Description of the Gaskell Eros Shape Model bundle V1.0 ======================================================= Bundle Generation Date: 2020-09-22 Peer Review: Neese_Richardson_Mueller_Migration Discipline node: Small Bodies Node Content description for the Gaskell Eros Shape Model bundle =========================================================== Note: This bundle was migrated to PDS4 from the PDS3 data set NEAR-A-MSI-5-EROSSHAPE-V1.0. For PDS3 data sets migrated to PDS4, the following text is taken verbatim from the data set description and confidence level note of the PDS3 data set catalog file. In these cases, some details may not be correct as a description of the PDS4 bundle. This shape model of asteroid 433 Eros is based on 21135 NEAR MSI images taken from Feb. 2000 through Feb. 2001. The shape model was derived by Robert Gaskell and is described in Gaskell et al. 2007. Four levels of resolution are included. Additional information about the method for deriving the model may be found in Gaskell et al. 2005. The version of the model included here was prepared on Feb. 23, 2008. The coordinate system of the model is described in the pck kernel prepared by Don Yeomans and Alex Konopliv, 'eros_alex.tpc.txt' in the document directory. Number of landmarks: 9002 (90 million vectors) Formal position uncertainty: 1.1 m/component Number of images: 21135 Pointing uncertainty: .025 mrad Spacecraft position uncertainty: 0.64 m Pointing residuals (relative to catalog file, not CK): 0.55 mrad Range residuals (relative to SPKs): 1.21 m Number of measurements: 1184010 Number of measurements per landmark: 131 RMS LMK location residual: 1.8 m/component The models were originally prepared in the Implicitly Connected Quadrilateral (ICQ) format, and files in four levels of resolution are provided in the directory 'data/quad'. The filenames are of the form quadxxxq.tab, where xxx is the value of Q (an indicator of the resolution). See below for the full definition of Q and the ICQ format. The models are also provided in a vertex-facet format, in directory 'data/vertex'. The four data files in this subdirectory are derived from the ICQ format files in the 'data/quad' directory. The filenames have the form verxxxq.tab, where xxx is the value of Q for the original ICQ model. In this way it is clear which vertex-facet model comes from which ICQ model. The file 'imagelist.tab' is a list of the NEAR MSI images used to generate this model. It is provided in the 'data' directory. A text file, 'icqmodel.txt' is provided in the 'document' directory which describes the ICQ format and the derivation of the vertex-facet versions. Some of the information in that file is reproduced below. ICQ Format Description =============== The global topography models (GTM) are presented here in an implicitly connected quadrilateral (ICQ) format. The vertices are labeled as though they were grid points on the faces of a cube 0 --------- I --------- Q 0 . . . . . . . . . | . . . . . . . . . | . . . . . . . . . | . . . . . . . . . J . . . . F. . . . . | . . . . . . . . . | . . . . . . . . . | . . . . . . . . . Q . . . . . . . . . so that each of the six faces (F) contains (Q+1)^2 vertices v(I,J,F) (I=0,Q; J=0,Q) and Q^2 facets f(I,J,F) (I=0,Q-1; J=0,Q-1). The facet f(I,J,F) implicitly has the vertices v(I,J,F), v(I,J+1,F), v(I+1,J+1,F), v(I+1,J,F). If the cube is unfolded, the six faces are arranged as ----------- | | | 1 | | | ----------------------------------------- | | | | | | 5 | 4 | 3 | 2 | | | | | | ----------------------------------------- | | | 6 | | | ----------- At each of the 12 edges of the cube, faces share common vertices so that, for example, the last row of face 1 has the same vertices as the first row of face 2. The common edge vertices are, with I=(0,Q), v(I,Q,6)=v(Q-I,Q,4) v(I,0,6)=v(I,Q,2) v(I,0,5)=v(Q,Q-I,1) v(I,0,4)=v(Q-i,0,1) v(I,0,3)=v(0,I,1) v(I,0,2)=v(I,Q,1) v(q,I,6)=v(I,Q,5) v(q,I,5)=v(0,I,4) v(q,I,4)=v(0,I,3) v(q,I,3)=v(0,I,2) v(0,I,6)=v(Q-I,Q,3) v(0,I,5)=v(Q,I,2) and the eight corners share vertices from three faces: v(0,0,1) = v(0,0,3) = v(Q,0,4) v(0,Q,1) = v(0,0,2) = v(Q,0,3) v(Q,0,1) = v(0,0,4) = v(Q,0,5) v(Q,Q,1) = v(0,0,5) = v(Q,0,2) v(0,0,6) = v(0,Q,2) = v(Q,Q,3) v(0,Q,6) = v(0,Q,3) = v(Q,Q,4) v(Q,0,6) = v(0,Q,5) = v(Q,Q,2) v(Q,Q,6) = v(0,Q,4) = v(Q,Q,5) Thus of the 6(Q+1)^2 labeled vertices, only 6Q^2+2 are independent. The file structure is quite simple. The first line contains the value of Q, and is followed by 6(Q+1)^2 lines containing the vertices. A piece of Fortran code for reading the file would look like: READ(10,*) Q DO F=1,6 DO J=0,Q DO I=0,Q READ(10,*) (V(K,I,J,F), K=1,3) ENDDO ENDDO ENDDO Here the vertices are represented by three-vectors. In some cases extra components are added representing albedo, color, surface gravity, or other surface characteristics. Since the labeling scheme implicitly contains the connectivity, no facet table is necessary. The quadrilateral facets in the model are not necessarily flat, since there is no guarantee that the four vertices are coplanar. The facet normals are defined by the cross product of their diagonals. This approximation presents no real difficulty because the spacings of the vertices are very small compared to the size of the body. The standard form (Q=512) has 1.57 million vertices. Although it is not necessary, it is convenient to take Q to be a power of 2. Because of this choice, it is easy to 'dumb down' a model by increasing the spacing by factors of 2. Vertices of the form v(2I,2J,F) are retained and the others discarded. Because of the quadrilateral facet structure, the models can also be 'densified' through bilinear interpolation. Caveats to the data user ======================== Note that the vertex-facet versions of the model have some duplicate vertices on the edges and corners of the cube. The duplicate vertices are not used in the facet table, resulting in the presence of some vertices in the vertex table which do not appear in the facet table. This does not affect the correctness of the vertex-facet version.