About Invalid, Valid and Clean Polygons

Oosterom, Peter van; Quak, Wilko; Tijssen, T.P.M.

doi:10.1007/3-540-26772-7_1

Cited by 25 publications

(21 citation statements)

References 4 publications

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“…The problem can be considered solved for 2D polygons (Oosterom, Quak, & Tilssen, 2005). Linear rings describing a polygon may touch in one common point (Coors & Gröger, 2010).…”

Section: Geometry Model Of Citygmlmentioning

confidence: 99%

Methods for Geometric Data Validation of 3d City Models

Wagner¹,

Alam²,

Wewetzer³

et al. 2015

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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ABSTRACT:Geometric quality of 3D city models is crucial for data analysis and simulation tasks, which are part of modern applications of the data (e.g. potential heating energy consumption of city quarters, solar potential, etc.). Geometric quality in these contexts is however a different concept as it is for 2D maps. In the latter case, aspects such as positional or temporal accuracy and correctness represent typical quality metrics of the data. They are defined in ISO 19157 and should be mentioned as part of the metadata. 3D data has a far wider range of aspects which influence their quality, plus the idea of quality itself is application dependent. Thus, concepts for definition of quality are needed, including methods to validate these definitions. Quality on this sense means internal validation and detection of inconsistent or wrong geometry according to a predefined set of rules. A useful starting point would be to have correct geometry in accordance with ISO 19107. A valid solid should consist of planar faces which touch their neighbours exclusively in defined corner points and edges. No gaps between them are allowed, and the whole feature must be 2-manifold. In this paper, we present methods to validate common geometric requirements for building geometry. Different checks based on several algorithms have been implemented to validate a set of rules derived from the solid definition mentioned above (e.g. water tightness of the solid or planarity of its polygons), as they were developed for the software tool CityDoctor. The method of each check is specified, with a special focus on the discussion of tolerance values where they are necessary. The checks include polygon level checks to validate the correctness of each polygon, i.e. closeness of the bounding linear ring and planarity. On the solid level, which is only validated if the polygons have passed validation, correct polygon orientation is checked, after self-intersections outside of defined corner points and edges are detected, among additional criteria. Self-intersection might lead to different results, e.g. intersection points, lines or areas. Depending on the geometric constellation, they might represent gaps between bounding polygons of the solids, overlaps, or violations of the 2-manifoldness. Not least due to the floating point problem in digital numbers, tolerances must be considered in some algorithms, e.g. planarity and solid self-intersection. Effects of different tolerance values and their handling is discussed; recommendations for suitable values are given. The goal of the paper is to give a clear understanding of geometric validation in the context of 3D city models. This should also enable the data holder to get a better comprehension of the validation results and their consequences on the deployment fields of the validated data set.

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“…The problem can be considered solved for 2D polygons (Oosterom, Quak, & Tilssen, 2005). Linear rings describing a polygon may touch in one common point (Coors & Gröger, 2010).…”

Section: Geometry Model Of Citygmlmentioning

confidence: 99%

Methods for Geometric Data Validation of 3d City Models

Wagner¹,

Alam²,

Wewetzer³

et al. 2015

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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“…Having this in mind, several standards to define what exactly is a valid polygon have been created, with the ISO 19107 [ISO, 2003] and the OGC Simple Features Specification [OGC, 2006] being heavily promoted by standardisation bodies, and together with the ESRI Shapefile specification, they have become predominant. Still, these are not only incompatible with each other, but individual implementations for a single standard yield significantly different results [van Oosterom et al, 2003;van Oosterom et al, 2004], creating a need to agree on a polygon definition, interpretation and a few more rules beforehand (e.g. tolerance values) before being able to establish what is valid in a certain context.…”

Section: Mmentioning

confidence: 99%

“…To this end, restrictions on a minimum separation between vertices and/or edges, minimum angles between edges and minimum area of rings and/or polygons may be defined [Milenkovic, 1993]. In this respect, the concept of a tolerance value is best defined in van Oosterom et al [2004], where it is able to provide a measure of the robustness of a given polygon.…”

Section: Valid Polygonsmentioning

confidence: 99%

“…For the purpose of this thesis, the rules for a valid polygon are based on van Oosterom et al [2004] as well, with polygons formed by rings composed of straight line segments. However, in order to promote having a unique representation for a given polygon, these rings should form only one outer boundary, which is oriented counterclockwise; and zero or more inner boundaries, which are oriented clockwise.…”

Section: Valid Polygonsmentioning

confidence: 99%

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Validation and Automatic Repair of Planar Partitions Using a Constrained Triangulation

Ohori¹,

Ledoux²,

Meijers³

2012

pfg

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“…Validation functions are available to determine whether or not a given feature is valid, i.e., a polygon is not selfintersecting. Although the validation process is not complicated, many implementation and definition problems exist (see Van Oosterom et al 2004;Van Oosterom et al 2005).…”

Section: Two-dimensional (2d) Boundary Representationmentioning

confidence: 99%

Towards a 3D Feature Overlay through a Tetrahedral Mesh Data Structure

Verbree¹,

Most²,

Quak³

et al. 2005

Cartography and Geographic Information Science

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ABSTRACT:The use of 3D features within GIS has been increasing due to the need to represent, query, manipulate, and analyze man-made objects in relationship to other 3D features related to the surface of the earth. This will yield an increased use of 3D boundary representations of the features. The spatial relationship between two or more features is often evaluated using a geometrical overlay of these features, which reveals whether these features overlap and-if they do-to which extent. We present the design of a 3D overlay algorithm which overlays 3D triangulated boundary representations through a constrained tetrahedral mesh. The intersections between the constrained facets of the 3D features are calculated on the fly and within a restricted neighborhood. We can identify and reconstruct the overlaid parts of the 3D boundary representation within the tetrahedral mesh. The implementation is based on the Computational Geometry Algorithms Library, which proved to have the functionality needed but also has its limitations.

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About Invalid, Valid and Clean Polygons

Cited by 25 publications

References 4 publications

Methods for Geometric Data Validation of 3d City Models

Methods for Geometric Data Validation of 3d City Models

Validation and Automatic Repair of Planar Partitions Using a Constrained Triangulation

Towards a 3D Feature Overlay through a Tetrahedral Mesh Data Structure

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