Hint: Parametrizing lines in Maple

One way to simplify the notation involved in parametrizing these surfaces in Maple is to make use of the Maple add command to add vectors. In order to use this command, you must have executed the command with(linalg): in order to tell Maple about this command.

If you have defined

T:=(s,t)-> [(2+cos(t))*cos(s),(2+cos(t))*sin(s),sin(t)];

then notice that

p := T(0,Pi/2);
q := T(0,3*Pi/2);

returns two vectors (points in 3-space).

One way to parametrize the line segment between any two points p and q is (1-t) p + t q, 0 <= t <= 1. In Maple, we cannot just type in this expression, since p and q are vectors. Instead we would type the command:

S := add(p, q, 1-t, t);

The expression S (which depends on t) is now a parametrization of the line segment from p to q. You may wish to look at the help page ?add for further examples and explanations.


Previous: Building a Surface from Torus Knots
Frederick J. Wicklin <fjw@geom.umn.edu>
Last modified: Tue Mar 5 14:27:00 1996