Using line-based Voronoi cells in GIS
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This document introduces line-based Voronoi diagrams and how they can be used in GIS applications. It discusses how most GIS software only supports point-based Voronoi diagrams, but the Boost library enables line-based Voronoi diagrams. It provides code examples for using Boost's Voronoi functionality with Python and C# for GIS applications. Proper preprocessing of GIS line data is discussed to avoid issues during Voronoi construction.
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Using line-based Voronoi cells in GIS
- 1. Using line-based Voronoi diagrams in GIS Fabien Ancelin 2016, Apr 21st
- 2. Introduction to Voronoi diagrams Voronoi diagrams are continuous set of cells generated from an set of input points. Each input geometry will generate one cell that define its area of influence. It is usually based on Euclidean distance. Any point inside that cell is closer to the input geometry of that cell than to any other input geometry Used to determine areas of influence
- 3. Limitation in current GIS software Software Support point input Support line input Esri ArcGIS Yes No QGIS Yes No PostGIS Yes No Mapinfo Yes ??? What is you want to determine areas of influence of a line… • Postal code out of a road network and buildings. • Divide a road network into zones based on attributes.
- 4. Let there be Boost Boost is a free, extensive C++ library. And there is a hidden gem.. http://www.boost.org/doc/libs/1_54_0/libs/polygon/doc/ voronoi_main.htm
- 5. Problems for the GIS community Few GIS users know of to code in C++. Python is definitely more popular, and so is .NET to a lesser extent. Here is how you can use boost Voronoi with your favorite language: Python: https://github.com/Voxel8/pyvoronoi .NET (C#): https://github.com/fabanc/SharpBoostVoronoi Those wrappers let you to use boost Voronoi library, but also give you built-in functions to manage curvy shapes in your GIS data.
- 6. How to prepare your GIS data Constraints raised by the boost Voronoi API: Coordinates of the input points and endpoints of the input segments should be of the integer type. Input segments should not overlap except their endpoints. Passing invalid data can: Cause the Voronoi construction to freeze. Return invalid results. Controlling your input data quality is paramount.
- 7. Example Good data Bad data (small overlap) From the Sample WPF App in SharpBoostVoronoi: https://github.com/fabanc/SharpBoostVoronoi/tree/master/SharpBoostVoronoi/SampleWPFApp
- 8. Building a graph with integers (no scale factor):
- 10. Using the output Three primitives: Cells … Are made of Edges … That are made of Vertices Complete information about Boost output at: http://www.boost.org/doc/libs/1_54_0 /libs/polygon/doc/voronoi_diagram.ht m
- 11. Output type: vertices Vertices X (double precision) The X coordinate Y (double precision) The Y coordinate.
- 12. Voronoi output objects: edges Edges Start The index of the start vertex of this segment. End The index of the end vertex of this segment. IsPrimary False if the edge goes through the endpoint of the segment site, else true. IsLinear True is a segment is a line, false if the segment is an arc. IsFinite True if the edge is delimited by two known vertices, False otherwise. Cell The index of the cell associated with this segment Twin The index of the twin cell associated with this segment
- 13. Voronoi output objects: cells Cells Index The voronoi cell identifier Site The index of the source feature ContainsPoint True if the cell is made from a point ContainsSegment True if the cell is made from a segment EdgesIndex Indexes of the segment that makes the cell IsOpen True if the cell has a segment that is infinite SourceCategory The type of element used to create the edge.
- 14. Code sample (C#)
- 16. Demo! Let’s use some real GIS data!
- 17. Wrapping up Any idea of what problems this could solve for you? Any comments or questions? If you’re working with ArcGIS, you can make a geoprocessing tool. Thank you!