MATHEMATICAL FORMULATION & DIGITAL ANALYSIS 1371 
COMPUTER ANALYSIS 
Unlimited flexibility is provided by the digital model in computer analysis. The type of 
numerical parameters to be computed and the computation algorithm will depend on the 
structure of the digital data as well as the project requirements. Generally, the computation 
algorithm makes use of either the finite element approach or the mathematical modeling 
approach. For objects of simple geometric shapes, the entire surface may be modeled with one 
or more mathematical expressions. However, for objects of complex shape such as the topo- 
graphic terrain, the finite element approach which treats each small surface element as either a 
plane or curved surface must be used in the computation. Following is a list of parameters that 
can be easily derived from digital models: 
€ geometric parameters such as area, volume, perimeters, curvature, radius, gradient, and aspects; 
© movement and change parameters such as velocity, acceleration, volume change, area change, and 
path of movement; 
© statistical parameters such as area distribution, volume distribution, mass distribution, sample 
variations, and time variations; 
* physical parameters such as center of gravity, stress, strain, and forces; and 
€ shape (through surface modeling). 
COMPUTER GRAPHICS 
Graphic products are used primarily for the purpose of illustration and visual display. They 
may be drawn from magnetic tape with a digital X-Y plotter or may be displayed on-line on a 
CRT screen. Among the most commonly used graphical products are contour maps, slope 
maps, thematic plots, perspective drawings, cross-section profiles, plan drawings, and histo- 
grams. 
SOFTWARE SYSTEM 
Figure 12 illustrates the conceptual design of a general purpose digital analysis software 
system. Both hardwares and softwares are presently available to perform the general purpose 
Z ni 
AS 
  
  
  
  
  
  
  
  
  
  
  
Digitizer Stereoplotter == 
Coordinate Transformation Image Refinement 
fransformation Modeling Phototriangulation 
Scaling Scale Transfer Intersection 
Absolute Orientation 
  
  
  
  
  
  
  
  
  
  
S e ain 
  
  
  
  
  
  
  
  
  
Gridded Non-Gr i dded 
Surface Fitting 
Linear. 
Data File LInterpolati Data File 
Genera] Purpose Problem-Oriented 
Application Application 
Programs Programs 
  
  
  
  
  
  
  
  
zZ Numerical & System 
2 ps Statistical Response 
=| 
Parameters 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Contour Perspective Slope Profile 
Map Zones 
Fic. 12. A general purpose digital analysis software system.