Publications related to Global radii of curvature, and the biarc approximation of space curves

On the Richter-Thomassen Conjecture about Pairwise Intersecting Closed Curves

A long-standing conjecture of Richter and Thomassen states that the total number of intersection points between any n simple closed Jordan curves in the plane, so that any pair of them intersect and no three curves pass through the same point, is at least ...

Cambridge Univ Press2016

An Inner-Product Calculus for Periodic Functions and Curves

Michaël Unser, Daniel Andreas Schmitter, Anaïs Laure Marie-Thérèse Badoual

Our motivation is the design of efficient algorithms to process closed curves represented by basis functions or wavelets. To that end, we introduce an inner-product calculus to evaluate correlations and

L _{ 2 }

distances between such curves. In partic ...

2016

Medial axis transformation as a solid modeling representation method for computer aided design software

Paul Xirouchakis, Mihai-Bogdan Lazar, Ian Anthony Stroud, Florian Barras, Guillaume Goualard

A method for achieving a representation of an object within a data structure for a Computer Aided Design system employing a Medial Axis Transformation (MAT), the representation of the object comprising a set of adjacent bounded surface elements called MAT ...

2016

A distance measure for colored curves

Seyed Mohsen Moosavi Dezfooli

In some computer vision applications, matching between shapes and colors are required. There are lots of similarity measures for shapes, especially curves, but as far as we know there are not many that deal with shapes and colors at the same time. In this ...

2015

Similarity-Based Shape Priors for 2D Spline Snakes

Michaël Unser, Daniel Andreas Schmitter

We present a new formulation of a shape space containing all continuously defined 2D spline curves up to a similarity transform of a reference shape. We are able to measure a distance between an arbitrary curve and the shape space itself. Our contribution ...

IEEE2015

Untangling the Mechanics and Topology in the Frictional Response of Long Overhand Elastic Knots

Pedro Miguel Nunes Pereira de Almeida Reis

We combine experiments and theory to study the mechanics of overhand knots in slender elastic rods under tension. The equilibrium shape of the knot is governed by an interplay between topology, friction, and bending. We use precision model experiments to q ...

American Physical Society2015

Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope

Maria Colombo

In this paper we make a survey of some recent developments of the theory of Sobolev spaces W-1,W-q (X, d, m), 1 < q < infinity, in metric measure spaces (X, d, m). In the final part of the paper we provide a new proof of the reflexivity of the Sobolev spac ...

2015

Well-Posedness, Regularity, and Convergence Analysis of the Finite Element Approximation of a Generalized Robin Boundary Value Problem

Alfio Quarteroni, Luca Dede', Claudia Maria Colciago

In this paper, we propose the mathematical and finite element analysis of a second-order partial differential equation endowed with a generalized Robin boundary condition which involves the Laplace--Beltrami operator by introducing a function space $H^1(\O ...

Society for Industrial and Applied Mathematics2015

Dissipative Boundary Conditions for Nonlinear 1-D Hyperbolic Systems: Sharp Conditions Through an Approach via Time-Delay Systems

Hoài-Minh Nguyên

We analyze dissipative boundary conditions for nonlinear hyperbolic systems in one space dimension. We show that a known sufficient condition for exponential stability with respect to the H-2-norm is not sufficient for the exponential stability with respec ...

Society for Industrial and Applied Mathematics2015

Global estimates for quasilinear parabolic equations on Reifenberg flat domains and its applications to Riccati type parabolic equations with distributional data

Quoc Hung Nguyen

In this paper, we prove global weighted Lorentz and Lorentz-Morrey estimates for gradients of solutions to the quasilinear parabolic equations: in a bounded domain , under minimal regularity assumptions on the boundary of domain and on nonlinearity A. Then ...

Springer Heidelberg2015

Global radii of curvature, and the biarc approximation of space curves

Graph Chatbot

Chat with Graph Search

On the Richter-Thomassen Conjecture about Pairwise Intersecting Closed Curves

An Inner-Product Calculus for Periodic Functions and Curves

Medial axis transformation as a solid modeling representation method for computer aided design software

A distance measure for colored curves

Similarity-Based Shape Priors for 2D Spline Snakes

Untangling the Mechanics and Topology in the Frictional Response of Long Overhand Elastic Knots

Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope

Well-Posedness, Regularity, and Convergence Analysis of the Finite Element Approximation of a Generalized Robin Boundary Value Problem

Dissipative Boundary Conditions for Nonlinear 1-D Hyperbolic Systems: Sharp Conditions Through an Approach via Time-Delay Systems

Global estimates for quasilinear parabolic equations on Reifenberg flat domains and its applications to Riccati type parabolic equations with distributional data

Medial axis transformation as a solid modeling representation method for computer aided design software

Well-Posedness, Regularity, and Convergence Analysis of the Finite Element Approximation of a Generalized Robin Boundary Value Problem

Dissipative Boundary Conditions for Nonlinear 1-D Hyperbolic Systems: Sharp Conditions Through an Approach via Time-Delay Systems

Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope

A distance measure for colored curves

Global estimates for quasilinear parabolic equations on Reifenberg flat domains and its applications to Riccati type parabolic equations with distributional data

Similarity-Based Shape Priors for 2D Spline Snakes

On the Richter-Thomassen Conjecture about Pairwise Intersecting Closed Curves

An Inner-Product Calculus for Periodic Functions and Curves

Untangling the Mechanics and Topology in the Frictional Response of Long Overhand Elastic Knots