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Murison" }}{PARA 256 "" 0 "" {TEXT -1 59 "Astronomical Applications Department\nU.S. Naval Observatory" }} {PARA 258 "" 0 "" {TEXT -1 58 "murison@aa.usno.navy.mil\nhttp://aa.usn o.navy.mil/murison./" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 19 1 "restart ;" "6#%(restartG" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 19 1 "with(curves );" "6#-%%withG6#%'curvesG" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7C%7Para metrizedToImplicitG%*arclengthG%(astroidG%)binormalG%)cardioidG%*cassi nianG%)catenaryG%'circleG%(cissoidG%)clothargG%)clothoidG%*curvatureG% (cycloidG%(deltoidG%(ellipseG%(evoluteG%'foliumG%&helixG%*hyperbolaG%* inversionG%)involuteG%+lemniscateG%*lissajousG%*logspiralG%)parabolaG% &pedalG%'radialG%(tangentG%(torsionG%*torusknotG%)tractrixG%)twicubicG %+unitnormalG" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 12 "Space Curves" } }{SECT 1 {PARA 4 "" 0 "" {TEXT -1 10 "Torus Knot" }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 19 1 "TorusKnot := (a,b,c,p,q,t)->[(a+b*cos(q*t))*cos(p* t),\n (a+b*cos(q*t))*sin(p*t),\n \+ c*sin(q*t)]:" "6#>%*TorusKnotGR6(%\"aG%\"bG%\"cG%\" pG%\"qG%\"tG7\"6$%)operatorG%&arrowG6\"7%*&,&F'\"\"\"*&F(F5-%$cosG6#*& F+F5F,F5F5F5F5-F86#*&F*F5F,F5F5*&,&F'F5*&F(F5-F86#*&F+F5F,F5F5F5F5-%$s inG6#*&F*F5F,F5F5*&F)F5-FE6#*&F+F5F,F5F5F1F1F1" }}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 25 "Plot (The Luge from Hell)" }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 19 1 "tubecurveplot( TorusKnot(10,3,5,2,5,t), 1.2, t=0..2*Pi, \n theta=0.5*Pi..2.0*Pi, axes=box, grid=[100,12], \n \+ orientation=[110,60], title=`Luge from Hell` );" "6#-%.tub ecurveplotG6*-%*TorusKnotG6(\"#5\"\"$\"\"&\"\"#\"\"&%\"tG$\"#7!\"\"/F. ;\"\"!*&\"\"#\"\"\"%#PiGF7/%&thetaG;*&$\"\"&!\"\"F7F8F7*&$\"#?!\"\"F7F 8F7/%%axesG%$boxG/%%gridG7$\"$+\"\"#7/%,orientationG7$\"$5\"\"#g/%&tit leG%/Luge~from~HellG" }}{PARA 13 "" 1 "" {GLPLOT3D 641 562 562 {PLOTDATA 3 "6,-%%MESHG6#W*[\\y\"_q\"-\"$402A000000000001BFEA9D893254C 2903FEBAE13CDF1C01A402AFF3B21C443E7BFE835CF6E642C103FE92DB9022ABD2F402 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**&F0F-F)\"\"%F.*&F0F-F)F-!#7*$F0F-\"#?*$%#a|irGF-\"\"*!\"\"F/" }}}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "More Junk" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 172 "jpgplot( tubecurveplot( Helix( Lemniscate(1,t), 0.1, t), \n 0.10, t=0..10, theta=0..2*Pi, axes=box, \n \+ scaling=unconstrained, grid=[100,10] ), `m:/foo.jpg` );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "resetplot();" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 42 "foo := kappa( TorusKnot(a,b,c,n,m,t), t ):" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "foo := simptrig( simplify( \+ expand(foo,trig), trig ), m*t );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>% $fooG*&,@*(,,*(%\"nG\"\"'%#a|irG\"\"\"%#b|irG\"\"$!\"%**F*\"\"%F,F-F.F /%\"mG\"\"#F4**F*F4F,F-F.F/F3F2F4*,%#c|irGF4F3F4F*F2F,F-F.F-!\"#*,F7F4 F3F2F.F-F*F4F,F-F8F--%$cosG6#*&F3F-%#t|irGF-F--%$sinGF " 0 "" {MPLTEXT 1 0 36 "kap := function( foo, a,b,c,n,m,t ):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "tor := simptrig( simplify( tau( TorusKnot(a,b,c, n,m,t), t ), trig ), m*t 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