5 papers
Compression Maps Between Polytopes
José Ayala, David Kirszenblat, J. Hyam Rubinstein
A shape of a combinatorial polytope is a convex embedding into Euclidean space. We provide necessary and sufficient conditions for a piecewise linear map between two shapes of the…
A Gradient Descent Method for The Dubins Traveling Salesman Problem
David Kirszenblat, José Ayala, J. Hyam Rubinstein
We propose a combination of a bounding procedure and gradient descent method for solving the Dubins traveling salesman problem, that is, the problem of finding a shortest curvature…
Immersed flat ribbon knots
José Ayala, David Kirszenblat, J. Hyam Rubinstein
We study the minimum ribbonlength for immersed planar ribbon knots and links. Our approach is to embed the space of such knots and links into a larger more tractable space of disk…
Minimal curvature-constrained networks
David Kirszenblat, Kashyapa Sirinanda, Marcus Brazil +3
This paper introduces an exact algorithm for the construction of a shortest curvature-constrained network interconnecting a given set of directed points in the plane and an iterati…
A geometric approach to shortest bounded curvature paths
José Ayala, David Kirszenblat, J. Hyam Rubinstein
Consider two elements in the tangent bundle of the Euclidean plane . In this work we address the problem of characterizing the paths of bounded curva…