2pi t02pi grid80 80 axesnone stylepatchnogrid

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Unformatted text preview: ere The hemisphere command makes a hemisphere. You can specify the radius and the coordinates of the center. Otherwise, leave an empty set of parentheses to accept the defaults. > cup := hemisphere(): > display( cup ); > cap := rotate( cup, Pi, 0, 0 ): > display( cap ); Dodecahedron All the sides of the dodecahedron mentioned earlier in this section are pentagons. If you raise the midpoint of each pentagon 148 • Chapter 5: Plotting by using the stellate command, the term for the resulting object is stellated dodecahedron. > a := stellate( dodecahedron() ): > display( a, scaling=constrained, style=patch ); > stelhs := stellate(cap, 2): > display( stelhs ); Instead of stellating the dodecahedron, you can cut out, for example, the inner three quarters of each pentagon. > a := cutout( dodecahedron(), 3/4 ): > display( a, scaling=constrained, orientation=[45, 30] ); 5.8 Code for Color Plates > hedgehog := [s1, s2, c3, stelhs]: > display( hedgehog, scaling=constrained, > style=patchnogrid ); • 149 5.8 Code for Color Plates Generating impressive graphics in Maple may require only a few lines of code as shown by the examples in this section. However, other graphics require many lines of code. Code for the color plates that do not have code included in this section can be found in the Maple Application Center. There are two ways to access the Maple Application Center. • Open your Internet browser of choice and enter http://www.mapleapps.com • From the Help menu, select Maple on the Web, and Maple Application Center. To access color plate code not included: 1. Go to the Maple Application Center. 2. Scroll to the bottom of the page. In the Maple Tools section, click Maple Color Plates. The code is available in both HTML and Maple Worksheet formats. Hundreds of graphics, including animations, are also available in the Maple Graphics Gallery and in the Maple Animation Gallery. To access these galleries, go to the Maple Application Center and click Maple Graphics. 150 • Chapter 5: Plotting Note: On some computers, the numpoints options value may need to be decreased to generate the plot. 1. Dirichlet Problem for a Circle > > > > > > > > > > > > > > > > with(plots): setoptions3d(scaling=constrained, projection=0.5, style=patchnogrid): f1 := (x, y) -> 0.5*sin(10*x*y): f2 := t -> f1(cos(t), sin(t)): a0 := evalf(Int(f2(t), t=-Pi..Pi)/Pi): a := seq(evalf(Int(f2(t)*cos(n*t), t=-Pi..Pi)/Pi), n=1..50): b := seq(evalf(Int(f2(t)*sin(n*t), t=-Pi..Pi)/Pi), n=1..50): L := (r, s) -> a0/2+sum(’r^n*(a[n]*cos(n*s)+b[n]*sin(n*s))’, ’n’=1..50): q := plot3d([r*cos(s), r*sin(s), L(r, s)], r=0..1, s=0..2*Pi, color=[L(r, s), -L(r, s), 0.2], grid=[29, 100], numpoints=10000): p := tubeplot([cos(t), sin(t), f2(t), t=-Pi..Pi, radius=0.015], tubepoints=70, numpoints=1500): display3d({q, p}, orientation=[3, 89], lightmodel=light3); 2. Mandelbrot Set The Mandelbrot Set is one of the most complex objects in mathematics given t...
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This note was uploaded on 08/27/2012 for the course MATH 1100 taught by Professor Nil during the Spring '12 term at National University of Singapore.

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