Iskanje ravninskih regij

Ribič, Uroš (author), Fijavž, Gašper (mentor), Cabello Justo, Sergio (comentor)

Preiskovali smo problem iskanja ravnin na trianguliranem terenu. Za množico točk v prostoru zgradimo Delaunayjevo triangulacijo in z dvema različnima metodama poiščemo ravnino na terenu. V prvi metodi uporabimo algoritem za iskanje največjega konveksnega poligona. Algoritem se dobro obnese na manjši množici točk, na večji množici točk, pa zaradi svoje kvadratične časovne zahtevnosti ne pride v poštev. V drugi metodi uporabimo aproksimacijski algoritem. Ta se bolje obnese tudi na večji množici podatkov, kot tudi na realnih geografskih podatkih, ki jih lahko dobimo na spletnem portalu LIDAR. Implementiran vmesnik nam pomaga, da na enostaven način testiramo obe metodi in vizualiziramo rezultate.

• Language: Slovenian
• Keywords: aproksimacijski algoritmi, ravnina, relief pokrajine, iskanje regij
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FRI - Faculty of Computer and Information Science
• Year: 2020
• PID: 20.500.12556/RUL-122368
• COBISS.SI-ID: 42017795
• Publication date in RUL: 04.12.2020

RIBIČ, Uroš, 2020, Iskanje ravninskih regij [online]. Master’s thesis. [Accessed 8 October 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=122368

Secondary language

• Language: English
• Title: Finding planar regions

Abstract

We studied the problem of finding planar regions in a triangulated terrain. For a set of points in 3-space, we construct the Delaunay triangulation. Then, with two different methods we look for a region which is flat. The first method uses an algorithm to find the largest convex polygon. The algorithm works well on smaller sets of points, but on larger sets of points it performs poorly due to its quadratic time complexity. In the second method, we use an approximation algorithm. It performs better on larger data sets, as well as on real geographical data, which can be obtained on the web portal LIDAR. The implemented interface helps us to test both methods in an easy way and visualize the results.

• Keywords: approximation algorithms, planarity, terrain, finding regions