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Optimal Area Polygonalization

Course project for INF562 - Computational Geometry from Theory to Applications (2019-2020), École Polytechnique

Martín Cepeda & Cédric Javault

Overview

Given a point cloud S of n 2D vertices, we implement two greedy approaches in order to approximate the MINimum Area simple Polygonalization and MAXimum Area simple Polygonalization of S (MINAP and MAXAP respectively), an NP-hard problem (Fekete, 2000). These two iterative approaches are based in the insertion of minimum area triangles at each step.

This problem was given at the CG:SHOP 2019 Competition a year earlier.

Requeriments

  • Java 1.8
  • core.jar (Processing 1.5.1 library, for 2D rendering of polygons and point clouds)
  • TC.jar (for dealing with I/O operations on text files, developed for INF361) doc
  • Jcg.jar (Java library for computational geometry, developed for INF562 by Luca Castelli Aleardi) doc

Usage

AreaOptimizer input_file_path saves minumum/maximum area polygon found

AreaOptimizer input_file_path solution_file_path shows saved solution and score S=areaPolygon/areaConvexHull

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Course project for INF562 - Computational Geometry from Theory to Applications (2019-2020), École Polytechnique

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