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Lecture 09: Data Structure Transformations

Lecture 09: Data Structure Transformations. Geography 128 Analytical and Computer Cartography Spring 2007 Department of Geography University of California, Santa Barbara.

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Lecture 09: Data Structure Transformations

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  1. Lecture 09: Data Structure Transformations Geography 128 Analytical and Computer Cartography Spring 2007 Department of Geography University of California, Santa Barbara

  2. "In virtually all mapping applications it becomes necessary to convert from one cartographic data structure to another. The ability to perform these object-to-object transformations often is the single most critical determinant of a mapping system's flexibility" (Clarke, 1995) Geocoding stamps coordinate system, resolution and projection onto objects Data usually in generic formats at first Can save space, gain flexibility, decrease processing time Suit demands of analysis and modeling Suit demands of map symbolization (e.g. fonts) Why Transform Between Structures?

  3. Conversion of data collected at higher resolutions to lower resolution. Less data and less detail. Simplicity -> clarity Information will be lost Generalization Transformations- Why Generalize? John Krygier and Denis Wood, Making Maps: a visual guide to map design for GIS

  4. Centroid Map projections Usually be seen as a part of Geocoding process Generalization Transformations - Point-to-Point USGS 1:250,000 3-arc second DEM format (1-degree block)

  5. N-th Point retention Equidistant re-sampling Douglas-Peucker Generalization Transformations - Line-to-Line Generalization Douglas-Peucker line generalization

  6. Splines Bezier Curves Polynomial Functions Trigonometric Functions (Fourier-based) Generalization Transformations - Line-to-Line Enhancement

  7. Problem is given one set of regions, convert to another Example: Convert census tract data to zip codes for marketing Example: Convert crime data by police precinct to school district May require dividing non-divisible measures, e.g population Areal Interpolation Greatest common geographic units: Full overlap set for reassignment Generalization Transformations - Area-to-Area Population at counties Population at watersheds=?

  8. Algorithm for Overlay 1. Intersections 2. Chain splitting 3. Polygon reassembly 4. Labeling and attribution Generalization Transformations - Area-to-Area

  9. Common conversion between two major data structures, vector (TIN) and grid Often via points and interpolation Change cell size Generate a new grid Compute the intersect Interpolate from neighboring cells Problem of VIPs Generalization Transformations Volume-to-Volume www.soi.city.ac.uk/~jwo/phd/04param.php

  10. Easy compared to inverse, a form of re-sampling Grid must relate to coordinates (extent, bounds, resolution, orientation) Rasters can be square, rectangular, hexagonal. Resample at minimum r/2 Vector-to-Raster Transformations • Problem: What value goes into the cell? • Dominant criterion • Center-point criterion • Separate arrays for dimensions and binary data? • Index entries & look up tables

  11. Convert form of vectors (e.g. to slope intercept) Sample and convert to grid indices Thin fat lines Compute implicit inclusion (anti-alias) Vector-to-Raster Transformations (cnt.)- Algorithm www.inf.u-szeged.hu/~palagyi/skel/skel.html

  12. Vector-to-Raster Transformations (cnt.)- Example

  13. Much harder, more error prone. May involve cartographer intervention Importance of alignment Can do points, lines, area Raster-to-Vector Transformations

  14. Skeletonization and Thinning Peeling Expanding Medial Axis Feature Extraction Topological Reconstruction Raster-to-Vector Transformations- Algorithm

  15. Grid Scan Matrix Algebra - filtering Raster-to-Vector Transformations- Edge Detection fourier.eng.hmc.edu/.../gradient/node9.html

  16. Scale transformations are lossy (re)storage produce error algorithmic error, systematic and random Types are: scale, structural (data structure), dimensional, vector-to-raster Data Structure Transformations

  17. Kate Beard: Source error, use error, process error Morrison: Method-produced error Error is inherent, can it be predicted, controlled or minimized? XT = X' X' T^-1 = X + E The Role of Error • Errors are • positional • attribute • systematic • random • known • uncertain • Errors can be attributed to poor choice of transformations • Incompatible sequences of T's (non-invertible) • "Hidden" Error=use error, not process error

  18. Map Design Next Lecture

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