{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 1 10 128 0 0 1 0 0 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 1 11 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "Hyperlink" -1 17 "" 0 0 0 0 255 1 0 0 1 0 0 0 0 0 0 } {CSTYLE "2D Comment" 2 18 "" 0 0 0 0 128 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 0 0 0 128 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "Non-prop ortional" -1 256 "Courier" 1 11 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "Courier" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 1 14 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 1 14 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 266 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 0 0 0 0 0 0 }0 1 0 -1 6 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2 " 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 4 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 " " 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Bullet Item" 0 15 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 3 3 0 0 0 0 0 0 15 2 }{PSTYLE "Address" 0 256 1 {CSTYLE "" -1 -1 "" 1 11 0 0 0 0 1 0 0 0 0 0 0 0 0 }3 1 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Date" 256 257 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 6 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Fon t 0" -1 258 1 {CSTYLE "" -1 -1 "Courier" 0 10 128 0 0 1 2 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 259 1 {CSTYLE "" -1 -1 "Courier" 0 10 0 0 0 1 2 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 15 260 1 {CSTYLE "" -1 -1 "Courier " 0 11 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 15 261 1 {CSTYLE "" -1 -1 "Courier" 0 11 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {SECT 0 {PARA 3 "" 0 "" {HYPERLNK 17 "AESOP" 2 "AESOP" "" } {TEXT -1 31 " routines quadric() and plane()" }}{SECT 0 {PARA 4 "" 0 " " {TEXT -1 6 "Syntax" }}{PARA 260 "" 0 "" {TEXT 260 32 "quadric( f, ep silon, [x, y, z] )" }}{PARA 261 "" 0 "" {TEXT -1 32 "plane( [nx, ny, n z], [x, y, z] )" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 7 "Purpose" }} {PARA 15 "" 0 "" {TEXT 261 9 "quadric()" }{TEXT -1 147 " returns the e quation in Cartesian coordinates of a quadric surface, with the Z axis as the axis of symmetry and vertex at the coordinate origin. " }} {PARA 15 "" 0 "" {TEXT 266 7 "plane()" }{TEXT -1 71 " returns the equa tion for a plane with vertex at the coordinate origin." }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Arguments" }}{PARA 15 "" 0 "" {TEXT 262 7 "quadric" }}{PARA 0 "" 0 "" {TEXT 257 5 " f" }{TEXT -1 35 " is the \+ focal length at the vertex." }}{PARA 0 "" 0 "" {TEXT 258 11 " epsil on" }{TEXT -1 23 " is the conic constant " }{XPPEDIT 18 0 "epsilon" "I (epsilonG6\"" }{TEXT -1 34 ", which controls the surface type:" }} {PARA 0 "" 0 "" {TEXT -1 14 " " }{XPPEDIT 18 0 "epsilon" "I(epsilonG6\"" }{TEXT -1 40 " = 0 paraboloid of focal length \+ " }{XPPEDIT 18 0 "f" "I\"fG6\"" }{TEXT -1 15 "\n " } {XPPEDIT 18 0 "epsilon" "I(epsilonG6\"" }{TEXT -1 32 " = 1 sph eroid of radius " }{XPPEDIT 18 0 "2*f" "*&\"\"#\"\"\"%\"fGF$" }{TEXT -1 15 "\n " }{XPPEDIT 18 0 "epsilon" "I(epsilonG6\"" } {TEXT -1 43 " < 0 hyperboloid\n 0 < " }{XPPEDIT 18 0 "epsilon" "I(epsilonG6\"" }{TEXT -1 38 " < 1 prolate spheroid, \+ eccentricity " }{XPPEDIT 18 0 "e = sqrt( (1 - epsilon)/epsilon )" "/% \"eG-%%sqrtG6#*&,&\"\"\"\"\"\"%(epsilonG!\"\"F*F+F," }{TEXT -1 15 "\n \+ " }{XPPEDIT 18 0 "epsilon" "I(epsilonG6\"" }{TEXT -1 44 " > 1 oblate spheroid, eccentricity " }{XPPEDIT 18 0 "e = sqrt ( (epsilon - 1)/epsilon )" "/%\"eG-%%sqrtG6#*&,&%(epsilonG\"\"\"\"\"\" !\"\"F*F)F," }}{PARA 0 "" 0 "" {TEXT -1 15 " Note that " } {XPPEDIT 18 0 "epsilon = kappa + 1" "/%(epsilonG,&%&kappaG\"\"\"\"\"\" F&" }{TEXT -1 8 ", where " }{XPPEDIT 18 0 "kappa" "I&kappaG6\"" } {TEXT -1 37 " is the \"traditional\" conic constant." }}{PARA 0 "" 0 " " {TEXT 259 11 " [x,y,z]" }{TEXT -1 30 " = (x,y,z) coordinates to u se." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 15 "" 0 "" {TEXT 263 5 "p lane" }}{PARA 0 "" 0 "" {TEXT -1 4 " " }{TEXT 265 10 "[nx,ny,nz]" } {TEXT -1 45 " = direction vector of a normal to the plane." }}{PARA 0 "" 0 "" {TEXT 264 10 " [x,y,z]" }{TEXT -1 30 " = (x,y,z) coordinates to use." }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 8 "Examples" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "coords := [u,v,w]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "F(u,v,w) = quadric( f, epsilon, coo rds );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"FG6%%\"uG%\"vG%\"wG,&F) \"\"\"*&,&*$F'\"\"#F+*$F(F/F+F+,&%\"fGF/*$,(*$F2F/\"\"%*&%(epsilonGF+F 'F/!\"\"*&F8F+F(F/F9#F+F/F+F9F9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "n := vector([A,B,C]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "G(u,v,w) = plane( n, coords );" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#/-%\"GG6%%\"uG%\"vG%\"wG,(*&%\"AG\"\"\"F'F-F-*&%\"BGF-F(F-F-*&%\"CGF -F)F-F-" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 18 "Contact the Author" }}{PARA 15 "" 0 "" {TEXT -1 123 "Dr. Marc A. Murison\nAstronomical App lications Dept.\nU.S. Naval Observatory\n3450 Massachusetts Ave., NW\n Washignton, DC 20392" }}{PARA 15 "" 0 "" {TEXT 256 29 "murison@riemann .usno.navy.mil" }}{PARA 15 "" 0 "" {TEXT 256 35 "http://riemann.usno.n avy.mil/AESOP/" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 8 "See Also" }} {PARA 0 "" 0 "" {HYPERLNK 17 "AESOP" 2 "AESOP" "" }{TEXT -1 2 ", " } {HYPERLNK 17 "beam_intersect" 2 "AESOP,beam_intersect" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "reflect" 2 "AESOP,reflect" "" }{TEXT -1 2 ", " } {HYPERLNK 17 "surfnorm" 2 "AESOP,surface_normal" "" }{TEXT -1 2 ", " } {HYPERLNK 17 "Zernike" 2 "AESOP,Zernike" "" }}}}}{MARK "0 2" 0 } {VIEWOPTS 1 1 0 1 1 1803 }