https://www.zhuzhugst.com/ 2026-04-22T12:02:37+00:00 https://www.zhuzhugst.com/ https://www.zhuzhugst.com/lib/exe/fetch.php?media=logo.png text/html 2025-09-25T03:50:23+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.zhuzhugst.com/doku.php?id=%E7%9B%B4%E9%AA%A8%E6%9E%B6%E7%9A%84%E7%A0%94%E7%A9%B6:introduction:preliminaries_and_definitions:roof_and_terrain_model&rev=1758772223&do=diff Aichholzer et al. [AAAG95] presented an interpretation for the straight skeleton of simple polygons, which was extended to planar straight-line graphs by Aichholzer and Aurenhammer [AA96]. It turns out that this interpretation is a versatile tool in proofs of geometric properties of the straight skeleton. Further, it leads to one of the prominent applications of straight skeletons: roof construction and terrain modeling, see Section 1.3.2. The basic idea is to embed the wavefront propagation pro… text/html 2025-09-25T04:10:06+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.zhuzhugst.com/doku.php?id=%E7%9B%B4%E9%AA%A8%E6%9E%B6%E7%9A%84%E7%A0%94%E7%A9%B6:introduction:preliminaries_and_definitions:the_motorcycle_graph&rev=1758773406&do=diff A straight-forward approach to computing the straight skeleton is through the simulation of the propagating wavefront. While edge events can be handled in a relatively efficient way the opposite holds for split events, see Section 1.4.2.1. It turns out to be non-trivial to efficiently determine which reflex wavefront vertex crashes into which wavefront edge. Let us consider for a moment only the simultaneous movement of the reflex wavefront vertices. In order to compute the straight skeleton it is imp… text/html 2025-09-25T03:30:55+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.zhuzhugst.com/doku.php?id=%E7%9B%B4%E9%AA%A8%E6%9E%B6%E7%9A%84%E7%A0%94%E7%A9%B6:introduction:preliminaries_and_definitions:the_straight_skeleton_of_a_planar_straight-line_graph&rev=1758771055&do=diff Aichholzer and Aurenhammer [AA96] generalized the concept of straight skeletons to planar straight-line graphs.11 Assume we are given a planar straight-line graph $G$ with no isolated12 vertices. The basic idea to define the straight skeleton S (G) of $G$$e$$G$$e$$e$$G$$v$$v$$v$$v$$G$$G$$e$$G$$e$$e$$G$$v$$v$$v$$v$$v$$G$$k$$v$$v$$G$$v$$k$$v$$v$$G$$G$$G$$e$$t$$G$$G$$e$$G$$G$$G$$G$$G$$v$$ϵ$$ϵ$$ϵ$$v$$ϵ$$G$$G$$G$$v$$ϵ$$ϵ$$ϵ$$v$$ϵ$$v$$e$$v$$e$$ϵ$$ϵ$$v$$e$$v$$e$$ϵ$$ϵ$ text/html 2025-09-25T03:15:49+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.zhuzhugst.com/doku.php?id=%E7%9B%B4%E9%AA%A8%E6%9E%B6%E7%9A%84%E7%A0%94%E7%A9%B6:introduction:preliminaries_and_definitions:the_straight_skeleton_of_a_simple_polygon&rev=1758770149&do=diff Aichholzer et al. [AAAG95] introduced the straight skeleton of simple polygons $P$ by considering a so-called wavefront-propagation process. Each edge $e$ of $P$ sends out a wavefront which moves inwards at unit speed and is parallel to $e$. The wavefront of $P$ can be thought to shrink in a self-parallel manner such that sharp corners at reflex6 vertices of $P$$P$$P$$P$$e$$e$$P$$P$$P$$P$$e$$P$$e$$S (P)$$P$$P$$S (P)$$P$$n$$P$$n$$P$$P$$P$$P$$n$$e$$P$$P$$n$$P$$n$$e$$P$$v$$u$$v$$e$$u$$v$$e$$u$$v$$u$…