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Modeling Guide for 3D Objects - Part 1: Basics (Rules for Validating GML Geometries in CityGML) (view source)
Revision as of 10:43, 11 November 2013
, 10:43, 11 November 2013→Planarity of Polygons
'''Definition 1:'''
'''Definition 1:'''
A Linear Ring <math>R</math> is '''planar''', if it is a valid Linear Ring and the distance of all points to any plane <math>E_{ijk}</math>, that is defined by three co-linear points <math>P_i</math>, <math>P_j</math> and <math>P_k</math> aufgespannt werden, is less than a given threshold <math>\epsilon</math> :
A Linear Ring <math>R</math> is '''planar''', if it is a valid Linear Ring and the distance of all points to any plane <math>E_{ijk}</math>, that is defined by three co-linear points <math>P_i</math>, <math>P_j</math> and <math>P_k</math>, is less than a given threshold <math>\epsilon</math> :
<math>\forall E_{ijk} \forall P_a = dist (P_a,E_{ijk})\le \epsilon</math>
<math>\forall E_{ijk} \forall P_a = dist (P_a,E_{ijk})\le \epsilon</math>