3 papers
cs.GR2025
Analyzing Time-Varying Scalar Fields using Piecewise-Linear Morse-Cerf Theory
Amritendu Dhar, Apratim Chakraborty, Vijay Natarajan
Morse-Cerf theory considers a one-parameter family of smooth functions defined on a manifold and studies the evolution of their critical points with the parameter. This paper prese…
cs.CG2024
Geometric Localization of Homology Cycles
Amritendu Dhar, Vijay Natarajan, Abhishek Rathod
Computing an optimal cycle in a given homology class, also referred to as the homology localization problem, is known to be an NP-hard problem in general. Furthermore, there is cur…
cs.CG2021
Fast Algorithms for Minimum Homology Basis
Amritendu Dhar, Vijay Natarajan, Abhishek Rathod
We study the problem of finding a minimum homology basis, that is, a lightest set of cycles that generates the -dimensional homology classes with coefficients in…