NASA Technical Reports Server (NTRS) 20090009767: Fast Ray Tracing of Lunar Digital Elevation Models

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FAST RAY TRACING OF LUNAR DIGITAL ELEVATION MODELS. T. P. McClanahan'
oth..icc1gnaii:nasa.ov. L.G. Evans2, R.D. Starr, I. Mitrofanov4, NASA Goddard Space Flight Center,
Building 2 Room 129, Greenbelt, MD 20771. 'Computer Sciences Corp. at NASAJGSFC 3Cathoiic University at
NASA!GSFC 4institute for Space Research, Moscow, Russia
Introduction: Ray-tracing (RT) of Lunar Digital increases effectively limit the scale or resolution of the
Elevation Models (DEM)'s is performed to virtually model size aL In this research, we effectively mini-
derive the degree of radiation incident to terrain as a mize the search space size si and floating point opera-
function of time, orbital and ephemeris constraints [I- tions [11, by using vector-point operations, thereby sig-
4]. This process is an integral modeling process in nificantly improving the algorithm run..tinw.
lunar polar research and exploration due to the present Methods: Significant computational performance
paucity of terrain information at the poles and mission gains are obtained by not triangulating the DEM sur-
planning activities for the anticipated spring 2009 face points into plates. instead, vector-point opera-
launch of the Lunar Reconnaissance Orbiter (LRO). tions facilitate fast evaluation for direct illumination
As part of the Lunar Exploration Neutron Detector and secondary illumination processes, lines (1-9). In
(LEND) and Lunar Crater Observation and Sensing this approach DEM surface points are warped to a
Satellite (LCROSS) preparations RI methods are used sphere (Moon 1734.8 km radius) illustrated in Figure
to estimate the critical conditions presented by the 1. Given point pi as an arbitrary pixel in image OEM
combined effects of high latitude, terrain and the fot which illumination conditions are required, each
moons low obliquity [5-7]. These factors yield low point must be evaluated for the possibility of shading.
incident solar illumination and subsequently extreme The Sun is oriented at Cartesian position sun. vi de-
thermal, and radiation conditions. fines the vector between the sun and p (1). sun to p
The presented research uses RT methods both for distance dist (2). (3) normalizes v. (4) defines a
radiation transport modeling in space and regolith re- linear set dvi of distance scalars from sun as interpo-
lated research as well as to derive permanently shad- lants along vi at interval, a (km). dv1 range [dirt, -
owed regions (PSR)'s in high latitude topographic min- range, distil. dvi' = range / a. (5) A discrete set of
ima, e.g craters. These regions are of scientific and Cartesian positions pos a vi are determined by project-
human exploration interest due to the near constant ing from sun along vi at distances defined by set dvi.
(6) npos defines the number of positions in pos to be
low temperatures in PSRs, inferred to be < 100' K.
evaluated for shading of p. (7-11) evaluates each
Hydrogen is thought to have accumulated in PSR's
point in pos as to its elevation by rounding its (xy)
through the combined effects of periodic cometary
coordinates to common coordinates that index the ele-
bombardment andior solar wind processes, and the
vation scalar in v and DEM. In conditions where the
extreme cold which minimizes hydrogen sublimation
elevation z value in the DEM is higher than the z value
[8-9]. RT methods are also of use in surface position
in v, a shade' condition is identified.
optimization for future illumination dependent on-
These steps provide a nearly direct access method-
surface resources e.g. power and communications
ology that significantly minimizes the search space for
equipment [10-Il].
evaluating illumination for each p, evaluating only
However, ray-tracing methods are computationally
possible occluding positions along vector, v,. Starting
slow due to the inherent vector transport process and
evaluation of pos at dirt,, and working towards the sun
the subsequent search phase required to evaluate, iden-
along v, facilitates a run time minimization of search-
tify, and interact with surfaces [12]. The issue is exac-
ing dv, by monitoring local elevation conditions and
erbated if the DEM point surface is converted to a
shaded status to terminate the loop. A consequence of
plate model due to the large number of floating point
this approach is that actual intersection points of v,
operations (48) required to evaluate each plate facet
with the surface are not determined. These may be
[13-14]. As a result, the computational complexity
approximated using interpolation with sun distances to
incurred in evaluating direct illumination without op-
nearest neighbor points.
timization constraints increases exponentially as a
Secondary vector projection processes require sur-
function of the product of the number of surfaces n in
face intersection points and surface normal informa-
the model evaluated against all other surfaces during
tion. A given vector-surface intersection point posi is
search s n-1, floating point operations per surface
obtained by proceeding through each element in pos
evaluation f number of vectors projected per pixel 1vi,
starting at pi to determine the closest shading point p
O(nsF). In this case, the exponential time-complexity
Surface normals at each point are pre-calculated for
each model by taking the vector cross product between ally occur in the bottoms of craters below the southern
adjacent points. These are averaged to yield DEM rim, area1661 km2 (red) Note: linear and blocky
normals for each point. structures in the DEM are false positives incurred by
elevation mis-registrations in the overlay of the
1. v-p,- sun Clementine source imagery during OEM formulation.
2. dist1 Updates to these products will increase the resolution
3. v v / dish and accuracy of OEM's, modifying the stated PSR and
4. dv, ±nterpol(dist, range, (X) illuminated areas.
5. pus = sun y*dv.
6 npos = range/o.
7. forjl,nposdo
8. x = round(os(0j))
9, v round(jos( if))
10. if DEM(x,y) gt pos(2f) then
Shade
11. endior
Clementine
North Pole Sun: point source
Max
North Polar
Illumination
1 54 deg
(0,00)
dv pdist *range
p9 = sun + Figure 2. North Polar Permanently Shadowed Regions
Shaded' it p(z) gt p9s,(2:)
derived from Clementine OEM using ray-tracing meth-
ods for 360, F rotation increments during North Polar
Figure 1. Example of single vector direct solar illumi- summer when polar inclination = 1 .54', yielding maxi-
nation. Illumination process is optimized by minimiz- mum illumination. Demonstration used the described
ing the number of floating point operations for surface enhanced ray-tracing methods to derive illumination.
evaluations as well as the ray-tracing search space.
Multiple vector projections are also supported References:
[1] Blewett T.B. LEAG-ICEUM-SSR, (2008) [2]
Results: Figure 2 illustrates both permanently shad- Slade M. A. Lun Crat Ohs and Sens, Sat Site Se!., [3]
owed and illuminated regions of the Clementine North Matsushima T. Earth and Space 2006, Const. and
Polar DEM containing 80-90 deg north latitude [15- Lag. in Chal!. Env. (2006) [4] Margot J.L. et, at. Sci-
16]. Image resolution (606x606) pixels 1km2/ pixel ence, 284:1658-1660 (1999) [5] Garrick-Bethell I. et.
during summer where the north pole is inclined I at. LPSC XXXVI, (2005) [6] Chin G. LPSC XXXVJI
(2006) [73 Chin G. Space Sci. Rev. 129:391-419
towards the sun, yielding maximum north polar illumi-
(2007) [81 Arnold J. JOR, 84:5659-5668 (1979) [9]
nation. In this approach, the sun position was rotated
Crider D.H. JGR 108(E7)(2002) [10] Fincannon H.J.
in I increments around the OEM for 360 degrees
6' Int, Energy Cony. and Eng. Conf., (2008) [11] Fin-
yielding 360 images. Without further optimization,
cannon ILL 46'' AJAA Aero. Sc!. Meet. and Exhib
each point's direct illumination is evaluated against all
(2008) [12] Hurley J. Intel Tech .Journ. 9(02) (2005)
points n for shading incurring Inj2 367236 evalua-
[13] Badouei D. Graphics Gems (1990) [14] O'Rourke
tions to determine the maps direct shading for each
Comp. Geom. in C (1997) [15] Nozette S. et. ai. Sci-
image. Only a spaced points along the incident solar
ence (1994) [16] Rosiek M.R. LPSC XXXVIII (2007)
vector v are evaluated with maximum required search
[17] Mitrofanov I. Astrobiology (2008)
map corner to corner range 808 points. By integrat-
ing through the image stack in each pixel, degree of
illumination is determined. Highlighted PSRs gener-