the 2D circle average of Lipovetsky and Dyn (2016) to a 3D binary average of point-normal pairs, and study its properties. We modify classical surface-gener-ating linear subdivision schemes with this average obtaining surface-generating schemes refining point-normal pairs. The modified schemes give the possibility to generat...
Preprint
In a previous paper [11] we introduced a weighted binary average of two 2D point-normal pairs, termed circle average, and investigated subdivision schemes based on it. These schemes refine point-normal pairs in 2D, and converge to limit curves and limit normals. Such a scheme has the disadvantage that the limit normals are not the normals of the li...
Article
Full-text available
The metric average is a binary operation between sets in Rn which is used in the approximation of set-valued functions. We introduce an algorithm that applies tools of computational geometry to the computation of the metric average of 2D sets with piecewise linear boundaries.
Article
Full-text available
Motivated by the method for the reconstruction of 3D objects from a set of parallel cross sections, based on the binary operation between 2D sets termed “metric average”, we developed an algorithm for the computation of the metric average between two intersecting convex polygons in 2D. For two 1D sets there is an algorithm for the computation of th...

## Projects

Projects (2)
Project
The goal is to design subdivision schemes generating surfaces by repeated refinements of 3D point-normal pairs, using Circle Average as the core procedure. See the following demo-videos: https://youtu.be/Mpj_1PsQ2Ug https://youtu.be/Hs1aTo0Gyn0