Advanced Programming Guide

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6.8 Animation • 271The gridpoints procedure is remarkably similar to the convert(...,gridpoints) procedure which is part of the standard Maple library. Thelibrary command includes more checking of the arguments and, therefore,is generally sufficient.6.8 AnimationMaple can generate animations in two or three dimensions. As with allMaple plotting facilities, such animations produce user-accessible datastructures. Data structures of the following type represent animations.orPLOT( ANIMATE( ... ) )PLOT3D( ANIMATE( ... ) )Inside the ANIMATE function is a sequence of frames; each frame isa list of the same plotting objects that can appear in a single plottingstructure. Every procedure that creates an animation builds such a sequenceof frames. You can see an example by printing the output of sucha procedure.> lprint( plots[animate]( x*t, x=-1..1, t = 1..3,> numpoints=3, frames = 3 ) );PLOT(ANIMATE([CURVES([[-1., -1.], [0., 0.], [1.0000000\00, 1.]],COLOUR(RGB,1.00000000,0.,0.))],[CURVES([[-1.,-2.], [0., 0.], [1.000000000, 2.]],COLOUR(RGB,1.000000\00,0.,0.))],[CURVES([[-1., -3.], [0., 0.], [1.00000000\0, 3.]],COLOUR(RGB,1.00000000,0.,0.))]),AXESLABELS(x,‘‘),VIEW(-1. .. 1.,DEFAULT))The function points is a parametrization of the curve (x, y) = (1 +cos(tπ/180) 2 , 1 + cos(tπ/180) sin(tπ/180)).> points := t -> evalf(> [ (1 + cos(t/180*Pi)) * cos(t/180*Pi ),> (1 + cos(t/180*Pi)) * sin(t/180*Pi ) ] ):For example,> points(2);
272 • Chapter 6: <strong>Programming</strong> with Maple Graphics[1.998172852, 0.06977773357]You can plot a sequence of points.> PLOT( POINTS( seq( points(t), t=0..90 ) ) );1.210.80.60.40.200.5 1 1.5 2You can now make an animation. Make each frame consist of thepolygon spanned by the origin, (0, 0), and the sequence of points on thecurve.> frame := n -> [ POLYGONS([ [ 0, 0 ],> seq( points(t), t = 0..60*n) ],> COLOR(RGB, 1.0/n, 1.0/n, 1.0/n) ) ]:The animation consists of six frames.> PLOT( ANIMATE( seq( frame(n), n = 1..6 ) ) );Animation in Static FormThe display command from the plots package can show an animationin static form.> with(plots):Warning, the name changecoords has been redefined> display( PLOT(ANIMATE(seq(frame(n), n = 1..6))) );
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ii•Waterloo Maple Inc.57 Erb Stre
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Contents • v3.6 Interfaces and Im
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Contents • viiPlotting Gears . .
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Contents • ixForeign Data . . . .
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1 Introduction1.1 Purpose of This B
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2 Procedures, Variables,and Extendi
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2.1 Nested Procedures • 5procedur
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2.1 Nested Procedures • 7> A[j] :
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2.1 Nested Procedures • 9> quicks
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2.1 Nested Procedures • 11> U :=
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2.2 Procedures That Return Procedur
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2.2 Procedures That Return Procedur
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2.3 Local Variables and Invoking Pr
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assign(another_a = a);> eqn;2.3 Loc
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[ seq( s[j][c[j]], j=1..2 ) ];2.3 L
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2.3 Local Variables and Invoking Pr
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2.4 Interactive Input • 25Improve
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2.4 Interactive Input • 27> reads
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2.5 Extending Maple • 29The parse
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2.5 Extending Maple • 31> ‘type
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2.5 Extending Maple • 33The follo
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2.5 Extending Maple • 3556 IIn th
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2.5 Extending Maple • 37Extending
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2.5 Extending Maple • 39The useri
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3 Programming withModulesProcedures
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• 43> gentemp := proc()> count :=
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3.1 Syntax and Semantics3.1 Syntax
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3.1 Syntax and Semantics • 47name
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3.1 Syntax and Semantics • 49> He
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3.1 Syntax and Semantics • 51mode
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3.1 Syntax and Semantics • 53The
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3.1 Syntax and Semantics • 55true
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3.1 Syntax and Semantics • 57modu
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3.1 Syntax and Semantics • 59> m
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This is achieved by the double assi
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3.1 Syntax and Semantics • 63This
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3.1 Syntax and Semantics • 65With
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3.1 Syntax and Semantics • 67> wh
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SpecFuncs := module()> export F; #
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3.2 Records • 71b> evalb( % = b )
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3.3 Packages • 73Packages in the
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3.3 Packages • 751 −1 + 1 21k x
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3.3 Packages • 77> "new types ‘
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3.3 Packages • 79definition. This
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3.3 Packages • 81true> member( 10
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3.3 Packages • 83The display show
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3.3 Packages • 85> end module:How
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3.3 Packages • 87From the output
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3.3 Packages • 89The final output
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3.3 Packages • 91shape-specific f
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3.3 Packages • 93The area Procedu
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"but got %1", shape> end if;>> # Ex
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3.4 The use Statement • 97> circl
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3.4 The use Statement • 99use sta
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3.4 The use Statement • 101C++),
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3.5 Modeling Objects3.5 Modeling Ob
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3.5 Modeling Objects • 10514 πFo
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3.5 Modeling Objects • 107> nitem
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3.5 Modeling Objects • 109> for i
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3.5 Modeling Objects • 111> lengt
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3.6 Interfaces and Implementations
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(−2790 T 6 − 77814+ 1943715124T
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4 Input and OutputAlthough Maple is
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4.1 A Tutorial Example • 157Openi
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4.1 A Tutorial Example • 159xy :=
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Buffered Files:4.2 File Types and M
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4.3 File Descriptors versus File Na
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f := fopen("testFile.txt",WRITE):>
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4.5 Input Commands • 167iostatus(
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4.5 Input Commands • 169otherwise
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4.5 Input Commands • 171y The nex
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4.5 Input Commands • 173various c
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4.5 Input Commands • 175Example T
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4.6 Output Commands • 177One-Dime
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4.6 Output Commands • 179the appr
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4.6 Output Commands • 181Writing
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4.6 Output Commands • 183z format
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4.6 Output Commands • 185• If n
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4.6 Output Commands • 187> writed
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4.7 Conversion Commands • 189Conv
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4.8 Notes to C Programmers • 191(
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5 Numerical Programmingin MapleFloa
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5.1 The Basics of evalf • 1953.14
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5.2 Hardware Floating-Point Numbers
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iterate(f, df, x0, N);> end proc:Us
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5.3 Floating-Point Models in Maple
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5.3 Floating-Point Models in Maple
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5.4 Extending the evalf Command •
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5.4 Extending the evalf Command •
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5.5 Using the Matlab Package • 21
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6 Programming with MapleGraphicsMap
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6.1 Basic Plot Functions • 217If
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6.2 Programming with Plotting Libra
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Page 268 and 269: 6.6 Vector Field Plots • 257Examp
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Page 300 and 301: 7 Advanced ConnectivityIn This Chap
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7.2 Using Compiled Code in Maple
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to_maple_char( kv, c )to_maple_comp
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7.3 System Integrity • 337by anot
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Table 7.3 Wrapper Compound TypesMap
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AInternal Representationand Manipul
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A.1 Internal Organization • 343wi
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A.2 Internal Representations of Dat
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Type Specification or TestA.2 Inter
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Length: 3 or moreA.2 Internal Repre
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A.3 The Use of Hashing in Maple •
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Index%, 174&, 31accuracy, 193, 195,
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Index • 375SAVE, 362SERIES, 363SE
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Index • 377defining numeric, 210n
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Index • 379name, 357name table, 3
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Index • 381statements, 174strings
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Waterloo Maple Inc.57 Erb Street We
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