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g1 = Plot[1 + Sin[x] {x, 0, 2 o}]; , g2 = Plot[2 + Sin[x] {x, 2 o, 4 o}]; , g3 = Plot[3 + Sin[x] {x, 4 o, 6 o}]; , Show[g1, g2, g3, PlotRange Automatic]
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Two-Dimensional Graphics
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4.2 Additional Graphics Commands
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Standard geometric shapes can be constructed with the Graphics command and viewed with the Show command.
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Graphics[ primitive]creates a two-dimensional graphics object.
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The following are a few of the more common graphics primitives available in Mathematica:
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Circle[{x, y}, r] creates a circle centered at (x, y) having radius r. Disk[{x, y}, r] creates a disk (filled circle) centered at (x, y) having radius r. Point[{x, y}] plots a point at coordinate (x, y). Line[{{x1, y1}, {x2, y2}, ...}] draws lines connecting points (x1, y1), (x2, y2), . . . Rectangle[{x1, y1}, {x2, y2}] creates a filled rectangle having (x1, y1) and (x2, y2) as opposite ends of a diagonal. Polygon[{{x1, y1}, {x2, y2}, ...}]constructs a filled polygon having points (x1, y1), (x2, y2), . . . as vertices. Text[textstring, {x, y}] prints a string of text centered at position (x, y). TextStyle allows you to change the default font and size used in the graph s text. TextStyle {FontFamily fontname, FontSize size} is a simple, but useful, application.
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When viewing graphics objects using Show, the default, Axes False, causes the object to be drawn without axes. If desired, Axes True may be included as an option.
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EXAMPLE 23
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g1 = Graphics[Circle[{0, 0}, 1]]; g2 = Graphics[Line[{{ 1, 1}, { 1, 1}, {1, 1}, {1, 1}, { 1, 1}}]]; g3 = Graphics[Polygon[{{ 1, 0}, {0, 1}, {1, 0}, {0, 1}}]];
g4 = Graphics[Text["Square in a Circle in a Square", {0, 1.2}, TextStyle {FontSize 20}]];
Show[g1, g2, g3, g4]
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Curves are sometimes defined parametrically, i.e., the x- and y-coordinates of points are defined as two independent functions of a third variable. Parametric curves, which are usually more complex in their behavior, can be viewed using ParametricPlot.
ParametricPlot[ { x[t], y[t] } , { t, tmin, tmax } ] plots the parametric curve x = x(t), y = y(t) over the interval tmin t tmax.
Two-Dimensional Graphics
ParametricPlot[{{x1[t], y1[t]}, {x2[t], y2[t]}, ...}, {t, tmin, tmax}] plots several sets of parametric equations over tmin t tmax.
EXAMPLE 24
ParametricPlot[{t3 2 t, t2 t}, {t, 2, 2}]
6 5 4 3 2 1
EXAMPLE 25
x[t_] = Cos[t] Cos[100 t] Sin[t]; y[t_] = 2 Sin[t] Sin[100 t]; ParametricPlot[{x[t], y[t]},{t, 0, 2 o}]
1.0 0.5
Two-Dimensional Graphics
Implicitly defined curves can be plotted with the ContourPlot command.
ContourPlot[equation, {x, xmin, xmax}, {y, ymin, ymax}] plots equation by treating it as a function in three-dimensional space, and generates a contour of the equation cutting through the plane where z equals zero.
equation must be of the form lhs rhs. Note the double equal sign in the middle.
ContourPlot[{equation1, equation2,...}, {x, xmin, xmax}, {y, ymin, ymax}] plots several implicitly defined curves.
By default, ContourPlot sets Axes False and Frame True. Additional options such as Dashing, Graylevel, Thickness, etc. determining the appearance of the graph may be included using ContourStyle.
EXAMPLE 26 Plot the equation x 2 y 2 = ( y + 1)2 (4 y 2 ) for 10 x 10, 2 y 2. (Conchoid of Nicomedes.)
ContourPlot[x2 y2 (y + 1)2(4 y2), {x, 10, 10}, {y, 2, 2}, AspectRatio Automatic]
2 1 0 1 2 10 5 0 5 10
ContourPlot[x2 y2 (y + 1)2(4 y2), {x, 10, 10}, {y, 2, 2}, AspectRatio Automatic, Axes True, Frame False]
2 1 10 5 1 2 EXAMPLE 27 Plot the equation x 3 + y3 = 6 xy for 4 x 4, 4 y 4. (Folium of DeCartes.) 5 10
ContourPlot[x3 + y3 6 x y, {x, 4, 4},{y, 4, 4}, Axes True, Frame False]
Two-Dimensional Graphics
EXAMPLE 28 Plot cos( x y) = y sin x and sin( x y) = y cos x, 2 x 2, 2 y 2 on one set of axes.
ContourPlot[{Cos[x y] y Sin[x], Sin[x y] y Cos[x]}, {x, 2, 2}, {y, 2, 2}, ContourStyle {Dashing[.01], Dashing[.03]}, Axes True]
2 2 1 0 1 2
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