From tduxbury@gmu.edu Wed Mar 6 14:10:25 2013 Date: Wed, 06 Mar 2013 11:10:22 -0800 From: Thomas Duxbury To: drbitboy@gmail.com Cc: sbnpsa@astro.umd.edu, Jian-Yang Li , "Edwin J. (GSFC-6901) Grayzeck" , thomas.h.morgan@nasa.gov, "William (HQ-DG000) Knopf" , Peter Thomas , "Kenneth P (382E) Klaasen" , Ludmilla Kolokolova Subject: Re: Shape model consistency metrics Brian, thank you for your analysis on summing the X,Y,Z coordinates of the various shape models, also finding that these sums were not zero. This is what I also did which made me wonder "why was the sum of the X,Y,Z cartesian coordinates not = zero the first iteration?" Since the sums were not zero, I then suggested (not required) that that a simple sentence be added to dataset.cat (and elsewhere as appropriate) defining / describing how / why the center was chosen. A lot of times, an early version of a shape model have the sums = zero but then this origin is not changed and additional vertices are added and the sums drift away from zero by small amounts. But if there was a reason why a center was chosen knowing that the sums of the cartesian coordinates are not zero, then this should be described, especially if the vertices were not uniformly distributed. As I recall, the most exact way of finding the center of figure is integrating the volume - the same for finding the principal axes and moments of inertia is to integrate something that deals with the volume. If this is done then I could imaging / guess / would not be surprised that this derived center of figure could give non-zero sums to the simple addition of the X, Y and Z coordinates. So someone producing a shape model for archive could give the following possible explanations of the center of the shape model: 1) The center of the shape model is the center of figure defined to be where the sum of the X, Y, Z cartesian coordinates are zero. 2) The center of the shape model is near the center of figure defined to be where the sum of the X, Y, Z cartesian coordinates would be zero. The offsets of the centers of the shape model and this center of figure are small / negligible / are not relevant in the use of the shape model / are = ??m meters in X, ??? meters in Y, ? meters in Z / or some other explanations 3) The center of the shape model is near the center of figure where the sum of the X, Y, Z cartesian coordinates would be zero but is offset in the ??? axis(es) by x,y,z meters so that vertices vectors are unique and only intercept the highly irregular surface as they extend from the center at only one point. 4) The center of the shape model and principal axes / radii were determined by numerically integrating the volume of the complex shape and iterating the integration by adjusting the vertices center and coordinate axes such that the cross-moments of inertia were zero. 5) The center of the shape model was chosen to align with the center of mass that is offset from the center of figure by X=?, Y=?, Z=? 6) other Then someone producing a shape model for archive could give the following possible explanations of how the radii / principal axes were computed 1) a tri-axial ellipse was fit to all vertices vectors assuming the the X,Y,Z cartesian coordinates were aligned with the principal axes solving for the 3 radii a,b,c. No adjustments were made to the vertices vectors. 2) a tri-axial ellipse was fit to all vertices vectors assuming the the X,Y,Z cartesian coordinates were aligned with the principal axes solving for the 3 radii a,b,c and a center of figure offset and was iterated until the center offset values were zero, translating the vertices vectors to the new center each iteration. 3) a tri-axial ellipse was fit to all vertices vectors solving for the 3 radii a,b,c, a center of figure offset and a rotation angle to best align the 3 radii with the principal axes and was iterated until the center offset values were zero. After each iteration, the vertices vectors were translated and rotated to remove a center offset and rotation angle. 4) The center of the shape model and principal axes/ radii were determined by numerically integrating the volume of the complex shape and iterating the integration by adjusting the vertices center and coordinate axes such that the cross-moments of inertia were zero. 5) OTHER If a spin pole and/or prime meridian were defined as givens, then the description of defining the center of the shape model and its radii should include how these constraints were implemented. In the shape model descriptions (dataset.cat), most of the above recommended descriptions are included to some extent so this is why I only made recommendation and not liens to add a little more detail. It would be nice to have just a little more detail on how the center, principal axes, radii, and moments of inertia were defined if some of this detail is lacking. Tom