.NH 1
Analysis of the Model
.PP
At any stage of the design,
the model can be used to make
realistic images and engineering drawings.
This capability is so powerful that it ordinarily justifies the
construction of the model.
However, the real payoff from building a geometric model
comes when it is time to analyze it.
The model can be subjected to
numerous engineering analyses, allowing
the effects of varying many parameters
to be studied in a controlled way.
.NH 2
Image Rendering
.PP
Many phenomena that are difficult to model with the more traditional
scan-line-order rendering of faceted objects
can be handled simply and elegantly with ray-tracing,
although with a much greater cost in processing time.
For example,
in most conventional rendering packages, shadows are implemented
by way of a subterfuge:
computing the \fIshadow volumes\fR cast from the light source by each object
as a set of ``neutral density''
polygons, and using them to influence the shading
decisions for the actual surfaces underneath them.
On the other hand, an illumination model
based on ray-tracing merely needs to fire a ray at each light source
to determine the total light energy at each point.
While the computational requirements of this strategy can be explosive
in a model with multiple light sources and many reflective objects,
the ease and accuracy of using ray-tracing to
model the laws of optics to
create very realistic renderings
has not yet been surpassed by other techniques.
.PP
By dithering the location of the light sources, this can also give
a statistically good rendition of shadow penumbra effects.
Unlike conventional rendering packages, ray-tracing also makes it
easy to deal with objects that are partly or entirely reflective,
and with transparent objects that have varying refractive indices.
Furthermore, by applying the proper sorts of dither,
.[
Cook distributed ray tracing
.]
motion-blur, depth-of-field, translucency, and other effects are
easily achieved.
The ease and flexibility
of modeling point-sampled optics with the ray-tracing paradigm
is demonstrated by the lighting model code supplied with RT, which implements
all of the features listed above
(reflection, refraction, perspective views, penumbras, texture maps
translucency, etc.)
in less than 400 lines of heavily-commented ``\fBC\fR'' code.
.PP
An example of these features is shown in plate 4.1.
Plate 4.2 shows the outside and inside (skin removed) views of
a BMP vehicle, and plate 4.3 depicts an M109 with glass armor.
Using simple techniques such as making selected parts of the model
invisible or transparent, a designer can create powerful images
for communicating the design.
.NH 2
Animation
.PP
Given that lighting model code exists for making static images,
it is a relatively straightforward matter to develop code which
can animate the position of the ``eye'' (camera) and light sources
within the model, and only a modest additional effort to develop
the capability of articulating the model geometry itself.
Using animation can be very beneficial when trying to gain
comprehension of complex geometry, especially when the object
being modeled has never actually been physically built before.
There is nothing that communicates complex structures
more clearly than observing them passing by smoothly.
In addition to assisting the design engineers understanding
the geometry that they are developing, an animation capability
is also very useful as a sales tool, both for aiding management
understanding of the design project, and also to convey
a strong message to potential customers.
.PP
In addition to being a valuable visualization tool,
animation capabilities can be used to experimentally
verify that moving assemblies do not interfere with each
other, and that adequate clearances exist.
This can be extended still further by explicitly modeling
the presence of humans as part of the geometry,
allowing pre-prototype testing and evaluation of
the ``human factors'' portions of the design.
Verification that the design provides
adequate space to move around in, easily accessible
operating controls, proper provisions for seating,
and doorways that are convenient for non-contortionists
can be achieved through animation studies.
.NH 2
Lens Design
.PP
The power of the lighting model code
can further extended by making a provision to record the paths of all
the rays followed when computing the light intensity for each pixel,
and recording them in an auxiliary file.
In addition to being a fantastic debugging tool, this capability
allows one to follow the path of the light rays passing through lenses
and being reflected by mirrors while performing image rendering.
All these calculations are necessary simply to obtain a rendering
of the scene, but if one is actually attempting to use the solid modeling
system to study optics, the effects on the actual light ray paths
can be obtained with no additional computation.
.PP
Studying the paths of light rays as they are repeatedly bent
by passing from air to glass and back again has traditionally
been a painstaking manual procedure for lens designers.
By developing a solid model of some set of optics under consideration,
it becomes possible to predict lens behavior, including making a
determination of the exact focal length, finding the precise influence of
spherical distortions and edge effects, determining the amount of
image distortion due to internal reflection and scattering,
and finding the level of reflections from the lens mounting hardware.
Furthermore, experiments can be conducted to
determine the effects of adding or removing
baffles, irises, special lens coatings, etc.
This is an unusual but highly profitable coupling of solid models and
analysis codes.
.NH 2
Property Calculations
.PP
In the design of vehicles,
moments and products of inertia play a central role.
Particularly when designing aircraft, weights,
the center of gravity,
and parameters related to inertia are vital aspects of
creating a stable design with high performance.
For ground vehicles and fixed structures these figures are
quite significant, providing a good first estimate of structural
loading, and allowing transportation costs to be assessed.
Moments of inertia are important in determining what conditions
a vehicle may be overturned by maneuvering or impact, and can also
help predict the vehicle's handling when maneuvering over rough terrain.
.[
Deitz improved materiel acquisition
.]
.PP
By applying the Fundamental Theorem of integral calculus and
performing spatial integration of the geometry as sampled by
the ray tracing process,
it is possible to compute
the presented areas and profile shapes from a given viewpoint,
important information to have both for styling and functional design.
.[
Lee Requicha algorithms for computing volume properties solid objects
.]
By combining this spatial integration procedure
with a knowledge of the properties of the various
materials involved (density, etc),
it becomes possible to compute
the mass, center of gravity, moments of inertia,
overturning moments, and other similar engineering assessments.
.[
Thomas calculus
.]
Plate 4.4 shows one planar set of material property samples
from the ray-tracing analysis of an M48 tank.
Such material samples comprise the input information
for the codes which make the property calculations.
.PP
The mass of an object distributed over a region $V$ and having
a density $delta (x, y, z)$ at the point $(x, y, z)$ of $V$
is given by the integral
.EQ
M ~=~ int int int ~ delta (x, y, z) ~ dV ~.
.EN
In the case of sampled geometry, this can be expressed as
.EQ
M ~=~ sum from x sum from y sum from z ~ delta (x, y, z) ~.
.EN
Similarly, the center of gravity is
.EQ
( { int int int ~ x ~ delta (x, y, z) ~ dV } over M ,~
{ int int int ~ y ~ delta (x, y, z) ~ dV } over M ,~
{ int int int ~ z ~ delta (x, y, z) ~ dV } over M ),
.EN
or for sampled geometry
.EQ
( { sum from x sum from y sum from z ~x~ delta (x, y, z) } over M ,~
{ sum from x sum from y sum from z ~y~ delta (x, y, z) } over M ,~
{ sum from x sum from y sum from z ~z~ delta (x, y, z) } over M ).
.EN
The moments of inertia $I$ can be found as
.EQ
I ~=~ (~
{ int int int ~ ( y sup 2 + z sup 2 )~ delta (x, y, z) ~ dV },~
{ int int int ~ ( x sup 2 + z sup 2 )~ delta (x, y, z) ~ dV },~
{ int int int ~ ( x sup 2 + y sup 2 )~ delta (x, y, z) ~ dV } ~ ) ~.
.EN
.PP
These computational techniques can be extended
.[
Blass theoretical physics
.]
to provide the principle second moments and cross products of inertia.
Due to the computational complexity of evaluating these
mechanical design parameters, they have typically
been unavailable to engineers using traditional design approaches.
.NH 2
Drafting
.PP
When a design created on a CAD system is to be produced in
traditional manufacturing facilities
rather than using a fully automated NC plant,
clear and  detailed drawings are a necessity.
Thus, the production of engineering drawings, including
orthogonal views, orthographic projections, and ``exploded views''
from the solid models is an important, if unglamorous, capability.
.[
Lamit teaching descriptive geometry
.]
Once the model is constructed, the designer may define drawings containing an
unlimited number of views,
either standard orthogonal views or views from an arbitrary azimuth and
elevation.
While tolerance specification, 
fully automatic dimensioning, and tolerance indication is a difficult area,
.[
Requicha historical summary
.]
recent research is beginning to provide strategies for implementing them,
.[
Hashimoto automatic dimensioning
.]
and future CAD systems should demand less human intervention
than current ones.
BRL does not have a well developed capability in this area
because of its heavy reliance on color shaded images to communicate
final designs.
.NH 2
Numerical Controlled Milling
.PP
Direct numerical control (NC) of a milling machine provides
the ultimate in ``hard copy'' output.
.[
Voelcker Hunt role solid machining NC verification
.]
NC milling can be
very useful for generating prototypes for initial testing,
where the goal is to produce correct
toolpath computation in a short amount of elapsed time, but
requiring minimal human intervention.
.PP
However, NC milling is
also very important in the mass production of final versions of the design.
In this case, the objective is to compute
toolpaths which result in maximum efficiency of the milling machine.
A man/machine team effort
with human-directed optimization of
the automatically produced NC programs
can result in maximum production rates from
factory automation equipment with minimum waste.
.PP
Automatic toolpath generation is still difficult
due to the complexity of tool/block interference testing,
but various researchers are currently investigating using
a ray-tracing paradigm for toolpath planning.
.NH 2
Structural Analysis
.PP
Currently, most structural analysis and hydrodynamics
analysis is done using finite element mesh (FEM) techniques.
FEM data is normally pre-processed by packages like PATRAN
to develop inputs for NASTRAN, EPIC, ANSYS and other similar programs to
to actually process the mesh data,
including stress testing, computing loading factors, etc.
.PP
An automatic interface from the modeling system to a finite element
representation is a very important capability.
G. Moss at BRL is currently developing a post-processor program which converts
CSG-rep solid models into a boundary form suitable for input to PATRAN-G,
but this is still an active research effort.
.NH 2
Vulnerability Assessments
.PP
An important extension to simple static and dynamic loading of
structures is to consider unexpected dynamic stress caused by
a high-energy source impacting the object being designed.
This could be as ordinary as a rock striking a car traveling at
80 kilometers per hour, hailstones falling from the sky, or
a collision with another vehicle.
On the other hand, if the object being designed is intended for
use in a military setting, the range of threats which must be considered
is greatly enlarged.
Not only designers have to worry about airplanes impacting with large birds,
hail, and rain, they also need to design airplanes to withstand the
buffeting from nearby explosions, flying shrapnel, and various projectiles.
.[
Weaver Deitz solid modeling aircraft survivability
.]
When designing tanks and other ground vehicles,
the designer needs to consider the effects of small arms fire, land mines,
projectiles, and missiles.
Similarly, designers of ocean-going vessels need to concern themselves
with the effects of torpedoes, projectiles, and missiles;
spacecraft designers need to contend with high-velocity particles,
laser beams, and other similar challenges.
For all designs, nuclear effects need to be considered.
.PP
To conduct a ballistic analysis of point burst effects,
BRL has developed a model for lethality and vulnerability estimation
which is used to evaluate the effects of antiarmor weapons used against
ground vehicles, based upon a ray-tracing approach.
.[
Brown slave user manual
.]
.[
Ringers slave analyst guide
.]
Following perforation of a vehicle armor shell by a penetrator, this code
evaluates behind-armor spall cloud effects, described by a cone of debris
extending from the point of armor penetration.
This process is illustrated in plate 4.5, where the red rods depict
the path of the main penetrator, and the blue cone represents the
extent of the debris.
Soft components located within the spall cone are considered to be destroyed
by the debris, while hard components survive unless they are impacted by the
main penetrator.
This code runs interactively and generates a color display to provide
immediate feedback into the design process,
.[
Ozolins islave interactive
.]
an example of which is shown in plate 4.6.
.NH 2
Nuclear Survivability
.PP
When a nuclear weapon is detonated, blast effects, thermal radiation,
electro-magnetic pulse, initial nuclear radiation, and fallout all
pose threats to
equipment and personnel.
The initial nuclear radiation has three main components:
prompt neutrons, neutron-induced secondary gamma particles,
and prompt gamma particles.
.[
Deitz materiel acquisition
.]
The Vehicle Code System (VCS)
.[
Rhodes VCS user manual
.]
.[
Rhodes radiation protection vehicles
.]
considers total dose effects by first deterministically calculating
the transport of radiation to an envelope that surrounds the vehicle, and
then making a stochastic relationship between the radiation at the
source envelope and at the detection point inside
by using ray-tracing to track each particle through the vehicle.
Plate 4.7 shows a rendering of a Tank Test Bed (TTB) concept vehicle,
and a version displayed with a false coloring scheme, depicting the
proportions of radiation leakage that reached the detection point inside.
A surprising result of this test was the unexpectedly high proportion of
radiation that entered the vehicle through the narrow front plate;
examination of the model did not suggest that it was inadequate.
The ability to find and correct this type of deficiency early in the
design process is extremely important, and can result in huge cost savings.
.NH 2
Signatures by ``Geometric Sampling''
.PP
In the next several sections the topic of predictive signature
analysis will be examined for a variety of wavelengths using
several slightly different approaches.
The development of predictive
signature analysis is like a double-edged sword;  it can be
useful both for developing techniques for reducing the
signatures of existing vehicles by guiding product improvement plans,
as well as ensuring that new vehicles being designed have an acceptably low
signature for frequency ranges of interest, but this kind of analysis
can also be used to guide testing and 
optimize designs for new or improved sensing systems.
.PP
It is very important to note that
point-sampled geometric optics
only bears a statistical relationship to the
effects actually obtained from a wave optics analysis (or experiment),
and that accounting for phase-related effects is difficult at best.
Thus, developing predictive models does not relieve the designer of
the responsibility for conducting tests with scale and full size physical
models of the prototype, but having these predictive models should
make the possibility of unexpected behaviors
in the prototypes quite small.
.NH 2
Vision Assessments
.PP
An interesting application for inside-out ray-tracing is to determine
the view from within a vehicle through the vision ports or windows.
This gives the designers the opportunity to adjust the shape, orientation,
and placement of the vision elements of each vehicle so as to optimize the
exterior field of view for the vehicle occupants.
.PP
Some modern weapons utilize a forward observer to designate
a target by laser illumination, with a missile-borne sensor
homing in on the reflected beam.
This scenario is illustrated in plate 4.8.
In order to determine how such
a sensor might perform, it is necessary to calculate the
laser energy reflected from a variety of candidate targets.
.[
Deitz high resolution weapons
.]
A related assessment is to determine the amount of optical radiation
that might enter a vehicle through each vision port when irradiated
with the light from a laser designator.  The result of this type of
study is usually a cardioid shaped plot showing the energy transmitted as
a function of azimuth angle.
.[
Deitz improved materiel acquisition
.]
.NH 2
Infrared Modeling
.PP
In the design of smart munitions, it is important to know the
nature of vehicle signatures over a range of detection bands
and for a variety of signal-processing schemes.
.[
Rapp estimating Infrared sensor response
.]
Actual predictive infrared modeling is possible based on solid modeling,
using finite element techniques.
To make predictions about the patterns of heat radiation,
it is necessary to calculate a complete internal heat
budget for the entire vehicle which accounts for all the sources and
radiators of heat, such as engines and cooling fins,
and then to take into account external thermal loading due to such factors as
the surface of the earth and solar radiation.
Heat flow is calculated from node to node in the model, with links between
mesh elements characterized by thermal coupling coefficients.
The methodology for performing this type of predictive modeling
was developed at BRL,
.[
Rapp predicting infrared emission signatures m60a1 tank
.]
but has never been implemented.
.NH 2
Millimeter Wave Signatures
.PP
Dihedral and trihedral metal elements act as particularly efficient
reflectors for millimeter wavelength radio transmissions,
to the extent that the return from such elements represents the great majority
of the return from vehicles.
.[
Deitz predictive signature modeling
.]
BRL has developed a predictive millimeter wave signature model
.[
Lacetera deterministic targets mmw radar systems
.]
which concerns itself strictly with processing the dihedral and trihedral
elements that compose a vehicle.  G. Moss at BRL has developed
a post-processor program which extracts these features,
regardless of size and orientation, from the existing
CSG-rep solid models to drive this analysis.
An example of the result of this type of processing is shown in Plate 4.9
.PP
Because there is a strong correlation between the quantity of
dihedral vehicle surface topology and the intensity of the millimeter wave
reflection, this feature extraction program can be used by itself
without running the full deterministic millimeter wave reflection model
to obtain initial estimates of the magnitudes of
the millimeter wave signature of a given structure.
.NH 2
Synthetic Aperture Radar
.PP
Synthetic aperture radar (SAR) is a technique with which a variety of
image information about a distant object can be obtained by correlating
multiple radar samples taken from various positions.
.[
Toomay radar principles
.]
While standard radars only report target backscatter and range information,
SAR techniques can resolve distinct scattering regions of a target.
.[
Deitz signature modeling
.]
In 1984, BRL merged the
Simulated Radar Image Modeling (SRIM)
predictive SAR model from
the Environmental Research Institute of Michigan (ERIM)
with BRL's raytracing capability.
The choice of ray density is based on the frequency of the radar being
simulated and the cross-range resolution of the process.
Any ray can reflect up to some preset number of times or until it leaves
the vicinity of the target.  An example of the ray paths for
the first and subsequent reflections is shown in plate 4.10.
The actual results of the SAR calculation with an M48 vehicle
using a single transmit/receive polarization is shown in plate 4.11
These calculations were made in a high-resolution mode
unconstrained by practical frequency or coherence considerations of
realizable radar systems.  The radar signal is propagating from left to right.
.NH 2
Tradeoff Analysis
.PP
The philosophy adopted at BRL has been to develop a broad set of
analyses which are supported from the same geometry database.
.[
Deitz predictive signature modeling
.]
These analyses cover the spectrum from engineering decision aids,
to design validators, to drafting and milling interfaces, to
the generation of manufacturing drawings,
to image generation for management comprehension and sales advantage.
Key analysis capabilities have been developed to assess the 
strength, weight, and ``protection'' levels offered by
the structures represented by a solid model.
Using this analysis information and additional domain-specific
applications tools makes it possible to produce highly detailed
vehicle designs
constructed with a philosophy of \fIsystem optimization\fR
right from the start.
This should allow the rapid
development of vehicles with the desired levels
of performance at the best attainable price.
.SH
Thanks
.PP
The author would like to thank
Bob Reschly for his assistance with creating the drawings using PIC and CIP,
his supervisors Dr. Stephen Wolff and Dr. Paul Deitz 
for their unflagging support,
Harry Reed for providing an environment that makes good research possible,
and Dr. Dave Rogers for persuading me to write it all down.
.[
$LIST$
.]
.bp
.SH
Plate Captions
.LP
.nf
1.1	ComGeom Primitive Solids
1.2	Rendered Spline Surface
1.3	AuBuC Wireframe
1.4	AuBuC Rendering
1.5	A-B-C Wireframe
1.6	A-B-C Rendering
1.7	(A-B)+C Wireframe
1.8	(A-B)+C Rendering
1.9	C-A-B Wireframe
1.10	C-A-B Rendering
1.11	Early Rendering of Vehicle

2.1	MGED Faceplate with First-level Menu
2.2	Engine Connecting Rod.  Unevaluated and Evaluated Wireframes
2.3	Close-up of Connecting Rod Joint
2.4	ARB8 Before Editing
2.5	ARB8 After Editing Edge 1-4

4.1	Ray-Tracing Features
4.2	Inside and Outside Views of BMP
4.3	M109 with Transparent Armor
4.4	M48 Ray-Tracing Sample, w/Materials Colored
4.5	Main Penetrator and Spall Cone
4.6	Output of Vulnerability Evaluation
4.7	Neutron Study of Testbed Vehicle
4.8	Optical Signature Modeling
4.9	Dihedral and Trihedral Plates
4.10	Ray Paths of Radar Bounces
4.11	Ultra-high Resolution M48 SAR Image
