Lecture Notes for Clarke, K. C. Analytical and Computer Cartography

Lecture 13: Data Structure Transformations

"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, p. 226)

Transformations

1. Map scale
2. Dimension (data type)
3. Symbolic content (map type)
4. Data structures

• So far have covered part of one and all of two and three

Why Transform Between Structures?

• 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 dmands of analysis and modeling
• Suit demands of map symbolization (e.g. fonts)

Generalization Transformations

• Conversion of data collected at higher resolutions to lower resolution. Less data and less detail.
• Simplicity -> clarity
• Can be loss-less or lossy.

Point-to-Point

Consquence of projection. E.g. 3-arc second DEMs.

Line-to-Line

Problem of "line character"

1. Algorithmic resampling i.e. reduce # of points in finite sample
2. Algorithmic reconstruction
3. Enhancement

Algorithms (Reviewed by McMaster)

• N-th Point retention
• Equidistant Resampling
• Douglas-Peucker
  

Example (Using Animation) Courtesy of Brad Allen and Waldo Tobler.

Enhancement

• Splines
• Bezier Curves
• Polynomial Functions
• Trigonometric Functions (Fourier-based)

3. Enhancement

• Fractal
• Fourier
• Manual

Area-to-Area

• 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
• Greatest common geographic units: Full overlap set for reassignment.
• May require dividing non-divisible measures, e.g population

Algorithms for Overlay

• 1. Intersections
• 2. Chain splitting
• 3. Polygon reassembly
• 4. Labeling and attribution

Volume-to-Volume

• Common conversion between two major data structures, vector (TIN) and grid.
• Often via points and interpolation.
• Problem of VIPs

Vector to Raster and Back Again

• Efficient V->R-> V has eliminated vector-raster debate, BUT is a major source of error
• major consumer of processing power

Vector to Raster

• Easy compared to inverse, a form of resampling
• Grid must realate to coordinates (extent, bounds, resolution, orientation)
• Rasters can be square, rectangular, hexagonal.
• Resample at minimum r/2
• Both structures may be tiled.
• Problem: What value goes into the cell?
• Separate arrays for dimensions and binary data?
• Index entries & look up tables

Algorithm (e.g. rasterize)

1. Convert form of vectors (e.g. to slope intercept)
2. Thin fat lines
3. Compute implicit inclusion (anti-alias)

Raster to Vector

• Much harder, more error prone.
• May involve cartographer intervention (e.g. Laserscan)
• Importance of allignment
• Can do points, lines, area.

Algorithms

1. Skeletonization and Thinning
   1. Peeling
   2. Expanding
   3. Medial Axis
2. Feature Extraction
3. Topological Reconstruction

Data Structure Transformations

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

The Role of Error

• 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

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

Keith Clarke Last Change 5/14/97 Copyright Prentice Hall, 1995