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{SECT 0 {EXCHG {PARA 4 "" 0 "" {TEXT -1 10 "Animations" }}{PARA 256 "
" 0 "" {TEXT -1 31 "by Bob Bradshaw, Ohlone College" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 54 "There are three
 forms of two-dimensional animation in " }{TEXT 256 5 "Maple" }{TEXT 
-1 32 ". The first form is the command " }{TEXT 257 12 "animatecurve" 
}{TEXT -1 131 ". This command imitates the gradual drawing of a graph \+
that you would see on a graphing calculator. The second form is the co
mmand " }{TEXT 258 7 "animate" }{TEXT -1 152 ". This command allows yo
u to modify an equation. The third form is through the use of sequence
s. This method provides the most control of the animation." }}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 100 "All thre
e of the forms require the use of the plotting subroutines so start by
 loading this package." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plot
s):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 200 "To see any of the following animations, execute the commands a
nd then click once on the picture. You should see a set of VCR-type co
ntrols at the top of the screen. Use these to control the animation." 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 41 "First w
e look at a simple example of the " }{TEXT 259 12 "animatecurve" }
{TEXT -1 149 " command. This command will produce animations of standa
rd functions or parametric equations. below is an animation of a set o
f parametric equations." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "animatec
urve([cos(3/2*t)*cos(t),cos(3/2*t)*sin(t),t=0..4*Pi],numpoints=400);" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 20 
"Now, we look at the " }{TEXT 260 7 "animate" }{TEXT -1 43 " command. \+
In the following example, we use " }{TEXT 261 7 "animate" }{TEXT -1 
64 " to see the effects of changing the amplitude of a sine curve.. " 
}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "animate(a*sin(6*x),x=-1..1,a=-4..
4,view=[-1..1,-4..4]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 89 "The most powerful method of creating anim
ations is through the use of sequences. A basic " }{TEXT 262 8 "sequen
ce" }{TEXT -1 32 " command has the following form." }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 16 "seq(i^2,i=1..6);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 19 "We can now use the " }{TEXT 
263 8 "sequence" }{TEXT -1 37 " command to generate the plot of sin(" 
}{TEXT 264 2 "ax" }{TEXT -1 32 ") for three different values of " }
{TEXT -1 41 "a. Create the sequence first and name it." }{TEXT -1 1 " \+
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "bb1:=seq(plot(sin(a*x),x=-6.3..
6.3,color=blue),a=1..3):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 38 "The animation is plotted by using the " }
{TEXT 266 7 "display" }{TEXT -1 32 " command. If you use the option " 
}{TEXT 267 16 "insequence=false" }{TEXT -1 58 ", all frames are shown \+
together and there is no animation." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
30 "display(bb1,insequence=false);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 17 "Using the option " }{TEXT 268 
15 "insequence=true" }{TEXT -1 32 " shows only one frame at a time." }
{TEXT -1 1 " " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "display(bb1,insequ
ence=true);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 70 "If we create a second sequence, you can compare the res
ults of making " }{TEXT 269 10 "insequence" }{TEXT -1 23 " either true
 or false. " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "bb2:=seq(plot(-sin(a
*x),x=-6.3..6.3,color=green),a=1..3):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 34 "display(bb1,bb2,insequence=true);\n" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 78 "You can also look at the \+
effect of chanign the order of what you are plotting." }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 33 "display(bb2,bb1,insequence=true);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 25 "If you cr
eate and name a " }{TEXT 270 7 "display" }{TEXT -1 41 " command, these
 can again be placed in a " }{TEXT 271 7 "display" }{TEXT -1 44 " comm
and. This may be a useful time to have " }{TEXT 272 16 "insequence=fal
se" }{TEXT -1 1 "." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "displaygreen:
=display(bb1,insequence=true):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "d
isplayblue:=display(bb2,insequence=true):" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 51 "display(displayblue,displaygreen,insequence=false);" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
125 "In the following, I first declare a set of parametric functions, \+
the number of frames in the animation, an initial and final " }{TEXT 
273 1 "t" }{TEXT -1 19 " value and a delta " }{TEXT 274 1 "t" }{TEXT 
-1 7 " value." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 124 "xt:=cos(3/2*t)*co
s(t);\nyt:=cos(3/2*t)*sin(t);\nnumframes:=60;\ninitialt:=0;\nfinalt:=1
2.56;\ndelta:=(finalt-initialt)/numframes;" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 126 "We can create a sequence
 in which the color is defined using the HUE command, where the HUE is
 a function of the frame number." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
121 "bb5:=seq(plot([xt,yt,t=initialt+(i-1)*delta..initialt+i*delta],co
lor=COLOR(HUE,i/numframes),thickness=3),i=1..numframes):" }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 30 "display(bb5,insequence=true);\n" }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 30 "display(bb5,insequence=false);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 85 "This is a
 repeat of the above animation with a slight change in the initial val
ue of " }{TEXT 275 1 "t" }{TEXT -1 1 "." }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 109 "bb6:=seq(plot([xt,yt,t=initialt..initialt+i*delta],color=COLO
R(HUE,i/numframes),thickness=3),i=1..numframes):" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "display(bb6,insequence=true);\n" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "16" 0 }{VIEWOPTS 1 1 0 1 1 1803 
1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }