GEOS isvalid operator

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Now, PostGIS is able to store 3D geometries as TIN and POLYHEDRALSURFACE and to import 3D data with the collada2pgsql command.
I decided to add functionalities in order to manipulate these new geometries. First, I implemented the isvalid operator in GEOS for TIN and POLYHEDRALSURFACE. GEOS (Geometry Engine Open Source) is a geometric library for PostGIS and the isvalid operator is based on the mathematical definition of geometries.

So It must check if:

• all faces are connected:

• there are no self-intersections:

• neighbour faces have the same orientation:

It's important to notice that a TIN or a POLYHEDRALSURFACE stored in PostGIS can represent a 3D volume but not be a valid geometry if we refer to its mathematical definition.



Some exemples of the isvalid operator use:









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Adding new geometries in PostGIS

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The first aim of my work was to add the support of 3D geometries in PostGIS. We have 12 geometries already existing in it : Point, MultiPoint, LineString, MultiLineString, Polygon, MultiPolygon, Curve, MultiCurve, PolygonCurve, MultiSurface, GeometryCollection. The two geometries I added are some specific MultiPolygon described in OGC SFS1.2 norm. They are:

• TIN for Triangular Irregular Network
• POLYHEDRALSURFACE.

This last one is a collection of contiguous 3D Polygons which share some edges and describe a 3D volume. A TIN is a POLYHEDRALSURFACE where all Polygons are Triangles.

The SQL syntax is the same for these two new geometries and MultiPolygons:

• -MULTIPOLYGON(((0 0 0, 0 1 0, 1 1 0, 1 0 0, 0 0 0)), ((0 0 0, 0 1 0, 0 1 1, 0 0 1, 0 0 0)))
• -TIN(((0 0 0, 1 0 0, 0 1 0, 0 0 0)),((0 0 0, 1 0 0, 0 0 1, 0 0 0)),((0 0 0, 0 0 1, 0 1 0, 0 0 0)),((0 0 1, 1 0 0, 0 1 0, 0 0 1)))

This TIN describes a tetrahedron.

• POLYHEDRALSURFACE(((0 0 0, 0 1 0, 1 1 0, 1 0 0, 0 0 0)), ((0 0 0, 0 0 1, 0 1 1, 0 1 0, 0 0 0)),((0 0 0, 1 0 0, 1 0 1, 0 0 1, 0 0 0)), ((0 0 1, 1 0 1, 1 1 1, 0 1 1, 0 0 1)),((1 0 0, 1 1 0, 1 1 1, 1 0 1, 1 0 0)),((1 1 0, 0 1 0, 0 0 1, 1 1 1, 1 1 0)))
  

This POLYHEDRALSURFACE describes a cube






It's possible to create some 2D TIN or POLYHEDRALSURFACE but their main aim is to describe 3D volumes.

It's not possible to create TIN & POLYHEDRALSURFACE with Multirings Polygons. It's in their mathematical definition, faces of PolyhedralSurfaces can't have holes.





Some PostGIS export functions are available for these geometries:

• asEWKB
• asEWKT
• asKML
• asSVG (only 2D output)
• asGML (only 2D output)
• Summary
  

Here are some examples of TIN and POLYHEDRALSURFACE manipulation:





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SELECT asewkt('TIN(((1 2 3, 3 4 5, 4 5 6, 1 2 3)))');


SELECT asSVG('POLYHEDRALSURFACE(((0 0, 0 1, 1 1, 1 0, 0 0)),((1 0, 2 0, 2 1, 1 1, 1 0)))');


SELECT asGML('POLYHEDRALSURFACE(((0 0, 0 1, 1 1, 1 0, 0 0)),((1 0, 2 0, 2 1, 1 1, 1 1, 1 0)))');
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