How To Draw A Sphere On Xyz Graph

Different varieties of three-dimensional plots in Maple

In add-on to the basic plot3d command, Maple has several other useful commands for plotting surfaces. For example, here are iii dissimilar ways that Maple knows to draw a sphere of radius2 centered at the origin. (Think outset to load the plots package via the with(plots): command.)

Viewing the sphere as being implicitly defined past the equation 10²+y²+z²=iv, you could plot the surface with the following Maple command.

implicitplot3d(10^2+y^2+z^2=iv, x=-2..2,   y=-two..two, z=-ii..2, scaling=constrained);      

Alternatively, you could view the sphere equally a parametric surface. For a ii-dimensional surface, you demand two parameters, say s andt. Try the following Maple command; tin can you place what s and t stand for in spherical coordinates?

plot3d( [ii*sin(south)*cos(t), 2*sin(southward)*sin(t), 2*cos(s)],          s=0..Pi, t=0..2*Pi, scaling=constrained);      

Maple knows virtually polar coordinates in 2 dimensions, and it knows almost spherical coordinates in three dimensions. Hither is a third way to plot the sphere.

sphereplot(ii, theta=0..2*Pi, phi=0..Pi,            scaling=constrained);      

A new feature appears in 3 dimensions that we did non see in ii dimensions. Since in that location is more than room in 3 dimensions, nosotros have the possibility of plotting either a two-dimensional surface or a one-dimensional bend. We just saw above how to plot a surface. To plot a i-dimensional parametrized bend, apply the spacecurve control. The following command plots a helix.

spacecurve( [cos(t), sin(t), t],              t=0..4*Pi, championship="helix");      

A common way to draw a three-dimensional object is to specify its cross section at each point along a curve. For example, a cylinder is but the Cartesian production of a line with a circumvolve. Maple has a tubeplot command that implements this idea. The post-obit command draws a tube of constant radius around the helix.

tubeplot( [cos(t), sin(t), t], t=0..4*Pi, radius=0.5, tubepoints=30, title="helix tube");      

What happens if you modify this example by setting radius=t/6 and scaling=constrained?

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The Math 696 class pages were last modified Apr 5, 2005.
These pages are copyright © 1995-2005 by Harold P. Boas. All rights reserved.

Source: https://www.math.tamu.edu/~boas/courses/math696/varieties-of-3d-Maple-plots.html

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