Description of the Gaskell Itokawa Shape Model bundle V1.1
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Bundle Generation Date: 2021-05-21
Peer Review: Neese_Richardson_Mueller_Migration
Discipline node: Small Bodies Node
Content description for the Gaskell Itokawa Shape Model bundle
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Note: This bundle was migrated to PDS4 from the PDS3 data set HAY-A-AMICA-5-ITOKAWASHAPE-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 25143 Itokawa is based on 775 Hayabusa AMICA
images taken from Sept. 11 through Nov. 12, 2005. The shape model was
derived by Robert Gaskell and is described in Gaskell et al. 2006. Four
levels of resolution are included.
Additional information about the model and the images from which it is
derived may be found in Gaskell et al. 2006b and Gaskell 2005. The
version of the model included here was prepared on August 29, 2007.
The model was constructed from 871 L-maps, three dimensional
representations of portions of the surface whose centers are control
points. Each L-map represents about 10,000 surface points. The
coordinate system is a right-handed Cartesian body-fixed frame defined
with the z-axis passing through the rotation pole and the x-axis passing
through zero longitude which is defined by the 'black rock' (lat 3.357 deg
S, lon 0), a named feature on the surface. The model is referred to the
following pole:
BODY2025143_POLE_RA = ( 90.02564 0 0 )
BODY2025143_POLE_DEC = (-67.02704 0 0 )
BODY2025143_PM = ( 129.73000 712.14376110 0 )
Some parameters relating to this model:
Number of control points: 871 (each tied to 99x99=9801 surface vectors)
Number of measurements: 90720 (104 per control point)
Number of images: 775
Formal 1 sigma uncertainties from the solution:
Control point location uncertainty: 35 cm
Spacecraft position uncertainty: 2 m
Camera pointing uncertainty: .15 mrad
(The control point location uncertainty refers to the vector with 3
degrees of
freedom. The uncertainty for each vector component separately is 20 cm.)
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 Hayabusa AMICA images used to
generate this model. It is provided in the 'data' directory.
A text file, 'icqm.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.
References
=======
Gaskell R., O. Barnouin-Jha, D. Scheeres, T. Mukai, N. Hirata, S. Abe, J.
Saito, M. Ishiguro, T. Kubota, T. Hashimoto, J. Kawaguchi, M. Yoshikawa,
K. Shirakawa, T. Kominato, Landmark navigation studies and target
characterization in the Hayabusa encounter with Itokawa, AIAA paper
2006-6660, AAS/AIAA Astrodynamics Specialists Conf., Keystone, CO, 2006.
[GASKELLETAL2006]
Gaskell R.W., J. Saito, M. Ishiguro, T. Kubota, T. Hashimoto, N. Hirata,
S. Abe, O. Barnouin-Jha, and D. Scheeres, Global topography of asteroid
25143 Itokawa, Abstract 1876, 37th Lunar and Planetary Science Conference,
2006. [GASKELLETAL2006B]
Gaskell R.W., Landmark navigation and target characterization in a
simulated Itokawa encounter, AAS paper 05-289, AAS/AIAA Astrodynamics
Specialists Conf., Lake Tahoe, CA, 2005. [GASKELL2005]"
Caveats to the data user
========================
The RMS formal uncertainty in control point location had a vector
magnitude of 35 cm, about 20 cm per degree of freedom (dof). The RMS post
fit residual of the control point solution was 15 cm/dof. 90720
observations of 775 images and 871 control points went into the solution,
including control point locations in the images, on the lit limbs and
relative to one another due to L-map overlaps. Although the model is
sufficiently detailed to do so, no attempt was made to provide an accurate
representation of the underside of the large Yoshinodai boulder.
Note that he 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.