Math 13 Fall 2004
Calculus of Vector-valued Functions
Examples of Parametrized Surfaces
November 16, 2004
Define a parametrized surface in the space
> | X := (s, t) -> [2 * cos(s) * sin(t), 2 * sin(s) * sin(t), 2 * cos(t)]; |
Let's render it with parameters taking values in some rectangle.
Looks like a slice of a sphere!
> | plot3d(X(s,t), s = 0 .. 2, t = 0 .. 1); |
Make the parametrizing rectangle larger . . .
> | plot3d(X(s,t), s = 0 .. 4, t = 0 .. 2); |
. . . and larger. It's indeed a sphere!
Black lines are the coordinate curves. "Meridians" and "latitude circles"
correspond to s and t being constants, respecively.
> | plot3d(X(s,t), s = 0 .. 2*Pi, t = 0 .. Pi); |
> |