A space curve is defined by three functions x = f (t), y = g(t), z = h(t) of a single variable. You can create a ``fat curve'' by specifying a radius for the curve in the Plot Properties dialog box. This radius can be constant or can be a function of t. The Sample Size is the number of computed points along the curve; the Number of Tube Points is the number of computed points in a cross section of the tube. Ranges refers to the range of computed values for the parameter t. The View Intervals include intervals for x, y, and z of the form x0≤x≤x1, y0≤y≤y1, z0≤z≤z1.
To plot a space curve
The ``fat curve'' is designed to show which parts of the curve are close to
the observer and which are far away. Otherwise, a curve in space is
difficult to visualize. In the following example, the radius is set to 1
and
0≤t≤6.28 (
2π).
Plot 3D + Tube
dtbpF3in2.0003in0ptYou can draw a ``thin curve,'' by setting the radius to 0 in the dialog box.
By typing an expression in t for the radius and choosing the curve to be a straight line, you can get surfaces of revolution. In the following example, the radius is set to 1 - sin t, the range for t is -2π≤t≤2π, and the number of tube points is 30.
Plot 3D + Tube
t, 0, 0
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The spine of the surface of revolution can be any line, as illustrated by the next example plotted with Radius: 4 + sin 3t + 2 cos 5t, Axes: Frame, Style: Hidden Line, and t Range: -5≤t≤5.
Plot 3D + Tube
2t, - 3t, t
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