Data sets that are not necessarily spatial in their original form can be spatialized by adding geoor spatial coordinates. Temporal and attribute data can be spatialized. For a single data set, identities of objects can become locations in one or more spaces; pairwise relationships between objects located in that space (based on the degrees of similarity, difference, and connection, where those relationships can reflect function, genesis, history, appearance, properties, etc.) can become distances; sets of multiple relationships between the locations of objects can become patterns (permitting the identification of spatial structures, deviations, and exceptions); and patterns can be explained in terms of the processes that generated them. Multiple spatialized data sets can be overlain and combined in different spaces. All spaces can be restructured along different axes with different distance metrics and different dimensionalities.

The capacity to spatialize is what motivates the process of spatial thinking.

2. Visualize working and final results by creating representations that capture the structure of spaces and the locations, relationships, and patterns of objects depicted in them.

There are numerous general classes of representations—maps, graphs, diagrams, charts, cross sections, drawings, photographs, animations, models, remotely sensed images, etc.—that can be adapted to meet the needs characteristic of a particular knowledge domain (see Chapter 3).

Similarly, there are numerous forms for representations. Representations can be static or dynamic (either cross-sectional or continuous); they can be still images or animations; they can be visual-graphic or expressed in a variety of sensory modes (e.g., three-dimensional tabletop models, globes, plastic maps with raised relief, braille maps); they can be in black and white or in color; they can be presented via a range of media (e.g., video, sound, vibrotactile) that can be converted to other media forms (e.g., voice-recognition and text-to-speech software).

The capacity to represent is integral to the process of spatial thinking.

3. Perform functions that manipulate the structural relations of spatialized data sets. These functions include the following:


  • Symbolizing (use of graphic markers [point, lines, and areas] and sensory media-appropriate variables [e.g., in the visual graphic case: size, shape, orientation, hue, value, chroma] to capture the identity of objects; similar variables can be created for sensory media such as touch [force feedback, tactile, and vibrotactile mapping symbols] and sound)

  • Scale change (zooming in [magnification] and zooming out [minification] in either a continuous or a discrete stepwise manner)

  • Replotting into different frames of reference (from projections using one coordinate system to another [e.g., abstract as in azimuthal versus Cartesian or specific as in cartographic mapping systems such as latitude and longitude, the universal transverse Mercator zones, the SPCS])

  • Reprojecting (within families of map projections that preserve properties such as area, shape, direction, and distance [e.g., the Molleweide equal area, which is used for world statistical maps where the areas of particular interest are in the midlatitudes])

  • Rescaling (converting from one distance metric to another [e.g., Euclidean versus Manhattan])

  • Perspective change (adopting different viewing azimuths [from 0° to 360° around an arbitrary reference] and viewing angles [from 0° to 90°, eye-level to orthogonal])

  • Spatial transformations (movements of objects in terms of translations and rotations in the plane, etc.)

  • Dimensional change (e.g., converting three-dimensional to two-dimensional depictions)

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