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{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)
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45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
382 "Read the animation program for the rolling circle very carefully.
 We can write this \"procedure\" in a file and \"read\" this file into
 your Maple Worksheet.  You can save the ASCII file \"cycloid.txt\" (I
t is on my web site along with this worksheet.) and read it into your \+
worksheet with the \"read\" command. For help writing programs in Mapl
e see the help pages \"proc\" and \"statements\"." }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "20 0 0" 245 }{VIEWOPTS 1 1 0 1 
1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }