Copyright © 2007 Open Geospatial Consortium, Inc. All Rights Reserved.
47
9 Hexagonal Grid Coverages
9.1 General
Coverages are sometimes based on tessellations composed of regular hexagons. Such tessellations are usually called hexagonal grids. In fact, the centers of a set of regular hexagons that form such a tessellation
correspond to the grid points of a quadrilateral grid Figure 20. That grid can be described as a rectified grid in which the two offset vectors are of equal length but differ in direction by 60°. The length of a side of the
hexagon is L = S tan 30°, where S is the length of the offset vector. This means that the values in the coverage range can be stored as a grid values matrix 8.14 and accessed through a sequence rule 8.15.
The hexagons are the Thiessen polygons that are generated around the grid points.
NOTE A set of Thiessen polygons generated from the grid points of any two-dimensional rectified grid described by
two offset vectors that are equal in length but not orthogonal will be a set of congruent hexagons. The hexagons will be irregular unless the offset vectors differ in direction by exactly 60°.
Figure 20 — A hexagonal grid
9.2 CV_HexagonalGridCoverage
9.2.1 General
A CV_HexagonalGridCoverage Figure 21 evaluates a coverage at direct positions within a network of hexagons centred on a set of grid points. Evaluation is based on interpolation between the centres of the
CV_ValueHexagons surrounding the input position.
9.2.2 interpolationType
The inherited attribute interpolationType: CV_InterpolationMethod = “lost area” shall identify the interpolation
method to be used in evaluating the coverage. The most common interpolation methods are ―lost area‖ C.9 and ―nearest neighbour‖ C.2. Lost area interpolation can return a different Record of feature attribute values
for each direct position within a CV_ValueHexagon. On the other hand, nearest neighbour interpolation will return for any direct position within a CV_ValueHexagon the Record associated with the
CV_GridPointValuePair at
the centre
of the
CV_ValueHexagon. In
other words,
a CV_HexagonalGridCoverage that uses nearest neighbour interpolation acts like a discrete surface coverage.
Copyright © 2007 Open Geospatial Consortium, Inc. All Rights Reserved.
48
9.2.3 locate
The operation locate p: DirectPosition: CV_ValueHexagon is inherited from CV_ContinuousCoverage with the restriction that it shall return a CV_ValueHexagon. It shall accept a DirectPosition as input and return the
CV_ValueHexagon that contains that DirectPosition.
Figure 21 — CV_HexagonalGridCoverage
9.2.4 evaluate
The operation evaluate p: DirectPosition, list: Sequence CharacterString: Record is inherited from
CV_Coverage. Evaluation of a CV_HexagonalGridCoverage involves two steps. The first is to find the CV_ValueHexagon that contains the input DirectPosition; the second is to interpolate the feature attribute
values at the DirectPosition from the CV_GridPointValuePairs at the centres of the surrounding CV_ValueHexagons.
