Cynthia Vaskis

SLM521 – Spring 2004

Dropin #5 Assignment

4/13/04

File: dropin5.htm

 

How Math is used in Computer Image Generator (CIG) Simulation to Generate CIG Object Models

 

(Click to see wire-frame CAD/CAM drawings.)

Picture of CAD/CAM drawing1      Picture of CAD/CAM drawing2      Picture of CAD/CAM drawing3

 

Who is this lesson for and what background is required?

 

This lesson is geared toward senior high school students (11th through 12th grades) who have had some exposure to 3D Cartesian coordinate systems and Polar coordinates as described in previous Drop-in 1 and understand some basic trigonometry as discussed with rotational matrices in Drop-in 2.

 

Introduction - Computer Image Generators (CIGs) Use Math to Define the CIG Environment and their Objects in Three Dimensional (3D) Space

 

Computer Image Generators create the images in simulators that are used to train military personnel for battle.  Some simulators are tanks and some are aircraft in support of ground tank crews.  The aircraft are usually ground support fighters or helicopters.  A tank simulator is a fabricated almost life-size tank-shaped shell containing all of the functions used by a tank crew during battle maneuvers.  There are switches and a turret loading compartment, turret steering and firing controls, commander radio controls and a separate driver compartment with steering and speed controls.  A tank crew consists of a commander who is in charge of the driver, the missile loader, and the gunner.  Pretend ammunition is loaded by the loader crew member and then fired by the gunner crew member.  The driver crew member takes directions from the commander crew member via radio for where to drive and how fast.  See the CIG Simulator Steel Beasts web site.

 

The simulation is played with two groups of tank simulators pitted one group against another in battle.  An individual tank simulator commander communicates with other commanders in his” friendly” group of tank simulators via radio just as it would happen in real life.  The “enemy” group of tank simulators can also hear any communications between the “friendly” commanders.  If a (pretend computer model) missile fired by a tank hits another tank (hopefully, an enemy tank) and does damage to the tank, then that tank’s simulator controls may stop working and they will not be able to move across the land.  That tank is considered dead because in real life the people probably would be dead.  Then the simulator unit’s computer has to be rebooted to get back into the simulation if required.  The simulators are on a network so that every simulator can respond to everyone else’s in battle.  They all see the same set of tank models on the land, they all “drive” across the same terrain database and they all react to any simulator missiles and machine guns fired on their position.

 

The tank simulators have computer screens inside that are placed where there would normally be a real window inside a real tank.  The screens display a view of computerized land which is a huge database model of polygons created from Digital Terrain Elevation Data (DTED) and colored with texture maps to make it look like land.  The land database has placed on it any “object models”, such as a tank, tree, house, person, or anything else used for the simulation.  If these “object models” are within the viewpoint angle for that computer “window” in the tank, then those “objects” are also seen in the tank’s “window” (really a computer display screen).  This allows the driver crew member to drive around objects placed on the terrain land and the gunner crew member to shoot at other tanks that are seen in the gunner’s window.  The same technique used to create the CIG land and CIG objects is used to create the background and models in many computer games that are played on home computers today.

 

Purpose – To design your own “object model” (tank, aircraft, person, robot) that could be placed on a CIG simulation’s terrain database

 

The purpose of this Drop-in 5 activity is in two parts.  The first part is for the student to understand how math models create CIG simulator “worlds” used in military training simulators.  This knowledge will be used by the student to complete the second part which is to have the student design an “object model” that could be placed on the CIG terrain database.  In the real world, CIG companies use 3D scanners to scan a small toy model of a tank, or vehicle, for a set of 3D points that model the shape of the object.  The computer enlarges the data set to make it an appropriate size when placed on the CIG simulation’s terrain database.  The objects and terrain data are used in a CIG simulation with people inside simulators viewing this terrain land and objects through computer screen “windows”.  The terrain database is a math model consisting of a huge set of polygons.  The object models are also a set of polygons that approximate the shape of the original toy model that was scanned or the object is generated by a person creating it with a CAD/CAM drawing routine which saves the shapes as data points that can be converted to polygon form.

 

The Task – To Design a CIG Object Model

 

The task is for the student to create their own CIG model of a mobile object (such as a vehicle, tank, car, aircraft, person, robot, or any object that is not fixed to the terrain) on graph paper or draw it with the aid of a computerized drawing program.  The student needs to label any appendages that move or don’t move and specify their appendage origin location relative to the object’s base model origin location.  See this diagram for an explanation of the origin labeling process.  An appendage origin is the point (x, y, z) where it attaches to the main body of the model or where it attaches to another appendage closer to the main body than their location.  “Closer to the main body” means that if you followed a pathway along the current appendage back toward the main body via crossing other appendages, the one that the current appendage is attached to that has less appendage parts to traverse to get to the main body is the one “closer to the main body”.

 

View the Web sites listed under CAD/CAM systems (below) to get an idea of how objects are drawn as wire frame models on computers.  This same technique can be used to generate a first cut model of the CIG objects.  Eventually, the object’s model data must be represented as a set of polygons which is usually much simpler than the detailed wire frame models.  A good CAD/CAM system should allow the user (or creator of the object models) a choice about how to save the object’s drawing data (as polygons instead of line drawings).  The computer programmers at a CIG company may need to create their own “object creation” tool to build the object models so that the stored model data is compatible with the design of their Simulator’s polygon processors and terrain database.

 

After reading the explanation below, the student should be able to draw their model and define its moving parts in terms of either rotation matrices or Polar angles.  The student must understand what was described in Drop-in 1 (coordinate systems) and Drop-in 2 (model rotations) because they will be asked to think about how each part of their model should be represented.  Each part of the model will either be represented in Cartesian or Polar coordinates.  The model, or appendage on the object’s base model (main body of the object), will move using a rotational matrix for those models defined in Cartesian coordinates.  Those base models, or appendages, defined in Polar coordinates shall rotate using Polar angles but their coordinates must be converted to Cartesian coordinates before being sent to the polygon processors.  Every object and land model must be represented as polygon point (x, y, z) data in Cartesian coordinates before it is sent to the polygon processors.  The polygon processors create the “window” image as described in the next section.

 

How a Terrain Database is Created Using a Math Model of Cartesian coordinates

 

A math model is created of the land, or terrain, using a Cartesian coordinate system by the CIG Company that makes the Simulation database. The CIG company obtains terrain elevation data for an area of land and uses it to build their own database of polygons that represent that land.  The terrain is modeled as a large grid of polygons that have a Cartesian coordinate (x, y, z) for every point of every polygon in the terrain (land) database.  There are some examples of land data available on the Web (see below under Terrain Elevation Data Web sites).

 

Usually, there is a specific area of the real world where the military want to practice maneuvers so the real Digital Terrain Elevation Data (DTED) files are obtained and used to generate the land model, or terrain database, in the form of a huge set of polygons.  The DTED files contain coordinates in the form of location (latitude and longitude) and elevation (above or below sea level).  These are converted to an X, Y, and Z coordinate model where X and Y are the horizontal location components (for latitude and longitude) and the Z coordinate is the elevation data (the land’s height above or below sea level at that (X,Y) location). 

 

The math objects and land (terrain) models are stored as a large set of polygons.  The polygon processors use the selected viewpoint angle to determine which polygons from the complete set of objects and which part of the terrain database needs to be displayed on the computer screens (or pretend “windows”) inside the Simulator.  The viewpoint angle is determined by which direction the tank or aircraft Simulator’s “window” is facing over the terrain database.  Before displaying the selected polygons, the polygon processors crop (truncate) them to fit the computer screen’s boundaries.  Then the final polygons are colored, or texture maps are applied to them, just before they are displayed in the Simulator “windows”.

 

In the late 1980’s, when CIG systems were just becoming feasible, the display process had to double buffer the images to the computer screen “windows” in order to avoid “flicker”.  The human eye can detect image flicker at less than 30 images displayed per second.  Today, the graphics speeds are so much faster that this is probably not an issue any more.  See how land data is shown graphically on the Web today at the sites listed below for Digital Terrain Elevation Data Sources.

 

Simulator Models are Defined Using Math Models in Cartesian or Polar Coordinates

 

Once the terrain data is established, the stationary models are defined and placed on the land database.  Each model must have an origin location that is defined as (x, y, z) = (0, 0, 0) for that computer model.  It is better to define it where the model touches the terrain database or in its center of gravity if it is an object that might rotate around its center position.  Some models may be better off defining their origin at a forward or rear corner coordinate so that every other location on that model can be described by measuring in the horizontal plane (X and Y coordinates) and vertical direction (Z coordinate) in positive measurement values.  Some object model’s have appendages that need to be defined relative to the base model’s origin and coordinate system.  See the origin labeling process again for the example of the leg’s origin definitions being defined by where the base model is located over the terrain database while the Simulation is running.

 

Appendages need to have the origin of their own coordinate system (could be Polar if it rotates like an arm or head) defined at the point where they are attached to the overall model.  The appendage’s description should include how long the appendage is, what type of shape it is (cylindrical, rectangular 3D stick shape, etc.) and whether or not it has an attached additional appendage that extends the overall length of the total appendage.  An example would be an upper arm is attached to a shoulder so the shoulder attachment point is the origin of the upper arm.  If there was a forearm, then the forearm’s origin is the elbow and its length is described as how long the forearm is until it comes to a wrist.  Then a hand’s origin is the forearm’s wrist and the hand extends out as far as the hand is long.  Each appendage origin is actually the starting point of a translation vector that extends outward along the center axis of the appendage its full length.

 

Assignment – Design an Object’s Model for Placement on a CIG Simulation Terrain Database

 

This exercise is for the student to make a few drawings of their object by hand on graph paper or in a computer drawing tool and then add the appropriate labels as mentioned below.  In a real CIG company, this drawing would be handed off to a model creator (software person) who would enter the parameters mentioned on the drawing to build the actual set of polygons representing that object in the CIG simulation database.  See the example drawing of an object with some labels.   Note that you may need additional labels mentioned below to complete the assignment than are shown on this example drawing.

 

1.  The student must select an object to model that is big enough for a person to see and interact with physically (by touching, holding, climbing on, or going in it).

 

2.  The object must be able to move (roll, walk, drive, fly, slide over) or change its position, ( x, y, z ) location, in the environment.   It must be an object that can move under its own source of power so that an animation of it would make sense.  In other words, don’t make inanimate objects that are stuck to the ground in one spot such as a building unless the building is on wheels and rolls around.  An example would be a vehicle (tank, car, flying machine) or a robot, animal, bird, person, or creature that is living and able to move under normal circumstances.

 

3.  The object must have at least one appendage that moves separately from the overall base model’s movement across the land.  For example, the turret on the tank moves up, down, left and right independent of the tank’s movement across the terrain.  The appendage will be used to illustrate a “translation” vector described in Drop-in 1.

 

4.  The student must draw several views of the object’s model.  The required views are from the front and the rear, from the top above the highest point of the model looking down and from the sides (only need one side picture if the sides are identical).  If it is appropriate, draw a view from underneath the model.  Also, if people can go in the object, the student must also draw views from inside the object (tank, aircraft) model such as where people are to be located and where the computerized “windows” are located.

 

5.  Once the overall shape of the object is drawn, the student must label the object’s overall length, height, and width beside the object’s drawing.

 

6.  Then, the student must draw any appendages that attach to the object’s base model (center body of the object) and define their overall length, width and height.  This overall length will be the length of a “translation” vector (used by simulation math routines) that starts at the appendage’s origin and extends out along the appendage’s axis to reach its end at another joint or the end of the appendage.

 

7.  After the whole object is drawn, it is time to label each appendage’s origin.  A joint is where an appendage attaches itself to the main model or to another appendage. The joint is the origin of the attached appendage.  An appendage should have recorded its origin, its overall length and the “center position” vector of its “mobility” range (or range of motion) that the appendage would normally point in.

 

8.  The next part of defining the object’s model is to establish its range of motion in all directions.  For example, a tank cannot drive sideways but only forward or backward with some turning ability (a turning radius).  The appendages need to have their limits of motion (or range of movement) defined so that they do not exceed what is normal for that type of appendage.  Also, the appendages should have their range of movement angles and speed limitations defined beside them on the object’s drawing.  The information in Drop-in 2 may be useful when considering how rotational matrices use angles to rotate an object and the angle rotations will probably have limits that need to be specified on the object’s drawing.

 

9.  The only other limitations for an object’s model would be its structural strength and whether it can hold up to a direct hit from enemy artillery or not.  Then, when the simulation game is played, the game playing routines will know whether they should leave the model alone or make it look blown up when it receives a direct hit.  Also, other types of attacks may cause other features in the Simulator to stop working.  If the Simulator stops working due to a software error, then it can be rebooted and re-enter the game.  If the Simulator stops working because it was fired upon and hit, then what has happened is representing real life and that Simulator is finished playing that simulation game.

 

10. Show your drawings to your teacher and other students to see if they can understand them.  If not, then simplify the object’s description so that a real CIG computer graphics person could enter them into a real CIG Simulation.

 

In summary, each object should have defined, on graph paper, its own origin, its overall length, width, and height measurements, its shape type (cylindrical tube, squared stick, spherical ball, etc.), where its appendages are located (attached) relative to the origin of  the object’s base (body center) model and how the appendages shall move during the Simulation.

 

How an object is used during the Simulation

 

Many CAD/CAM object modeling tools first draw the object in a wire-frame drawing tool.  This wire-frame model needs to be converted to a set of polygon points in the (x, y, z) format.  The polygon processors crop the set of partially visible polygons so that what remains is the part seen from the selected viewpoint.  Then, the polygon processors apply color and texture to those prepared object’s polygons.  The last step is to send the object’s cropped and colored polygons to the computer screen “windows” in the Simulators. 

 

An object’s movement can be described or shown during the Simulation by using rotational matrices or Polar angle rotations.  Animation techniques perform math routines that rotate an object about its axes or translate the object to a different part of 3D space.  A “scenario” is a previously setup pattern of movement for an object or set of objects.  The object(s) may fly or move through 3D space by following a selected set of data points represented by a mathematical equation called a “spline”.

 

Visit the CIG Simulation Web site below to download a CIG tank simulation computer game demo below (Steel Beasts).  Also, look at real world Digital Terrain Elevation Data for any where in the world (and oceans too) under the Digital Terrain Elevation Data Web sites.  The Army site has a CIG tank simulation used to train soldiers in groups to prepare for real battle.

 

Computer Image Generator (CIG) Simulation Web Sites

 

eSim Games – Steel Beasts – The company eSim has made an Army tank simulation game called Steel Beasts which is a simulator of the US M1A1 and German Leopard 2A4 tanks that let the players create modern armored war scenarios and play them on their PCs.  You can go to the game’s web site at SteelBeasts.com from the left column choices.  The web page’s Download choice takes you to the page http://www.esimgames.com/Downloads.htm which has a choice to download the Steel Beasts Demo (20MB, 10/11/01) which takes about an hour and a half (SBDemo1-195.zip) and save into a new folder you create called SBTemp.  Then you run the setup.exe file in the folder SBTemp.  This is a computer game that runs as a demo version with computer modeled tanks moving across simulated terrain.

Date visited – 4/13/04

http://www.steelbeasts.com

 

eSimgames Company home page – Home page for the eSim company, select “Play Games” to get to the “Steel Beasts” game.

http://www.esimgames.com

 

Computer Aided Design (CAD)/ Computer Aided Modeling (CAM) Web sites

 

BobCAD- CAM web site –Click “Click here to Watch a Video” on creating a wire frame model for machining a new object.

http://www.bobcadcam.com/index.php

 

BobCAD- CAM steps to creating a tool – Shows you how to make a tool and illustrates the object in a wire frame format.

http://www.bobcadcam.com/downloads/documentation/sample3cad/Sample3Lesson.htm

 

SURFCAM CAD/CAM Systems by Surfware, Inc. – Company that created the JPL Mars Lander by making the drawings and machining it.

http://www.surfware.com/PA-199712-jpl.htm

 

SURFCAM 2003 page – Shows some nice photos of the drawings made in the CAD/CAM system.

http://www.surfware.com/prod-SC2003.htm

 

Wizard makes hybrid CAD/CAM easy for shop – Article on computer CAD/CAM program capabilities.

http://www.manufacturingtalk.com/news/one/one100.html

 

Rhinoceros – NURBS modeling for Windows home page – CAD/CAM company home page.  Select “Try Rhino” which brings up a download page where you can actually try Rhino but cannot save it to your computer.

http://www.rhino3d.com/

 

The Rhino download page – The download page to try Rhino’s CAD/CAM design tool demonstration version.

http://www.rhino3d.com/download.htm

 

Kellysearch for CAD/CAM systems – List several companies that sell CAD/CAM services in the United Kingdom.

http://www.kellysearch.com/gb-product-120021.html

 

Army Training Center at Fort Knox, KY uses CIG tank simulators

 

Fort Knox, KY Army Training Center Home Page - The Fort Knox home page shows where the Army battalion troops are trained in CIG tank simulators.

http://www.knox.army.mil/

 

Tank Driver Simulators at Ft. Knox  - This article is about how the simulators caused some “simulator sickness” but they seem to have a solution.

http://www.ets-news.com/driverfatigue.htm

 

Training Development at Fort Knox – The Fort’s training program page.

http://www.ott.navy.mil/view_detail.cfm?RID=WEB_OT_1000397&outside_flag=

 

Digital Terrain Elevation Data Sources on the Web

 

The land data is displayed in colored maps with elevations represented by different colors.  The actual data is elevation data (above or below sea level) of a latitude and longitude pair (which defines its location on the Earth).

                        

NGDC Surface of the Earth grid to select an area – You can select an area of the Earth and it will show you a colorized map with elevation be noted by different colors.  All of this data being displayed is from elevation data that has been collected by satellite altimetry observations for seafloor depths and by several means for collecting the topography or land data such as normal surveyed data and satellite photography.

http://www.ngdc.noaa.gov/mgg/image/2minrelief.html

 

NGDC – Topography, Digital Terrain Data – Lets you pick your state to see a digital map.  First pick “The Global land One-kilometer Base Elevation”, then pick “U.S. State Images” and then pick the state of your choice.  It brings up a colored map of the state with the elevation data in colors by height above sea-level.

http://www.ngdc.noaa.gov/seg/topo/topo.shtml

 

National Geophysical Data Center (NGDC) – Home Page - Lets you select “Get GLOBE Data” elevation data in a one–km increment format.  You can even see the Earth’s oceans in colorful maps of their depths by picking the “Smith/Sandwell” choice at the bottom of the page.  There is an option to purchase data and download it to your computer from the GEODAS choice.

http://www.ngdc.noaa.gov/seg/topo/globe.shtml

 

Bruce Gittings’ Digital Elevation Data Catalogue – This is a home page where you can get to the catalog of available terrain data, some for purchase and some are free.

http://www.geo.ed.ac.uk/home/ded.html

 

Land Processes Distributed Active Archive Center home page – Select one of the grid areas on the map and it will provide information on how to order that data or look at a drawing of that area.

http://edcdaac.usgs.gov/gtopo30/gtopo30.asp

 

Land Processes Documentation about Land Data – Documentation about the land data.

http://edcdaac.usgs.gov/gtopo30/README.asp#h1

 

Antarctic Land Mass Image from Land Data – An example area of the Earth that was selected to show a grid line drawing map over the Antarctic polar land mass.

http://edcdaac.usgs.gov/gtopo30/antart_tile_img.asp

 

Land Processes Distributed Active Archive Center - Ask questions of the experts to find out about digitized land.

http://edcdaac.usgs.gov/custhelp/help_home.asp

 

US Land Cover Digital Data – Includes many types of data for the land covered including maps.

http://www.epa.gov/OWOW/watershed/landcover/