{VERSION 6 0 "IBM INTEL LINUX" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 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 "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 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 "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "T itle" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 21 "An Animation Tutorial" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 177 "Maple has an animation program w hich is OK for some simple animations such as tracing out parametric c urves. The example that we have used to animate is that of the polar g raph " }{XPPEDIT 18 0 "r := exp(cos(theta))-2*cos(4*theta)+sin(theta/1 2)^5;" "6#>%\"rG,(-%\$expG6#-%\$cosG6#%&thetaG\"\"\"*&\"\"#F--F*6#*&\"\" %F-F,F-F-!\"\"*\$)-%\$sinG6#*&F,F-\"#7F4\"\"&F-F-" }{TEXT -1 219 ". We \+ have changed to the parametric form since we can't seem to animate pol ar graphs. Just change the colon to a semicolon if you wish to view th e animation. (Note the command for viewing the help page for animation s.)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "?plots,animate" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 261 "plots[animate](plot,[[(exp(cos(t))-2*cos(4*t)+(sin(t/12))^5)* cos(t),(exp(cos(t))-2*cos(4*t)+(sin(t/12))^5)*sin(t),t=0..A]],A=0..2*P i, scaling=constrained, frames=50 ): #To run, just click on the graph \+ and the triangle symbol above. Guess the name of this curve." }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 112 "F or more complicated animations we need to learn about the structure o f a plot. We start with a simple example." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "p:=plot([[-1,0],[13. 5,0]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG-%/INTERFACE_PLOTG6%- %'CURVESG6\$7\$7\$\$!\"\"\"\"!\$F/F/7\$\$\"3+++++++]8!#;F0-%'COLOURG6&%\$RGBG\$ \"#5F.F0F0-%+AXESLABELSG6\$Q!6\"F>-%%VIEWG6\$%(DEFAULTGFC" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 168 "Study th e help page \"?plot, structure\" where, CURVES, COLOR (or Canadian sp elling COLOUR), VIEW, etc. are defined. Then view the help page \"?op \" to see how op is used." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "op(1,p);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'CURVESG6\$7\$7\$\$!\"\"\"\"!\$F*F*7\$\$\"3+++++++]8!#;F+-%' COLOURG6&%\$RGBG\$\"#5F)F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "op(1,%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7\$7\$\$!\"\"\"\"!\$F'F'7\$\$ \"3+++++++]8!#;F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 123 "The percentage symbol refers to the last output. \+ We will want to capture the points of a graph. This we can do in one s tep:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "op(1,op(1,p));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7\$7 \$\$!\"\"\"\"!\$F'F'7\$\$\"3+++++++]8!#;F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 51 "The next plot is that of \+ a circle with centre at ( " }{XPPEDIT 18 0 "1.5,1;" "6\$-%&FloatG6\$\"#: !\"\"\"\"\"" }{TEXT -1 1 ")" }{TEXT -1 100 " and radius 1. If you dele te the \"p1:=\" and replace the colon by a semicolon, you can see the \+ graph." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "p1:=plot([1.5+cos(v),1+sin(v),v=0..2*Pi]):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "op(1,op(1,p1)): #Replace the colon by a semicolon to see what you get." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 143 "The trace of a fixed poi nt on the circumference of a rolling circle of radius 1 is given next, where the circle rolls two complete revolutions." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 143 "plot([u-si n(u),1-cos(u),u=0..4*Pi]): #Note the graph may not look right unless y ou click on the graph and click the 1:1 button above the graph." }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "No w we are ready to run the animation." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 305 "p1:=plot([[-1,0],[13.5,0 ]]):data:=op(1,op(1,p1)):p:=NULL:n:=50:for theta to n do t:=evalf(4*th eta*Pi/n):p1:=plot([t+cos(u),1+sin(u),u=0..2*Pi]):p2:=plot([u-sin(u),1 -cos(u),u=0..t]):data1:=data,op(1,op(1,p1)),op(1,op(1,p2)):colours:=RG B,0,0,0,0,0,0,1,0,0:p3:=PLOT(CURVES(data1,COLOUR(colours))):p:=p,p3:od :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "plots[display]([p],ins equence=true,axes=none,scaling=constrained):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "plots[display](p3,axes=none,scaling=constrained) ;" }}{PARA 13 "" 1 "" {GLPLOT2D 400 400 400 {PLOTDATA 2 "6%-%'CURVESG6 &7\$7\$\$!\"\"\"\"!\$F*F*7\$\$\"3+++++++]8!#;F+7S7\$\$\"32+++iqjc8F/\$\"\"\"F*7 \$\$\"3\"4hRdo+dN\"F/\$\"3KmdD=y_O6!#<7\$\$\"3j%>;!yJ\"F/\$\"3[@@&\\!>8\"z\"F;7\$\$\"3KuIcxZu18F/\$\"3I>p (Qh-a'=F;7\$\$\"3O3nWe%Q[H\"F/\$\"3..g5^l:C>F;7\$\$\"3#[@iZ#4*=G\"F/\$\"3ZQ \"[M\"oen>F;7\$\$\"3R^hAI%)3q7F/\$\"3!)fVPO<\"4*>F;7\$\$\"3pfAI^tdc7F/\$\"3% 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