Help for TIECONM

PURPOSE

     tieconm prepares a gridded dataset for POLYGEOM, GEOMA, 
     LGEOM,  MGEOM,  or  GEOMZ  transformations.   Input  is 
     paired sets of tiepoints with no restrictions.   It is, 
     in principle, a surface generation routine, but creates 
     the  gridded  dataset so as to best interface with  the 
     VICAR routines above.   The sequence GEN,  tieconm, and 
     GEOMZ can be used to generate a surface in image format 
     through an arbitrary set of points.
     tieconm uses the finite element method  (triangulation) 
     for  surface  fitting.   It is anticipated  that  other 
     surface  fitting methods will be integrated into  VICAR 
     in  the same fashion as tieconm so that users will have 
     maximum flexibility both in terms of choice of  surface 
     fit and in terms on application.
TAE COMMAND LINE FORMAT

     tieconm OUT=B PARAMS
     tieconm PARMS=parm_file OUT=B PARAMS
     tieconm INP=tiep  OUT=B  PARAMS

     where

     parm_file           is an optional disk parameter dataset 
			   containing the input tiepoints.
     tiep		 is an optional IBIS tabular file containing
			   the input tiepoints.
     B                   is the output parameter dataset.
     PARAMS              is a standard VICAR parameter field.
OPERATION

     tieconm operates in two phases.   In phase 1, the input 
     points  are fully triangulated by the Manacher  version 
     of  the greedy algorithm.   This operates by  selecting 
     shortest   edges   first   and  adding  them   to   the 
     triangulation  so long as they do not cross  previously 
     added (shorter) edges.  The algorithm proceed until all 
     edges are examined.   Four extra points are added  five 
     diameters away from the convex hull so that the surface 
     will extend smoothly beyond the input tiepoints.

     In  phase 2,  the output grid is formed by  evaluating 
     the  triangular surface at grid point locations.   That 
     is,  a grid point will fall in some triangle,  and  the 
     GEOM  shift  will  be the linear interpolation  of  the 
     input shifts at the three corners of the triangle.  The 
     user  should  note  that  the  triangular  surface   is 
     continuous but not differentiable and it passes through 
     all  of  the input  points.   Point-surface  generation 
     routines can e compared in the following table.
|       \ PROPERTIES| CONTI-|DIFFEREN-| EVALUATES |   WELL   |
|        \    OF    | NUOUS |TIABLE   | AT INPUT  |  BEHAVE  |
| METHOD  \ SURFACE |       |         |   POINT   | NO MESAS |
|-------------------|-------|---------|-----------|----------|
| Triangulation     |  yes  |    no   |    yes    |   yes    |
|-------------------|-------|---------|-----------|----------|
|                -1 |       |         |           |          |
| Interpolation r   |   no  |    no   |    yes    |   yes    |
|-------------------|-------|---------|-----------|----------|
|                -p |       |         |           |          |
| Interpolation r   |   no  |    no   |    yes    |    no    |
|-------------------|-------|---------|-----------|----------|
| Polynomial Fit    |  yes  |    yes  |    no     |    no    |
|-------------------|-------|---------|-----------|----------|
| Potential Fcn.    |  yes  |    ye  s|    yes    |     ?    |
EXAMPLE

     tieconm OUT=B 'GEOMA NAH=44 NAV=24
           TIEPOINT=(   346       432       353      422
                        479       316       482      313
                         .
                         .
                         .
                        723       529       715      527)
     POLYGEOM INP=X PARMS=B OUT=Y

     In this example,  the tiepoints are used to set up a 44 
     x  24 grid for use by POLYGEOM.   The tiepoints can  be 
     scattered  over  the  image  in  any  fashion   whereas 
     POLYGEOM requires a regular grid.

     GEN OUT=X NL=1000 NS=1000 IVAL=0 LINC=0 SINC=0
     tieconm OUT=B 'GEOMZ              TIEPOINTS=(
               1   1    0
               1000   1    0
               1    1000     0
               1000  1000      0
               500   500       255)
     GEOMZ INP=X PARMS=B OUT=Y

     this  example constructs a "pyramid" shaped  brightness 
     surface in the image Y.

TIMING

     Timing  is dominated by the triangulation method  which 
     is 0(n2) where n is the number of input points.  A case 
     with  235  points  was run in 2-1/2 minutes  CPU  time, 
     hence,  900 points could be run in thirty-seven minutes 
     or less (IBM timing).


RESTRICTIONS

   The maximum number of input tiepoints is 1600.
   The maximum number of output tiepoints is 40000.


REFERENCES

     Manacher,  G.  K.,  and Zobrist, A. L., "A Fast, Space-
     Efficient   Average-Case  Algorithm  for   the   greedy 
     Triangulation   of  a  Point  Set",   SIAM  Journal  of 
     Computing (submitted).


WRITTEN BY:            A. L. Zobrist, 29 August 1979

COGNIZANT PROGRAMMER:  K. F. Evans

REVISIONS: 
  PORTED TO UNIX	C. R. Schenk (CRI)  31-Oct 1994