Transformations between measurement frameworks

Objectives of lecture:

1. Surface transformations as an example
   More demonstrations of surface operations
   Interpolation, Triangulation and the rest
   Reformulating these into more general groups
2. A Scheme for Transformations
   Neighborhood Construction
   Attribute Assumptions

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Transformations: Background in Cartography

The transformational view of cartography is the basis for 'analytical cartography' (Waldo Tobler and others). [An alternative to the 'communication' school.]

Transformations presented first as projections (alter spatial measurements), then as transformations between primitives (point, line area).

The operations discussed so far in this course work for a particular measurement framework. There have been hints of a need to convert from one framework to another, and variations of the operations already discussed will do exactly this job.

The question, as it has been all quarter, is how an operation can "create" new information? The secret is to exploit relationships, to generate new ways to compare attributes through the spatial structure of the geographic information.

Surface transformations

Surfaces provide a relatively confined example of the transformation process. A matrix gives the procedure used to convert from one measurement framework (rows) to another (columns - same list).

Demonstrations: working with the LIDAR data for Bainbridge Island (bi_patch)

These procedures can be reclassified according to the combination of neighborhood relationships and attribute assumptions in Table 9-3.

Scheme for Transformations

Table 9-2: Scheme for Transformations
	Attribute Assumptions
Neighborhood Construction	Implicit	External
Implicit	Case 0	Case 1A
Discovered	Case 1N	Case 2

Case 0: transformation by extraction:

source contains information required for create target. Eg. topological structure contains 'spaghetti'.

Case 1A: attribute assumptions required:

geometry remains, attributes changed. Simplest case: Groupings; add information; rules do not have to remain local. Remotely sensed imagery: multiple continuous measures=> clusters (classes)

Case 1N: geometric processing only

(to construct neighborhood): Eg. TIN operations to locate point in triangle

Case 2: Complete

requires geometry and attribute assumptions. Eg. areal interpolation John K. Wright, Cape Cod dasymetric map (image copyright by American Geographical Society, 1936)