Antony, JomsReghunath, MinuMuthuganapathy, RamanathanChen, RenjieRitschel, TobiasWhiting, Emily2024-10-132024-10-132024978-3-03868-250-9https://doi.org/10.2312/pg.20241329https://diglib.eg.org/handle/10.2312/pg20241329Given a planar point set S ∈ R2 (where S = {v1, . . . , vn}) sampled from an unknown curve Σ, the goal is to obtain a piece-wise linear reconstruction the curve from S that best approximates Σ. In this work, we propose a simple and intuitive Delaunay triangulation(DT)-based algorithm for curve reconstruction. We start by constructing a Delaunay Triangulation (DT) of the input point set. Next, we identify the set of edges, ENp in the natural neighborhood of each point p in the DT. From the set of edges in ENp, we retain the first two shorter edges connected to each point. To take care of open curves, one of the retained edges has to be removed based on a parameter δ. Here, δ is a parameter used to eliminate the longer edge based on the allowable ratio between the maximum and minimum edge lengths. Our algorithm inherently handles self-intersections, multiple components, sharp corners, and different levels of Gaussian noise, all without requiring any parameters, pre-processing, or post-processing.Attribution 4.0 International LicenseCCS Concepts: Computing methodologies → Shape modelingComputing methodologies → Shape modeling10.2312/pg.202413292 pages