Surfaces: properties and representation

Surfaces are a thematic concept, assuming a single valued Z for all points (x,y)
Two basic kinds: discontinuous.(prisms) and continuous
Discontinuous surfaces are implied by the thematic mapping covered previously

Particular continuous surfaces

• Elevation of landforms : topographic maps (photogrammetry)
• Depth of sea bed: Bathymetric maps, [charts] (hydrographic surveying)
• other physical surfaces
• Gravity anomaly (gravimetry), atmospheric pressure (barometers), temperature ...
• examples of non-physical surfaces
• Land rent, population density [or potential field], man-boom miles (sonic booms) ...
  

Properties of Surfaces

• Point heights : the surface has a given value at a given location
• Slope: a combination of gradient and aspect
  • Gradient: the surface has a given rate of change (derivative of function)
  • Aspect: the slope has a direction (vector field, not just scalar field)
• Volume: integral of quantity under (or between) surfaces
• other quantities: viewshed (area of intervisibility), downhill flow (actually a vector surface with direction), cut and fill
  

Representation of Surfaces

Depicting terrain: shaded relief, classed elevation (filled contours), hachures, illuminated (Tanaka) contours, block diagrams, nominal symbols (hill, not hill)- Now, Virtual Reality, Augmented Reality.

Computer Data Structures:

Height (Z), and horizontal location (x,y); one can be controlled (made regular), other measured
Regular height implies irregular horizontal location: CONTOURS
Contour Interval: vertical distance between contours
Contours can be directly measured on photogrammetry equipment: stereoplotter

Regular horizontal location implies iregular height: ELEVATION MATRIX (DEM)
also called Digital Terrain Model (DTM); USGS distributes DEMs.
Profiles: straight lines with regular sampling along them (Z measured)
turns into grid if profiles as dense as samples along them.
Stereoplotter can also track profiles, many DEMs are made by digitizing old contour maps, and interpolating.

Recognition of areas of shared slope and aspect, bounded by surface-specific features
Triangular facets, Triangular Irregular Network (TIN): spot heights connected by lines. An example of Palestine/Israel, another more evidently based on TIN, BIG TIN of Illinois.

Resources: Wisconsin State Cartographer's Office description.