21. ENHANCED IMAGING OF CORROSION IN AIRCRAFT STRUCTURES WITH REVERSE corrosion in aircraft structures is presented. Reverse geometry Xray® is a unique system that http://www.galaxyscientific.com/agingaircraft/pdfs/7c/7c2a.pdf

22. Gridgen Case Study - C-5 Transport Aircraft C5 Transport aircraft geometry Repair. The starting point for this study is an IGESfile containing geometry information for a Lockheed C5A Galaxy aircraft. http://www.pointwise.com/case/c5.htm

C5 Transport Aircraft Geometry Repair (an example of work described in the paper "Gridgen's Synergistic Implementation of CAD and Grid Geometry Modeling", from the proceedings of the 5th International Conference on Numerical Grid Generation in Computational Field Simulations, held at Mississippi State University, 01-05 Apr 96.) The goal of this study is to demonstrate some of Gridgen's geometry modeling tools that are useful in repairing geometry models in preparation for gridding. Useful features of Gridgen shown in this study are: removing extraneous components from a geometry model to make the grid generation process simpler, copying and translating pieces of geometry to replace missing parts of a geometry model, constructing surfaces of revolution to build axisymmetric parts, and constructing polyconic surfaces to fair over gaps with a smooth angular transition. The starting point for this study is an IGES file containing geometry information for a Lockheed C-5A Galaxy aircraft. The original IGES file includes 431 entities, consisting of 412 curves and 19 surfaces. They are shown in Figure 1. Most of the geometry needed to build a grid for external airflow analysis of this aircraft is in the file: aircraft fuselage, T-tail, nacelles, pylons, wings, and front landing gear pod. The model includes additional geometric details not needed for the analysis: front and rear landing gear, pilot seats, and wing and fuselage bulkheads at a variety of butt-lines and fuselage stations.

23. Gridgen Case Study - JSF engine inlet and auxiliary inlet guide vanes, as well as the boundary layer aroundthe surface of the aircraft. They drew connectors on the geometry to define http://www.pointwise.com/case/b2jsf.htm

One Of Larger CFD Models Ever Helps Optimize Advanced Fighter Aircraft By Mike Malone Engineer/Specialist Northrop Grumman Corporation Pico Rivera, California (as seen in Silicon Graphics World, July 1998 issue, page 14) One of the larger computational fluid dynamics (CFD) models ever developed helped to optimize the performance of an advanced fighter aircraft. The 5,000,000 grid point model was used by Northrop Grumman Corporation to investigate straight vertical landing for the Joint Strike Fighter, the U. S. Air Force's next generation combat plane. The model, which covered the entire exterior of the proposed aircraft, helped engineers investigate the effects of entrainment, which produces negative lift and must by counteracted by additional engine thrust. A special preprocessor automated most of the model creation process, including strategically distributing grid points for high accuracy while minimizing computation time. Northrop Grumman Corporation, headquartered in Los Angeles, Calif., is a leading designer, systems integrator and manufacturer of military surveillance and combat aircraft, defense electronics and systems, airspace management systems, information systems, marine systems, precision weapons, space systems and commercial and military aerostructures. The company was formed in 1994 when Northrop Corporation acquired Grumman Corporation. Since then, it has acquired Vought Aircraft, the defense and electronics systems business of Westinghouse Electric Corporation, and Logicon Inc. Northrop Grumman employs about 52,000 people and reported sales last year of $8.1 billion.

24. Aircraft Design Software Rev. school. In that study, Mike's Quickmod code was judged to be betterthan FLOFT/WLOFT for developing aircraft geometry. AutoCAD was http://www.aoe.vt.edu/aoe/faculty/Mason_f/ACDesSR/softgeom.html

Geometry This section includes descriptions of several purely geometry related programs. FOIL 1.2 Virginia Tech Collection FLOFT/WLOFT Back to Software Review ... Back to Content FOIL 1.2 Use :airfoil library and graphics Author :Gregory Payne Address :550 Del Ray Avenue, Sunnyvale, CA 94086, greg@aerometrics.com, or 1119 Bridle Drive, Richland, WA 99352 Platform :Macintosh Documentation :code comes with manual Availability :Downloaded from America Online License :Foil is free, but not public domain. The author retains all rights. It may be distributed freely, but may not be sold. Foil may be included on disks that are sold for a small charge to cover costs, but only with express written permission from the author. Code :user gets executable code Graphics :yes Discussion :This program contains a huge library of airfoils. Practically every airfoil which has had its coordinates published is included. This also means that most of the airfoils are of mainly historical interest. The program can compare airfoils graphically. Back to Geometry Menu Virginia Tech Collection Use :various Author :collected from various sources Address :mason@aoe.vt.edu

25. Aircraft Design Software Rev. License CodeThe user gets the compiled QuickBASIC code Graphicsyes,both aircraft geometry and performance graphs. Discussion http://www.aoe.vt.edu/aoe/faculty/Mason_f/ACDesSR/softperf.html

Aircraft Performance/Mission Analysis Most of the sizing program necessarily can also operate as mission analysis codes. They can also evaluate poitn performance. The codes listed here are limited to performance only. BASIC Aircraft Performance Airplane Performance EGADS V1.3.1 TAKEOFF ... Back to Content BASIC Aircraft Performance Use :Aircraft performance (also estimates drag from geometry) Author :Sid Powers Address :KERN International, Inc., 575 Washington Street, Pembroke, MA 02359, (617) 826-0095 Platform :IBM or Apple ][ (!) Documentation :Powers has written a book including the user's manual (Powers, 1984) Availability :from Kern, with volume discounts. License :not for distribution to others Code :The user gets the BASIC source code Graphics :no Discussion :A series of computer programs for the IBM PC that model the full size dedicated mission analysis programs used in industry reasonably well. It's the closest to a real mission program I've seen for students. Originally it was developed on an Apple ][. The source code is provided, and a version of several of the programs that run in QuickBASIC on a Macintosh is available at VPI. It consists of a system of codes. They are driven from a main graphical interface. The key ones are DRAG to estimate drag, TABLE to input your own DRAG table, THRUST to generate an engine deck, MISSION to define the mission, PERF computes the mission performance, and E/M, which computes the performance envelope, Ps contours and turn rate. I would like to see this updated to current standards. I had to modify it for use on a Mac because our design team had airplanes over a million pounds a few years ago, and the output formatting was inadequate.

26. Nat'l Academies Press, Frontiers Of Engineering: (1997), Virtual Reality And Aug designs, wearable computer, real object, reality , cad geometry, visualizing aircraft,aircraft aerodynamic, aircraft geometry, aircraft industry, aircraft http://www.nap.edu/books/0309057264/html/29.html

Frontiers of Engineering: Reports on Leading Edge Engineering from the 1996 NAE Symposium on Frontiers of Engineering National Academy of Engineering ( NAE Related Books Openbook Linked Table of Contents Front Matter, pp. i-x Design Research, pp. 1-2 Designing Vehicles in Changing Time..., pp. 3-8 Development of Performance-Based Se..., pp. 9-12 Information in the Design Process, pp. 13-16 Product Modularity: A Key Concept i..., pp. 17-22 Visualization for Design and Displa..., pp. 23-24 Visualizing Aircraft Aerodynamic De..., pp. 25-28 Virtual Reality and Augmented Reali..., pp. 29-31 The Frontiers of Virtual reality Ap..., pp. 32-36 Digitizing the Shape and Apperance ..., pp. 37-46 Microelectromechanical Systems, pp. 47-56 Fabrication Technology and the Chal..., pp. 57-62 Frontiers in MEMS Design, pp. 63-66 Large-Market Applications of MEMS, pp. 67-72 Innovations in Materials and Proces..., pp. 73-82 Novel Ceramic Ferroelectric Composi..., pp. 83-85 Co-Continuous Composite Materials f..., pp. 86-90 Dinner Speech, pp. 91-94 Institutional Cultures and Individu..., pp. 95-96

27. RAYMER RDS AIRCRAFT DESIGN CONCEPTUAL RESEARCH SHORTCOURSE LECTURE 4 ANALYTICAL geometry FOR aircraft LOFT Geometric reference systems, Cartesianvectors, coordinate transformations, rotations and direction cosines http://www.aircraftdesign.com/newcrs.html

ADVANCED COURSE IN AIRCRAFT presented by Daniel P. Raymer At last, a course just for real (or future) Aircraft Configuration Designers! The Advanced Follow-On Course for Dan Raymer's Popular 5-day Aircraft Conceptual Design Short Course . Learn the Insiders' Techniques and Tricks for: Quickly Getting The Design Started Configuration Design Graphical Techniques Computer-Aided Configuration Design NEXT PUBLIC OFFERINGS: March 17-18 2003, Los Angeles, CA IN-HOUSE OFFERINGS: Contact Conceptual Research Corp. for price and schedule availability. This intensive two-day short course in aircraft configuration design, layout, and loft offers an in-depth presentation of the technical skills needed for creating a new and viable aircraft configuration design drawing, and includes an overview of aircraft surface definition and lofting. The class includes an overview of computer-aided configuration design and loft, and covers the key mathematics and graphical techniques for both CAD and drafting-table design layout and loft. Those attending will learn how to put a new aircraft design together, and will learn specific useful skills to create smooth aerodynamic contours, incorporate concerns for production and maintenance, and construct and model component intersections (including considerations for geometric input to CFD and RCS analysis). Primarily aimed at the working configuration design engineer in industry or government, the course is also useful for those who teach aircraft design and desire a better insight into "how it's really done."

28. RAYMER RDS AIRCRAFT DESIGN CONCEPTUAL RESEARCH SHORTCOURSE LECTURE 5 CONFIGURATION LAYOUT AND LOFT Design layout of a credible aircraft configurationarrangement including external geometry, conic lofting, flatwrap http://www.aircraftdesign.com/shortcrs.html

Executive Short Course in Aircraft Conceptual Design and Requirements Definition AIRCRAFT CONCEPTUAL DESIGN SHORTCOURSE presented by Daniel P. Raymer The popular Aircraft Configuration Design Short Course that covers it all! A broad and intensive course for everybody involved in new or modified Aircraft Design. This class starts from fundamentals and takes you all the way through the design process including: - Developing a design in response to requirements - Laying out the design on a drafting table or CAD screen - Analyzing it for aerodynamics, propulsion, structure, weights, stability, cost, and performance - Calculation of range or sizing to a specified mission - Trade Studies, carpet plots, and multivariable optimization, and...... - Learning from your work to make the next design version better! Prior participants have said... "Well qualified, extraordinary presenter..invaluable to me as a propulsion company representative." "A great course - better than I could have imagined." K. Williams, Alaska Independent Research

29. About "Historical Developments Of The Aircraft Industry With Mathematical Applic Historical Developments of the aircraft Industry with Mathematical Applications. unitwritten as an enrichment lesson for students in basic geometry or geometry http://mathforum.org/library/view/11884.html

Historical Developments of the Aircraft Industry with Mathematical Applications Library Home Full Table of Contents Suggest a Link Library Help Visit this site: http://www.cis.yale.edu/ynhti/curriculum/guides/1990/7/90.07.10.x.html Author: Hermine E. Smikle - Yale-New Haven Teachers Institute Description: A unit written as an enrichment lesson for students in basic geometry or geometry; also, the section on spherical geometry can be used in an Algebra II Trigonometry class as an extension or an introduction to spherical geometry. It includes an introduction to graph theory. Levels: High School (9-12) Languages: English Resource Types: Lesson Plans and Activities Math Topics: Graph Theory Higher-Dimensional Geometry Euclidean Plane Geometry History and Biography ... Search http://mathforum.org/ webmaster@mathforum.org

30. Fixed Wing Aircraft - Wikipedia their wings during flight. In the early days of their development, thesewere termed variable geometry aircraft. When the wings of http://www.wikipedia.org/wiki/Fixed_wing_aircraft

31. SUN REFLECTION GEOMETRY (Table Of Contents) SUN REFLECTION geometry (TECHNICAL REPORT). TABLE OF CONTENTS. 3.0 ANALYSIS TOOLSLocating the aircraft; Locating the Sun; Application of Sun Reflection Data. http://www.rolandresearch.com/SRGv1/C-Report0.htm

SUN REFLECTION GEOMETRY (TECHNICAL REPORT) TABLE OF CONTENTS 1.0 INTRODUCTION 2.0 BACKGROUND Flash Signature Explanations The Infrared Sensor What is an Infrared Picture? Flash Signature Characteristics What Makes the Flashes? Flash Timing/Locations Analysis Context 3.0 ANALYSIS TOOLS Locating the Aircraft Locating the Sun Application of Sun Reflection Data 4.0 FAILURE of the SUN REFLECTION EXPLANATION - BROKEN GLASS Failure Modes 4.1 Failure Based on Aircraft Position (Azimuth) 4.2 Failure Based on Aircraft Position (Altitude) 4.3 Failure Based on Glass Shard Characteristics 4.4 Failure Based on Aircraft Position (Multiple Signatures - Uneven Ground) ... 5.0 FAILURE of the SUN REFLECTION EXPLANATION - BLOWING DEBRIS What "Bits of Blowing Debris?" Size and Shape of Debris The "Sag" Problem Another Infernal Machine A Free-rolling Machine A Horizontal Reflection Windmill 6.0 CONCLUSION

32. USGS Spectroscopy Lab - AVIRIS Geometry Corrections, Rectification with the roll, pitch yaw, velocity and direction changes in the moving aircraft. theequations for such a system using first principles and simple geometry. http://speclab.cr.usgs.gov/PAPERS/aviris.geom.1998a/aviris.geom5.html

USGS Spectroscopy Lab http://speclab.cr.usgs.gov From: Geometric Correction of AVIRIS Imagery Using On-Board Navigation and Engineering Data Roger N. Clark, K. Eric Livo and Raymond F. Kokaly, Summaries of the 7th Annual JPL Airborne Earth Science Workshop , R.O. Green, Ed., JPL Publication 97-21 Jan 12-14, pp57-65, 1998. Geometric Correction of AVIRIS Imagery Using On-Board Navigation and Engineering Data by Roger N. Clark, K. Eric Livo and Raymond F. Kokaly U. S. Geological Survey, MS 964 Box 25046 Federal Center Denver, CO 80225 (303) 236-1371 FAX rclark@speclab.cr.usgs.gov Introduction From 1989 through 1997 the NASA Airborne Visible and Infrared Imaging Spectrometer (AVIRIS) has been flown on multiple flights on an ER-2 aircraft at approximately 20 km altitude (e.g. see Vane et al ., 1984, Porter and Enmark, 1987, Chrien et a l., 1990). At the USGS, AVIRIS data have been used to make materials maps (e.g. see our web site http://speclab.cr.usgs.gov) but registration to a map base using classical control point registration methods with n-term polynomial or rubber sheeting image warping techniques has not fulfilled our expectations or needs, despite significant investment in people time. The Jet Propulsion Laboratory AVIRIS Data Facility delivers numerous engineering, aircraft state, and Global Positioning System (GPS) data sets that can be used to facilitate geometrical rectification of the imagery. Using the JPL data, combined with Digital Elevation Models (DEM), which can crudely, but adequately, be derived from atmospheric absorptions in the AVIRIS data, complete geometric correction appears possible. This paper derives the equations and compares the magnitudes of effects of the ER-2 plane motions on the AVIRIS imagery using example 1995 data over Arches National Park.

33. Enhanced Imaging Of Corrosion In Aircraft Structures With Reverse Geometry X-Ray Willima P. Winfree, Noreen A. CmarMascis and F. Raymond Parker, Enhanced Imagingof Corrosion in aircraft Structures With Reverse geometry X-Ray \TM , Third http://techreports.larc.nasa.gov/ltrs/refer/1999/mtg/NASA-99-3jcaa-wpw.refer.htm

Langley Technical Report Server Acrobat Reader Ghostscript Willima P. Winfree, Noreen A. Cmar-Mascis and F. Raymond Parker, Third Joint FAA/DoD/NASA Conference on Aging Aircraft Albuquerque, New Mexico September 20-23, 1999 Format(s): Postscript , or PDF Keywords Nondestructive evaluation; Corrosion detection; X-ray imaging; Aging aircraft; Inspection Abstract NASA STI: , Posted Date:

34. Dassault Falcon Aircraft / Aircraft / Falcon Philosophy / ACHIEVING HIGH/LOWSPEED COMPATIBILITY THE VARIABLE geometry AIRFOIL. During theinitial design of a business aircraft, the decisive factor in choosing the http://www.falconjet.com/aircraft/falcon_philosophy_aerodynamics.jsp

35. Aircraft Hangar With Digiray Mobile System Below the left wing Digiray's Reverse geometry Xray® (RGX®) tubeis under the wing. -stress the aircraft structure by drilling. http://www.digiray.com/hangar/

Digiray Portable System in the Aircraft Hangar See Also Results (Radiographs) Obtained by Portable System Digiray Systems Finds Cracks in Aircraft Digiray Success with Navy Aircraft ... Larger Image of the Crack Digiray® Reverse Geometry X-ray® (RGX®) system enables commercial and military aircraft inspection to be faster, less expensive, and more reliable eliminates the need for slow, costly manual disassembly, eddy current inspection, and reassembly provides return on investment with the very first aircraft inspected Boeing 707 (aft) at Northrop-Grumman Air Force/Army Joint Stars Program (May 1998: Lake Charles, LA) Digiray's Reverse Geometry X-ray (RGX ) software runs on a standard Pentium personal computer with Windows NT 4.0 The display monitors enable inspectors to view images and set controls. The x-ray tube source and detectors (shown below) examine the left wing. Below the left wing Digiray's Reverse Geometry X-ray (RGX ) tube is under the wing. An array of eight (8) detectors is above the wing. No longer is it necessary to have the human worker drill out each of the many thousands of rivet holes stress the aircraft structure by drilling wait for eddy current or film inspection Above the left wing An array of eight (8) detectors is above the wing.

36. Reverse-Geometry Digital X-Ray System Seismic safety inspections and detection of residual stress and chemical compositionof alloys and corrosion in aircraft using Reverse geometry Xray http://sbir.gsfc.nasa.gov/SBIR/successes/ss/043text.html

Langley Research Center 1992 Phase II Reverse-Geometry Digital X-Ray System Digiray Corporation San Ramon, CA INNOVATION RGX is the only portable real-time X-ray nondestructive testing system, detects defects conventional systems cannot see Optional Powerpoint file ACCOMPLISHMENTS X-ray system to detect defects conventional system cannot see RGX is the only portable real-time X-ray nondestructive testing system Scanning X-ray beam replaces mechanical motion Multiple detectors for 3-D stereo or layer-by-layer viewing COMMERCIALIZATION Seismic safety inspections and detection of residual stress and chemical composition of alloys and corrosion in aircraft using Reverse Geometry X-ray diffraction Joint Digiray-NIST U.S. Patent pending Over $ 3,000.000 total sales to date in the following markets: Aircraft safety, National Security, Corrosion/cracks (petrochemical industry), Electronics GOVERNMENT/SCIENCE APPLICATIONS NASA - inspection of X-33 cryotanks; space shuttle pipe weld and tile inspection; detection and location of hidden corrosion in aircraft at NASA LaRC

37. Guide Entry 90.07.10 at the developments that took place in the aircraft industry; 2) for Mathematicsto be taught as an enrichment lesson for students in Basic geometry or geometry http://www.yale.edu/ynhti/curriculum/guides/1990/7/90.07.10.x.html

Yale-New Haven Teachers Institute Home Historical Developments of the Aircraft Industry with Mathematical Applications, by Hermine E. Smikle Guide Entry to 90.07.10: This unit is written with several audiences in mind: 1) for History—a junior high school grade 8 class to take a look at the developments that took place in the aircraft industry; 2) for Mathematics to be taught as an enrichment lesson for students in Basic Geometry or Geometry. Also, the section on spherical geometry can be used in a class of Algebra II Trigonometry as an extension or an introduction to spherical geometry. This unit makes an attempt to present new content ideas into the mathematics curriculum. The focus of the unit is on problem solving, using graphs as a model. The unit also considers the new standards that will be put in place for mathematics, and has considered some of the topics that have been targeted for increased attention. Because of the limitation placed on the numbers of pages in the unit, only a sample of the extension activities and worksheets presented for the students is included. The user, however, can make ditto of the examples presented, and, with the use of an atlas, can come up with more examples (spherical geometry). In the section on graphs and matrices, students can draw or design their own networks (good example of open-ended problems). The unit, therefore, lends itself to extensive use of one’s imagination. Examples can be found from newspapers, advertisements, a map, the atlas, and everyday activities. If there is the need for any other material or explanation I will be willing to provide these through the office of the Teachers Institute.

38. SimHQ.com Air Combat Where you position the nose of the aircraft is very important when a pilot attacksthe bandit. The use of attack pursuit geometry will be explained later on in http://www.simhq.com/simhq3/sims/air_combat/f3manual/bfm1.shtml

SimHQ.com Affiliates SimHQ.com Sponsors The Falcon 3.0 Manual Tactics Section - Introduction to the Geometry of Air Combat Edited by Ed "Skater" Lynch October 19, 1999 For those of you that are "old salts" when it comes to flight sims, and for those of you that are new to flight sims, this article should be of some value to you. This is largely a reprint from the manual of one of the best combat flight sims ever released. Spectrum Holobyte's Falcon 3.0 was indeed the father of all modern, "realistic" combat flight sims. The F3 manual was one hell of a paper weight. Weighing in at something like seven pounds, the F3 manual was jam packed with information on flying the sim, and the usage of tactics, and the deployment of weapons and the employment of the aircraft. Here is a little jewel from the tactics section. Enjoy! Credit goes to Microprose / Hasbro Interactive, Spectrum Holobyte, and the Falcon 3.0 team. Introduction to the Geometry of Air Combat In order to become a great fighter pilot, you must perform great BFM. Now, in order to perform BFM, a fighter pilot must understand his positional relationship to the target from three perspectives: positional geometry, attack geometry and the weapons envelope.

39. A Week At The Zenith Aircraft Factory A geometry teaches relates her experience after spendinga week with an aircraft manufacturer. http://www.zenithair.com/misc/week@zac.html

A Week at the Zenith Aircraft Factory By Linda Kirchner Math Instructor, Mexico High School, Mexico, Missouri [Linda Kirchner spent a week at the Zenith Aircraft factory in August 1997 to learn more about "real life" applications for geometry and math]. As a high school geometry teacher I long to bring workplace applications into my classroom, so I spent a week at the Zenith Aircraft factory in Mexico, Missouri . Three things stand out after having completing a week at Zenith Aircraft: the shop test, the workmanship, and the work atmosphere. Potential employees at Zenith Aircraft must first take a shop test. First thing on Monday morning the shop foreman laid aside some tools, various pieces of sheet metal and a drawing I was to build. The test is designed to demonstrate the ability to measure, drill and rivet. But more than that, Zenith wants to verify that you can problem solve, ask questions, and use resources. Ninety percent of the applicants who take the test fail to construct the item. Some walk away without even trying! I was relieved to know I passed and could have been placed in the "consider-for-hire" category! After completing the test, I worked with various Zenith personnel throughout the week. The workers were glad to see a teacher trying to bring useful, meaningful work to the classroom. The employees are real craftsmen, making certain all parts built are within tolerance. The tolerance, I found, was frequently 0.0005 mm. On some items produced the tolerance was

40. Format And Basic Geometry Of A Perspective Display Of Air Traffic For The Cockpi Display devices; Computer graphics; Mancomputer interface; Space perception; Airtraffic; aircraft instruments; Computer programs; Projective geometry; Perspective. http://human-factors.arc.nasa.gov/IHpublications/McGreevy.AFO.WWW/VERT/TM86680.a

Format and Basic Geometry of a Perspective Display of Air Traffic for the Cockpit Michael W. McGreevy , NASA Ames Research Center, Moffett Field, California Stephen R. Ellis , NASA Ames Research Center, Moffett Field, California June 1991 Based on: McGreevy, M. W. (1983). A Perspective Display of Air Traffic for the Cockpit . Master's report, Univerity of California, Berkeley. NASA Technical Memorandum 86680 Subject terms: Display devices Computer graphics Man-computer interface Space perception Air traffic Aircraft instruments Computer programs Projective geometry Perspective McGreevy, M. W. and Ellis, S. R. (1991). Format and basic geometry of a perspective display of air traffic for the cockpit. NASA Technical Memorandum 86680. Ames Research Center, Moffett Field, California. (48 pages) Hardcopies are available from the first author. Send requests to: mmcgreevy@mail.arc.nasa.gov Comments are encouraged. Please send them to the above e-mail address. Abstract The design and implementation of a perspective display of air traffic for the cockpit is discussed. Parameters of the perspective are variable and interactive so that the appearance of the projected image can be widely varied. This approach makes allowances for exploration of perspective parameters and their interactions. The display was initially used to study the caused of horizontal maneuver biases found in experiments involving a plan view air traffic display format. Experiments to determine the effect of perspective geometry on spatial judgments have evolved from the display program.

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