Category B

Version 3.0


This program is used to increase the resolution of a shape model by interpolating heights between landmarks.

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. The new surface vector is V = V0 + A*N0.

The picture below is a visual representation of the paragraph above.

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

The new surface vector V will differ from V0 more noticeably when tiling at lower resolution because there are mismatches in maplet locations simply due to the formal uncertainties of the estimation process. Therefore, 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.

Required Files

Optional Files

Output Files

Using densify

Although densify can be run interactively, the input commands are usually prearranged in a file (e.g., "tmpRun.txt") and you invoke the program from the command line like this:

~/bin/densify < tmpRun.txt

Here is an annotated sample "tmpRun.txt" file showing the input commands:

SHAPEFILES/PreviousShapeFile       (input shape)
2 100 1.67773                      (K (power of 2), search range (km), random seed)
SHAPEFILES/CurrentShapeFile        (output shape) <--At this point the map-averaged shape at a higher resolution is made
1                                  (more iteration) <--At this point we begin the slopes to heights integration
.005                               (fraction of points used for conditioning) <--These are sample heights we select for the slope->heights integration 
.025                               (conditioning weight)
1                                  (more iterations) <--More slope to heights integration
0                                  (end program)

The input commands are:

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 proceeds 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 and vast areas are unknown. In these cases, conditioning heights are also taken from the input model as well. Specify this option by using a negative value for K (usually -2).

densify then 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. SIGMA.TXT can be displayed as an image to show areas that might need further work.

After it completes the commands in the file, densify gives these options:

     0. end program
     1. proceed to iteration

If you enter '0', the output shape model will be the height averaged result.

The entire script, with the output model called SHAPEX.TXT and '0' entered to the perform no iterations, looks like this:

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

If you enter '1', the program prompts:

     input fraction

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

The program prompts:

     input weight

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

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

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

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

By tradition, usually use:

If there have been no problems after you complete this run, at the command line enter:


After another densification, when SHAPEX.TXT is Q=512, at the command line enter:


SHAPE.TXT is also Q=512 and you need to update that as well.

At the command line enter:

     chmod +w SHAPE.TXT


If you want to run densify interactively, the initial inputs are:

densify will then prompt you for the remaining inputs and iterations.

(Compiled by TC)