SHAP7 version of the 67P/Churyumov-Gerasimenko nucleus shape model

The SPG versions of the dataset represent the shape models of the nucleus
of comet 67P/Churyumov-Gerasimenko that have been derived using stereo-
photogrammetric methods. Images obtained with the Narrow Angle Camera of
the Optical, Spectroscopic, and Infrared Remote Imaging System (OSIRIS)
instrument were used in constructing these models.

The shape models presented here were developed at DLR (Berlin, Germany)
by Frank Preusker and Frank Scholten using the stereo-photogrammetric 
(SPG) technique. Details about the SPG technique as well as details about
the full reconstruction process of comet 67P/Churyumov-Gerasimenko from
SPG techniques can be found in Preusker et al., 'Shape model, reference
system definition, and cartographic mapping standards for comet
67P/Churyumov-Gerasimenko - Stereo-photogrammetric analysis of
Rosetta/OSIRIS image data' A&A 583, A33, 2015 [PREUSKERETAL2015], and in
Preusker et al., “The global meter-level shape model of comet
67P/Churyumov-Gerasimenko” A&A 607, L1, 2017 [PREUSKERETAL2017].

Additional information about the nucleus of 67P can be found in Sierks et
al., 'On the nucleus structure and activity of comet
67P/Churyumov-Gerasimenko', Science 347, aaa1044, 2014 [SIERKSETAL2014].

SHAP7 version of the model
---------------------------

The SHAP7 model represents the final version of the SPG shape models. It
has been derived from 1531 OSIRIS/NAC images acquired between 5 Aug 2014
and 13 Feb 2016 (see below). During this time frame, both, the northern
and the southern hemisphere, were illuminated in a way that the selected
dataset allowed for a global SPG processing and the derived SHAP7 model
covers the entire surface of 67P. The SHAP7 model is defined in the
Cheops reference frame [PREUSKERETAL2015].

The original full resolution version of the SHAP7 model consists of ~44M
facets. It has an average lateral sampling distance of ~1-1.5 m.
The derived reduced resolution versions (4M, 2M, 500K, 125K, 50K facets)
have larger sampling distances, scaling inversely with the number of
facets.


TABLE: Parameters of images used to reconstruct the SPG SHAP7 model.

  UTC date of first NAC image:         2014 AUG 05 23:19:14.571
  UTC date of last NAC image:          2016 FEB 13 19:07:40.736
  Number of NAC images:                1531
  Lowest image resolution:             5.2 m/pixel
  Highest image resolution:            0.15 m/pixel
  Typical image resolution:            ~1 m/pixel


Reference Frame and Coordinate System
---------------------------------------

The Cheops reference frame was defined using the SHAP4S shape model and
has been adopted for the standard for all other formats of the 67P shape
model. The orientation of the models in the J2000 Equatorial frame
(EME2000) is described in Scholten, F. et al., 'Reference Frames and
Mapping Schemes of Comet 67P/C-G' in the PDF document
CHEOPS_REF_FRAME_V1.PDF in the DOCUMENTS directory.
The body's coordinate system was defined with the +Z axis in the
direction of the spin axis and the prime meridian (+X axis) is defined
such that the center of the large boulder named Cheops is at a longitude
+142.35 degrees, following the IAU definition presented in the document
CHEOPS_REF_FRAME_V1.PDF. The +Y axis completes the right-hand coordinate
system. The body center is not exactly coincident with its center of
gravity, but the offset is within the uncertainties derived for the
surface positions. 

Data Formats
--------------

The models are presented in the standard PDSSBN vertex/triangular plate
format (see PDSSBN_PLATE_SHAPE_DEF.ASC in the documents directory) with
dimensions of km in cartesian coordinates. The files are presented with
VRML wrappers that allow the model to be displayed with existing VRML
viewers that are freely available (e.g. INSTANT PLAYER, OCTAGA, CORTONA,
etc.).

In addition to the PDS formatted files, the models have also been
converted to DSK kernels that can be used with the SPICE utilities.

For the complex shape of 67P, spherical coordinates (lat/long/radius)
result in multiple values in some regions of the nucleus, so the model is
not presented in this form.

Model Resolutions
-------------------

The SPG SHAP7 model is provided in multiple resolutions, allowing
calculations to be optimized for a given problem when the highest
resolution is not needed. The highest resolution model has ~44M facets,
with additional versions degraded to resolutions with 4M, 2M, 500k, 125k
and 50k facets. The reduction in resolution was achieved using a
quadratic edge-collapse decimation technique.

Information contained in the filenames: 

CG_DLR_SPG_SHAP7_500K.WRL
^   ^    ^    ^    ^   ^---- File format (VRML, SPICE DSK) 
|   |    |    |    |-------- Resolution (# triangular plates)
|   |    |    |------------- Shape model generation SHAPXXX
|   |    |------------------ Production Technique (SPG)
|   |----------------------- Site of model development
|--------------------------- Comet C-G

Details about the SPG SHAP7 files

CG_DLR_SPG_SHAP7_4M.WRL   - 1999975 vertices / 3999962 triang. plates
CG_DLR_SPG_SHAP7_2M.WRL   -  999928 vertices / 1999860 triang. plates
CG_DLR_SPG_SHAP7_500K.WRL -  249953 vertices /  499902 triang. plates
CG_DLR_SPG_SHAP7_125K.WRL -   62471 vertices /  124938 triang. plates
CG_DLR_SPG_SHAP7_50K.WRL  -   24990 vertices /   49976 triang. plates

TABLE: Shape Model Characteristics (for the SPG SHAP7 model).

  Surface Area:          51.7 km^2
  Volume:                18.56 +/- 0.02 km^3
  Mean diameter:         3.285 km (diameter of sphere of equivalent vol.)