Title: Description of Shape Models Author: Eric E. Palmer Date: 24 July 2021 To support the testing of the shape modeling software for the OSIRIS-REx mission, four shape models were synthetically generated: Shape1, Shape2, Shape3, Shape4. These models were all based upon the Nolan, et al., (2013) radar digital terrain model (DTM). The first step of generating a synthetic DTM was to vary the source object based upon the uncertainty of the model. The radar data for the radar model (Nolan et al., 2013) was quite good which meant that there was high confidence that the radar DTM of Bennu was close to the actual shape of Bennu. The level of error was expected to be about four meters at the equator and 20 meters near the poles. Dr. Robert Gaskell took the general shape of the Nolan model and added an overall height variation that fell within these error expectations. The second step of generating a synthetic DTM is to add realistic features to its surface. Dr. Gaskell used a program called CreatorP, which is a FORTRAN program that adds craters, boulders (rocks), albedo features and warps the overall surface to create different length scales of roughness. While there is a parameter file that is used to configure some of the software's distribution and size of features, usually the program itself is modified to tailor its output to match the desired output, i.e. both the code and the parameter file are tweaked until the output model approaches the expectations for a particular asteroid/target. ---------------------------------------------------------------------------- Shape1 - Global This shape was never used for testing. It was used to provide synthetic images that were used in public relations. It contains some typical asteroid features (craters and boulders) but the overall shape was not changed. It is not available for archiving. ---------------------------------------------------------------------------- Shape2 - Global Shape2 was used during the mission's first attempt to demonstrate that the software could functioned. This test was called a "System Level" test. Shape2 consisted of a 1,600,000 vector model, which is approximately 75cm GSD. The overall model shape had been varied from the radar shape model. The model did not have albedo or any higher resolution DTMs associated with it. While it allowed the simulation of the Approach mission phase, it lacked sufficient ground sample distance (GSD) to provide usable images during Preliminary Survey, which needed 15cm GSD. This model is of limited use because it lacks both albedo and any associated high resolution data. ---------------------------------------------------------------------------- Shape3 - Global The Shape3 model was used quite extensively during the testing of the SPC software. The model had an overall shape modification which included small scale roughness, large boulders, craters and albedo features. There were very large boulders scattered across the surface, some of which were over 20m wide. A circular annulus of slightly brighter terrain around craters was added to simulate impact ejecta based upon what is seen with lunar craters. Three locations were denoted as sample collection sites (a.k.a touch and go or TAG sites). These sites provided a wide range of areas in which to test the functionality of the software. TAG 1 -8.0 Latitude, 97.2 East Longitude - Least rough region, low latitude Tag 2 -10.2 Latitude, 25.8 East Longitude - Medium roughness, low latitude Tag 3 +45.5 Latitude, 245.3 East Longitude - Rough region, high latitude TAG 1 was the main site that was used for testing and planning. It was the one in which extra high resolution DTMs were created. This dataset was used to show that SPC could generate a shape model that met mission requirements, both without and with navigation error. Additionally, an expansive suite of tests were conducted to identify parameters that impacted the quality of the testing DTMs. They included the impact of navigator error, latitude, number of images, observation angles of the images, resolution of the images, photometric function and benefits of limb images. More information on these tests are available at Palmer et al., (2021) ---------------------------------------------------------------------------- Shape4 - Global Shape4 was created in order to conduct end-to-end testing of the shape modeling process. The shape model was created and tests conducted without the shape modeling team having access to the truth model, which simulates what it will be like in flight -- having only images and not a truth DTM. Shape4 was not as rough as Shape3, which was done on purpose. The OSIRIS-REx mission, before launch, was expecting to find a region on the surface that was mostly devoid of hazards of 25 meters in radius. Shape3 had no regions that met the OSIRIS-REx design parameters. Thus, Shape4 was created with a smoother shape, to simulate regolith ponding regions on Eros. The first versions of Shape4 were still too rough to meet OSIRIS-REx's requirements for a suitable site to conduct sample collection operations. Several iterations of smoothing were conducted until the variation in slopes in the TAG site was suitable. The TAG site used for Shape4 was -10 latitude and 350 longitude. More information on these tests are available at Weirich et al., (2021). The overall shape of Shape4 was altered, as before, from the radar DTMs. In order to support wide variations in testing, boulders and roughness were added into the model as two separate functions. Boulders were set to be smaller than with Shape3. The frequency distribution was set to be a minimum near 0 longitude and a maximum at 180 degrees longitude, with an increasing/decreasing sinusoidal function. Roughness was also set as a sinusoidal function, but a shorter period. Minimum roughness was at 0 and 180 degrees longitude, while maximum roughness was set at 90 and 270 degrees longitude. ---------------------------------------------------------------------------- Testing Results Model - 75cm Global As part of the testing, Shape 4 was used to create images that were used during the mission evaluation test called F4. This simulated the mission phases Approach and Preliminary Survey. It was based upon the synthetic data that covered Approach that had a pixel size down to 35cm in the equatorial regions. It also include the Preliminary Survey that flew over the poles and had a higher phase angle over the equator, but the images' pixel size was about 75cm. This shape model was sampled at 75cm from 35cm data source DTM data. ---------------------------------------------------------------------------- Testing Results Model - 35cm Global As part of the testing, Shape 4 was used to create images that were used during the mission evaluation test called F6. This simulated the mission phases Detailed Survey and was a continuation of the F4 test. It was based upon the synthetic data that was used in the F4 test and included the original Detailed Survey data that has two observation stations at mid-latitudes at 5cm image pixel size. This shape model was sampled at 35cm from 18cm data source DTM data. ---------------------------------------------------------------------------- Formats The data are provided in the following formats and resolutions. ICQ Implicitly Connected Quadrangles format is described in the icqmodel.txt document. This is the working format for the SPC shape model. It contains a single parameter that defines the number of vertices of the model. For this distribution the following GSD are provided. All of the resolutions of the DTMs are derived from the highest GSD model and downsampled (JRW edit: Arn't they progressively built up from the worst resolution?). Q Vertices GSD 64 25,000 600cm 128 100,000 300cm 256 400,000 150cm 512 1,600,000 75cm These vertices are in body-fixed space with the X-axis denoting 0 longitude and the Z-axis the pole. The list of vertices are in Cartesian space as an X, Y, Z set. The file can contain a fourth parameter, which for SPC is the surface albedo of the vertex. The albedo values range between 0 and 2.0. While physical albedo's range between 0 and 1.0, to save memory space, SPC rescales the values from a 8-bit byte that ranges between 0 and 200 to 0 to 2.00. (JRW edit: Not sure how this saves memory space. As written it sounds more like it was done to produce a finer scale for the albedo.)