**RSIC COMPUTER CODE PSR-008**

**1. NAME AND TITLE**

AUTOJOM-JOMREAD: Computer Programs to Generate or Check Coefficients for Quadratic
Equations Describing 3D Geometries.

**2. CONTRIBUTOR**

Research and Technology Division, Air Force Weapons Laboratory, Kirtland Air Force Base, New
Mexico.

**3. CODING LANGUAGE AND COMPUTER**

Fortran IV; CDC 6600.

**4. NATURE OF PROBLEM SOLVED**

AUTOJOM generates the coefficients of any quadratic equation used to define conic volumes (cones, ellipsoids, spheres, cylinders, paraboloids) and also the coefficients of the planes needed to define parallelepipeds, wedges and pyramids. The amount of user input is minimal (a single reference point, a few directional vectors to orient the surface in space, and a few scalars).

JOMREAD is designed to check 3D geometries composed of and constructed with quadratic
surfaces.

**5. METHOD OF SOLUTION**

In AUTOJOM the derivation of the equation of any conic quadratic surface is performed by assuming first that the surface is symmetric about the origin and oriented along the X-axis. The X, Y, and Z coordinate axis system is then rotated in turn about the X, Y, and Z axes until the surface has the same orientation as its height vector (HXO, HYO, HZO). It is then displaced by translatory motion until the reference vertex is at its final (given) location (Po). The transformation of axes during the rotations is performed by matrix multiplication. The derivation of the equations of parallelepipeds, wedges, and pyramids is performed using the basic equation for a plane. The input needed is a vertex point and height vectors locating the positions and giving the length and edges of the volume.

JOMREAD requires the presence of the following: a grid network to help subdivide the spacial volume of interest, a list of which surfaces are relevant to each volume, identifiers to indicate on which side of the surface the flume of interest lies, and identifiers for the type of volume.

The coefficients are printed or punched out into cards in the format of PHOTRAN, AFWL-TR-65-171, Vol. I (March 1966), by C. D. Zerby and J. Agresta.

**6. RESTRICTIONS OR LIMITATIONS**

At least 60 K of core memory is needed.

**7. TYPICAL RUNNING TIME**

No study has been made by RSIC of typical running times for AUTOJOM-JOMREAD.

**8. COMPUTER HARDWARE REQUIREMENTS**

AUTOJOM-JOMREAD was designed for and is operable on the CDC 6600 computer.

**9. COMPUTER SOFTWARE REQUIREMENTS**

A Fortran IV compiler is required.

**10. REFERENCES**

R. J. Cahill, "AUTOJOM: A Computer Program to Generate Coefficients for Quadratic Equations," AFWL-TR-67-60 (July 1967).

R. J. Cahill and G. C. Spitale, "JOMREAD, A Computer Code Designed to Check 3D
Geometries," AFWL-TR-67-36 (June 1967).

**11. CONTENTS OF CODE PACKAGE**

Included are the referenced documents and one (1.2MB) DOS diskette which contains the source
codes.

**12. DATE OF ABSTRACT**

November 1972.

**KEYWORD: ** GEOMETRY DATA PROCESSING