densify

(Compiled by TC)

Description

The program densify first constructs a reference surface by interpolating the surface points of a lower resolution shape model. At each point of the reference there is a vector V0 from the model center to that point and a normal N0 to the surface. That normal is extended some distance until it pierces one or more of the ensemble of maplets, and the average A of those distances is taken to represent the piercing point on the new model's surface, so the new surface vector is V = V0 + A*N0.

                ___...-------...___
                   |           |
                   |           |A*N0
             ______|___________|_________ reference
                   \          /
                    \        / V0
                     \      /

Because, especially at the early stages, there are mismatches in maplet locations simply due to the formal uncertainties of the estimation process, we have found it better to average the maplet normals N at each point, keeping a small randomly selected set of the A as conditioning heights.

The initial inputs to the procedure are the names of the input and output SHAPE file along with a line with K (usually 2), a limit in km specifying how far along the surface normal the program should search for a maplet, and a random seed in the form of a large integer. This seed will be superceeded if one is entered on the command line following the densify invocation.

In most cases, the maplets will cover most of the surface. Where it is not covered, the normals to the input model provide the "slopes" and the integration procedes without any randomly chosen conditioning heights from these areas. In some cases, such as fast flybys of small bodies, only a small fraction of the surface is visible - vast areas are unknown. In these cases, conditioning heights are also taken from the input model as well. This option is specified by using a negative value for K (usually -2).

The procedure now determines the average height along each surface normal from each reference point of the densified shape. It also determines the average maplet surface normal and the standard deviation of the heights, used as a measure of uncertainty. It produces the output SHAPE file and a similar file called SIGMA.TXT that has an extra column representing the uncertainty. This latter file can be displayed as an image to show areas that might need further work. The program now gives the options:

     0. end program
     1. proceed to iteration

If '0' is chosen, the output shape model will be the height averaged result. The entire script, with the output model called SHAPEX.TXT, is:

     densify
     SHAPEFILES/SHAPE1.TXT        < input shape
     2, 1.0, 5639                 < K, search range (km), random SEED
     SHAPEFILES/SHAPEX.TXT        < output shape
     0                            < end program

If '1' is chosen, the program asks for:

     input fraction

the fraction of averaged heights (and empty heights if K<0) used to condition the integration (usually .005) and:

     input weight

the weight given to the conditioning heights (usually .025).

The program produces an output SHAPE file and gives the options:

     0. end program
     1. more iteration
     2. change weight

The interim shape can be viewed to see whether we want to change the weight given to the conditioning heights using a procedure described below. Usually, we just continue iterating or, finally, exit the program.

By tradition, we usually use SHAPE0 for Q=64, SHAPE1 for Q=128, SHAPE2 for Q=256 and SHAPE3 for Q=512, so after this is run, if there have been no problems, we want to:

• cp SHAPEFILES/SHAPEX.TXT SHAPEFILES/SHAPE2.TXT

After another densification, when SHAPEX.TXT is Q=512, we would:

• cp SHAPEFILES/SHAPEX.TXT SHAPEFILES/SHAPE3.TXT

SHAPE.TXT is also Q=512 and we want to update that as well. For historical reasons, some scripts change permissions on SHAPE.TXT to read only, so we want to:

• chmod +w SHAPE.TXT cp SHAPEFILES/SHAPEX.TXT SHAPEFILES/SHAPE.TXT

Requires

• LMRKLIST.TXT - list of all landmarks to be used

• LMKFILES/ - directory of .LMK files for each maplet

• MAPFILES/ - directory of .MAP files

• SHAPEFILES/ - directory of built shapes

Optional

• LMRKLISTR.TXT - specific list of landmarks desired

Input

The commands sent to densify are usually prearranged in a file which can be used as follows:

~/bin/densify < tmpRun.txt

Input File

SHAPEFILES/PreviousShapeFile       (input shape)
2 100 1.67773                      (K (power of 2), search range (km), random seed)
SHAPEFILES/CurrentShapeFile        (output shape)
1                                  (more iteration)
.005                               (fraction of points used for conditioning)
.025                               (conditioning weight)
1                                  (more iterations)
1
1
1
1
1
1
1
1
1
1
1
1
1
0                                  (end program)

Output

• SIGMA.TXT - list of sigma values associated with the shape model (found in SHAPEFILES/)

• Shape file in ICQ format