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Line 511: − + − Aus (1) und (2) ergibt sich, dass die Oberfläche, die durch <math>C</math> beschrieben wird, keine Löcher enthalten darf. Mit den weiteren Bedingungen (4) und (5) ergibt sich, dass das Innere des durch <math>C</math> beschriebenen Festkörpers zusammenhängend sein muss. + − +
Modeling Guide for 3D Objects - Part 1: Basics (Rules for Validating GML Geometries in CityGML) (view source)
Revision as of 14:52, 11 November 2013
, 14:52, 11 November 2013→gml:Solid
# All polygons in <math>C</math> are oriented such that the normal vector of each polygon points to the outside of the solid.
# All polygons in <math>C</math> are oriented such that the normal vector of each polygon points to the outside of the solid.
# All polygons in <math>C</math> are connected, that is the dual graph of <math>C</math> has a path containing all nodes. The dual graph G<sub>C</sub> =(V<sub>C</sub>, E<sub>C</sub>) of <math>C</math> consists of a set V<sub>C</sub> of nodes and a set E<sub>C</sub> of edges. Every node v of V<sub>C</sub> represents exactly one polygon of <math>C</math>. An edge shared by two polygons <math>S_k</math> and <math>S_l</math> of <math>C</math> is represented by an edge <math>e=(v_{s_k},v_{s_l})</math> in E<sub>C</sub>.
# All polygons in <math>C</math> are connected, that is the dual graph of <math>C</math> has a path containing all nodes. The dual graph G<sub>C</sub> =(V<sub>C</sub>, E<sub>C</sub>) of <math>C</math> consists of a set V<sub>C</sub> of nodes and a set E<sub>C</sub> of edges. Every node v of V<sub>C</sub> represents exactly one polygon of <math>C</math>. An edge shared by two polygons <math>S_k</math> and <math>S_l</math> of <math>C</math> is represented by an edge <math>e=(v_{s_k},v_{s_l})</math> in E<sub>C</sub>.
# Für jeden Punkt <math>P</math>, der in einem linearen Ring eines Polygons aus <math>C </math> vorkommt, gilt: Der Graph <math>G_P =(V_P, E_P)</math>, der aus Polygonen und Kanten gebildet wird, die <math>P</math> berühren, ist zusammenhängend. Dabei repräsentiert jeder Knoten <math>v</math> aus <math>V_P</math> genau ein Polygon, dessen linearer Ring <math>P</math> enthält. Zwei Knoten sind genau dann mit einer Kante <math>e</math> aus <math>E_P</math> verbunden, wenn die Polygone, die durch die Knoten repräsentiert werden, eine gemeinsame Kante haben, die <math>P</math> berührt .
# For every point <math>P</math> of a Linear Ring of a polygon of <math>C </math> applies: The graph <math>G_P =(V_P, E_P)</math>, that is only build by polygons and edges that touch<math>P</math> is connected. Each node <math>v</math> of <math>V_P</math> represents a polygon which Linear Ring contains <math>P</math>. Two nodes are connected by an edge <math>e</math> of <math>E_P</math> if the two polygons represented by the nodes have a common edge that touches <math>P</math>.
It follows from (i) and (ii) that the surface defined by <math>C</math> has no holes. Together with conditions (4) and (5) it follows that the inner of the solid defined by <math>C</math> is connected
<math>S</math> wird auch als geschlossene [http://www.schemacentral.com/sc/niem21/e-gml32_CompositeSurface.html '''CompositeSurface'''] bezeichnet.
<math>S</math> is denoted as closed [http://www.schemacentral.com/sc/niem21/e-gml32_CompositeSurface.html '''CompositeSurface'''].