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b[k]:=rand() od: randomize:\na[n]: =a[1]:b[n]:=b[1]:\nQ:=plot([seq([[a[k],b[k]],[a[k+1],b[k+1]]],k=1..n-1 )],color=blue):\nT:=plot([bezier([seq(a[k],k=1..n)],t),bezier([seq(b[k ],k=1..n)],t),t=0..1],color=red):\ndisplay([T,Q],scaling=constrained,a xes=none);\n" }}{PARA 13 "" 1 "" {GLPLOT2D 486 486 486 {PLOTDATA 2 "6, -%'CURVESG6$7en7$$\"3++++AcO\"[(!\"($\"3+++WQWUQk!\"'7$$\"3Ye3\\E;)=3) F*$\"35#RaMMe@['F-7$$\"37VHFV\"3(z&)F*$\"3*3\"*>=.3(QlF-7$$\"3Pmk-PUjG \"*F*$\"3o:)>\"zbl=mF-7$$\"3yBJVTm%\\o*F*$\"3cXHAkWS7nF-7$$\"3d*[J#Q6i D5F-$\"3>>M^MV%[\"oF-7$$\"3=Jx%[Rz63\"F-$\"3wuGU6F-$\"3+YYF6\">)>qF-7$$\"3`'y>$Q1v47F-$\"3;1Q)y2 #>#G\"F-$\"3o<1=n/#4B(F-7$$\"3C2*HRf_CO\"F-$\"3\\r2G%\\0/L(F-7$$\"3^8K FWO=Q9F-$\"3,ep_u;B5uF-7$$\"3?(okW**o\"H:F-$\"3]rKN%*oK*[(F-7$$\"3qUJk KdcE;F-$\"3Y*omQX#QbvF-7$$\"3_bc&Q!p$fs\"F-$\"3Ia1nZ6z/wF-7$$\"3>))yO4 Vd?=F-$\"3!>p'p0*okj(F-7$$\"3XBiXeu0Q>F-$\"3q/t#yL:nl(F-7$$\"3\"zyHv>r 7/#F-$\"3UE$eM)4QewF-7$$\"3/\"=hPhR[;#F-$\"3$GR^bA()=k(F-7$$\"3gGCNn%> mF#F-$\"3'3QDhK(\\5wF-7$$\"32ajd'**44S#F-$\"3]+bW6!))yb(F-7$$\"3%G;Bd! *z)>DF-$\"37CZ.l`L!\\(F-7$$\"3OV>#)G-]VEF-$\"3a[(z1o%=-uF-7$$\"3G)45>B yav#F-$\"3b*y,B]#*fI(F-7$$\"31_$oGl^L(GF-$\"3A*>RwGAo=(F-7$$\"3'p()3Y# 37\"*HF-$\"3GAGHf:UZqF-7$$\"3QhmWLt\\)3$F-$\"3O?@HhJU9pF-7$$\"3-b2&fn= p=$F-$\"3E1R&o.%=gnF-7$$\"3%oDGR\"HqzKF-$\"3Ia1@TnB\"f'F-7$$\"35#Ra(ef 7gLF-$\"3zc>zIDt=kF-7$$\"3>kE!z2imU$F-$\"3[QpMj[LZiF-7$$\"3EP>3w]q&[$F -$\"3CMj(etM[0'F-7$$\"3^?5'pt#yBNF-$\"3G))Hn!)\\y#)eF-7$$\"3/;$=.L'*pa $F-$\"3/6QI*>'Q.dF-7$$\"3'Gb)o^=$4b$F-$\"3K^Qqw2sZbF-7$$\"3xjGa!e7\\`$ F-$\"3o%yw@rq')Q&F-7$$\"35&fbk5_))\\$F-$\"3W-]20'QKD&F-7$$\"3\"z(z)**f 1xV$F-$\"3L]F-7$$\"3D_5vk4YO KF-$\"3'H-O?=[-'\\F-7$$\"3Ua^'G\\(H&4$F-$\"36LR4D$oF#\\F-7$$\"3'G$*R&[ <**>HF-$\"3lL2#f)*3H#\\F-7$$\"3z`2#pC*e8FF-$\"3'**>\"HJ*po'\\F-7$$\"3/ E^\"oP[ug#F-$\"3,RP.#)HC.]F-7$$\"3mjIc\"ouR\\#F-$\"3m*)of#=!e]]F-7$$\" 3Wv52=-raBF-$\"3,NY/e!f!>^F-7$$\"32@Zg(Q'R0AF-$\"3QNcp&=wN?&F-7$$\"37_ $H^ZdJ1#F-$\"3G3T2`?\\$H&F-7$$\"3i]4l*HaD\">F-$\"3q&3HAH9wR&F-7$$\"3c \"4?sS*fU\"F-$\"3mu-:(yu0+'F-7$$\" 3=\"3?7-cS3\"F-$\"3C]xBbLr,hF-7$$\"3%Q6lsBt'[(*F*$\"3Y*p&*=W?$3iF-7$$ \"3Q'4%z\"46!H')F*$\"3ZCQw\\o^?jF-F'-%'COLOURG6&%$RGBG$\"*++++\"!\")$ \"\"!Fc]lFb]l-F$6$7$F'7$$\"3+++lXv0>8F-$\"3+++\"Re`2s'F--F\\]l6&F^]lFb ]lFb]lF_]l-F$6$7$Fg]l7$$\"3+++&z3r`N\"F-$\"3+++ua:Q;**F-F\\^l-F$6$7$Fa ^l7$$\"3+++4V(3h_%F-$\"3+++g8BnGuF-F\\^l-F$6$7$Fi^l7$$\"3+++#Q3Ba-&F-$ \"3+++#fvO0*>F-F\\^l-F$6$7$Fa_lF'F\\^l-%+AXESLABELSG6%Q!6\"F\\`l-%%FON TG6#%(DEFAULTG-%(SCALINGG6#%,CONSTRAINEDG-%*AXESSTYLEG6#%%NONEG-%%VIEW G6$Fa`lFa`l" 1 2 0 1 10 0 2 9 1 1 1 1.000000 45.000000 45.000000 0 0 " Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 418 "n:=6: for k to n do a[k]:=rand(); \+ b[k]:=rand() ; c[k]:=rand() od: randomize:\nfor k to n-1 do Q[k]:=spac ecurve([t*a[k]+(1-t)*a[k+1],t*b[k]+(1-t)*b[k+1],t*c[k]+(1-t)*c[k+1],t= 0..1],numpoints=2,color=blue,thickness=2) od:\nT:=spacecurve([bezier([ seq(a[k],k=1..n)],t),bezier([seq(b[k],k=1..n)],t),bezier([seq(c[k],k=1 ..n)],t),t=0..1],color=red,thickness=2):\ndisplay3d([T,seq(Q[k],k=1..n -1)],scaling=constrained,axes=none);\n" }}{PARA 13 "" 1 "" {GLPLOT3D 486 486 486 {PLOTDATA 3 "6*-%'CURVESG6%7T7%%*undefinedGF(F(F'F'F'F'F'F 'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F 'F'F'F'F'F'F'F'F'-%'COLOURG6&%$RGBG$\"*++++\"!\")$\"\"!F1F0-%*THICKNES SG6#\"\"#-F$6%7$7%$\"+`RJSkF5$\"+t%\\i?*F5$\"+,``5&*F57%$\"+T$))\\g*F5 $\"+zX?H\")F5$\"+&>qu`%F5-F*6&F,F0F0F-F2-F$6%7$7%$\"+sI'[Y\"F5$\"+Nw!f b\"F5$\"+Pn#RH%F5F9FGF2-F$6%7$7%$\"+5^Ga_F5$\"+!41gs#F5$\"+%*4g(>#F5FL FGF2-F$6%7$7%$\"+Q$H)fnF5$\"+&4NZX)F5$\"+$)yqknF5FVFGF2-F$6%7$7%$\"+#z (Q8GF5$\"+/!f\\#zF5$\"+$R&47vF5FjnFGF2-%(SCALINGG6#%,CONSTRAINEDG-%*AX ESSTYLEG6#%%NONEG" 1 2 0 1 10 0 2 1 1 1 1 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 402 "n:=5: r:=rand(100): for k to n do a[k]:=r(); b[k]:=r() ; c[k]:=r() od: randomize:\nfor k t o n-1 do Q[k]:=spacecurve([t*a[k]+(1-t)*a[k+1],t*b[k]+(1-t)*b[k+1],t*c [k]+(1-t)*c[k+1],t=0..1],numpoints=2,color=blue) od:\nT:=tubeplot([bez ier([seq(a[k],k=1..n)],t),bezier([seq(b[k],k=1..n)],t),bezier([seq(c[k ],k=1..n)],t),t=0..1],radius=0.8):\nU:=display3d([T,seq(Q[k],k=1..n-1) ],scaling=constrained,axes=none):U;\n" }}{PARA 8 "" 1 "" {TEXT -1 65 " Error, (in plots/tubeplot/tubesf1) All curvepoints are undefined\n" }} {PARA 13 "" 1 "" {GLPLOT3D 486 486 486 {PLOTDATA 3 "6)-%'CURVESG6%7T7% %*undefinedGF(F(F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F' F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'F'-%'COLOURG6&%$RGBG$\"*++++ \"!\")$\"\"!F1F0-%*THICKNESSG6#\"\"#-F$6$7$7%$\"#?F1$\"#WF1$\"#lF17%$ \"#6F1$\"#QF1$\"#8F1-F*6&F,F0F0F--F$6$7$7%$\"#\"*F1$\"#&*F1$\"#uF1F9FG -F$6$7$7%$\"\"*F1$\"#gF1$\"##)F1FLFG-F$6$7$7%$\"##*F1FE$\"#xF1FVFG-%(S CALINGG6#%,CONSTRAINEDG-%*AXESSTYLEG6#%%NONEG" 1 2 0 1 10 0 2 1 1 1 1 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve \+ 4" "Curve 5" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "libname;\n \+ libname := \"C:/Program Files/Maple 8/JavaViewLib\", libname;\n with(J avaViewLib);\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "exportHTM(\"bezie r3d applet.html\",U);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#Q=C:\\Program ~Files\\Maple~8/lib6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(libnameG6 $QEC:/Program~Files/Maple~8/JavaViewLib6\"Q=C:\\Program~Files\\Maple~8 /libF'" }}{PARA 6 "" 1 "" {TEXT -1 127 "Warning: Unable to locate brow ser via the path environment variable. Please set and reload the packa ge. Using default browser. " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#70%*exp ortHTMG%.exportHTMLiteG%*exportJVXG%*exportMPLG%'genTagG%+genTagLiteG% (getInfoG%'importG%*runAppletG%.runAppletLiteG%,runJavaViewG%.runMarku pTreeG%$setG%,viewGalleryG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%gnC:\\P rogram~Files\\Maple~8\\JavaViewLib\\htm\\bezier3d~applet.htmG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 104 "for l from 0 to 9 do C[l]:= display3d([T,seq(Q[k],k=1..n-1)],scaling=constrained,orientation=[0,9* l]) od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "display3d(seq(C[ l],l=0..9),insequence=true);\n" }}{PARA 13 "" 1 "" {GLPLOT3D 486 486 486 {PLOTDATA 3 "6#-%(ANIMATEG6,7)-%%MESHG6#7T7,7%$\"3#\\(3H!3W^z&!#;$ \"3IB@Oy)>@()*F/$\"3O\"[)Q))*\\pQ*F/7%$\"3S!\\-Sf%)Gx&F/$\"3ky02&o#R^) *F/$\"3GW'HO'*>#[%*F/7%$\"3b1$ehf@lr&F/$\"3GVYk%R4M&)*F/$\"3M%H$)>GFp[ *F/7%$\"3ciX&)fzU_cF/$\"3)4QhiOEs()*F/$\"3aMy+f.'\\[*F/7%$\"31.#R)4Qf5 cF/$\"3#>;0UP*p6**F/$\"3/&RB)R&RKW*F/7%FJ$\"3s*GM\\6)pS**F/$\"3CL;SfkG 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1-t)*c[k+1],t=0..1],numpoints=2,radius=a[1]/20,color=red) od:\nT:=tube plot([bezier([seq(a[k],k=1..n)],t),bezier([seq(b[k],k=1..n)],t),bezier ([seq(c[k],k=1..n)],t),t=0..1],radius=a[1]/20):\ndisplay3d([T,seq(Q[k] ,k=1..n-1)],scaling=constrained,axes=none);" }}{PARA 13 "" 1 "" {GLPLOT3D 486 486 486 {PLOTDATA 3 "6*-%%MESHG6#7T7,7%$\"39!e!)[GOl\"p! \"($\"3].`8(GKn>\"!\"'$\"3'z:y_7tMu&F.7%$\"35%[4lIT,%oF+$\"3a9I!*[x/#= \"F.$\"3!40w%oKwv6F.$\"3#Q\"zR&oL$= dF.7%$\"3$*4(fv&=tEkF+$\"3a6/4C%>3=\"F.$\"3bPA\"F.$\"3F?qiUA+HdF.7%FG$\"3'3Q!*p!4H67F.$\"3%)zI)pTqWu& F.7%F@$\"38&Gu()G[CA\"F.$\"3G.'\\N$o%yv&F.7%F9$\"3Uhdvm=5B7F.$\"3%)3GN =D(Gw&F.7%F2$\"3?nN`Ce%H@\"F.$\"3O1!>w*e>ddF.F(7,7%$\"3-k=prX'3$yF+$\" 3,X9%=3Emi\"F.$\"3Mp5C(\\,\")G&F.7%$\"3iNu&G!z_ixF+$\"3d\"za,L_Ah\"F.$ \"3g:T(4k$4s_F.7%$\"3M3,Ipo&Qd(F+$\"3VS95%>\\fg\"F.$\"3;M\"[.@B9E&F.7% $\"3MAjYWF8`tF+$\"3N3B4\")fm5;F.$\"37Y;W=I3h_F.7%$\"3T47W*zMO?(F+$\"3t ?J2ac>C;F.$\"3w5&G[CK7F&F.7%$\"3O2m=%y9`>(F+$\"3**)e!pGv?S;F.$\"3#oA'o 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