TRIANGULATION ALGORITHMS USING A SWEEPING STRATEGY

Osnovni cilj doktorske naloge je razviti lasten postopek omejene Delaunayeve triangulacije z metodo prebiranja, ki bo vsaj enako učinkovit kot do sedaj razviti postopki in pokazati, da je s prebiranjem možno rešiti tudi veliko težjo nalogo rekonstrukcije površja v 3D. V nalogi najprej definiramo klasično in omejeno Delaunayevo triangulacijo, opišemo obstoječe postopke, nato pa se osredotočimo na lasten postopek omejene Delaunayeve triangulacije. Podrobneje opišemo njegovo delovanje in razširitve, ki vodijo k učinkovitemu algoritmu omejene Delaunayeve triangulacije. Temelj algoritma je pomikanje napredujoče fronte s prebirno premico in razvoj hevristik, ki poskrbijo za uspešno vodenje napredujoče fronte in hkrati minimizirajo število menjav trikotnikov. Nato preidemo na problem rekonstrukcije površja, kjer podamo pregled sorodnih raziskav. Dva postopka podrobneje opišemo, temu pa sledi opis lastnega postopka rekonstrukcije površja s prebiranjem. Algoritem temelji na širitvi napredujočih front s pomikanjem prebirne ravnine in hevristikah za uspešno upravljanje s frontami. Na koncu analiziramo oba razvita algoritma in potrdimo zastavljeni hipotezi.The main goal of our disertation is implementation of a new constrained Delaunay triangulation algorithm based on the sweeping strategy, which is at least as efficient as the existing solutions. Another aim is to show that using the same algorithmic paradigm in three dimensions can solve a much harder problem, namely a surface reconstruction from a point cloud. We start by introducing the sweeping strategy. After that, we define Delaunay and constrained Delaunay triangulation, which is followed by a brief survey of the existing algorithms. Then we describe our own sweep-line algorithm in detail, where constrained triangulation is built by propagating the advancing front using heuristics. The apployment of heuristcs and constraining edges insertion at the same time with their end-vertices importanly increases the speed of the algorithm. In the second part of our disertation we introduce the problem of surface reconstruction and make an overview of the previous work. We describe our own implementation based on the sweeping strategy, where the surface is built by propagating the advancing fronts with the sweep-plane. We describe heuristics for managing the fronts in detail. Finally, we summarize our contributions and confirm the proposed theses