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

Lecture 15: Terrain Analysis II

Surface Specific Point Sampling

• If the structure of the terrain is known, then intelligent design of sampling and interpolation is best
• Terrain Skeleton determines most of surface variance
• Knowledge of skeleton often critical for applications e.g. LOS
  
  
• Source of much terrain data is existing contour maps
• Problems of contour->TIN or Grid are many
• Biggest problem is the wedding cake effect
• Sampling along contour "fills in" interpolated values
  
  

Surface Models

• Alternative to LOCAL operators is to model the whole surface at once
• Often must be an inexact fit, e.g. when there are many points
• Sometimes Model is surface is sufficient for analysis

Polynomial Series

• Least squares fit of polynomial function in 2D.
• z = bo + b1x + b2y etc.
• Simplest form is the linear trend surface
• Most complex forms have bends and twists
  

Fourier Series

• Fit trigonometric series of cosine waves with different wavelengths and amplitudes.
• Analytically, can generalize surface by "extracting" harmonics

Filtering

• Convolution of filter matrix with map matrix
• Filter has a response function
• Filter weights add to one
• Can enhance properties, or generalize

Volumetric Transformations

• Many possible analytical transformations of 3D data that show interesting map properties
• Simplest is slope (first derivative) and aspect (direction of max. slope)
  
  
  
  
• Terrain partitioning: Often to extract VIPs or a TIN from a grid.
• Terrain Simulation (many methods e.g. fractals)
• Intervisibility
  
  
  
  

Terrain Symbolization

Automated Contouring

• Many problems
  • Saddle Point
  • Spline smoothing
  • Line crossing
  • Loops
  • Sharp breaks
• Most problems well cataloged by Krajewski and Gibbs.

Analytical Hill Shading

• Simulate illumination from an infinite distance light source
• Light source has azimuth and zenith angle
• Surface can be reflected light or use log transform
• Can add shadows for realism, or multiple light sources
  
  

Gridded and Realistic Perspectives

• Create view from a particular camera geometry
• Can include or excluded perspective
• Colors should include shading
• Multiple sequences can generate fly-bys and fly-thrus e.g. Truflite
  
  

Keith Clarke Last Change 5/22/97 Copyright Prentice Hall, 1995