Drawing Space Curves

Maxima has a powerful graphics function draw3d interactively. For a fixed picture inside wxMaxima panel, use wxdraw3d instead. In order to use it we must first load the "draw" package.

--> load(draw)

We can draw a twisted cubic curve $\mathrm{r}(t) = \langle t, t^2, t^3 \rangle$ for $-2 \le t \le 2$ . The parametric curve must be defined in draw3d using

$\displaystyle {\tt parametric}(r_x(t), r_y(t), r_z(t), t, a, b)$

for the range $a \le t \le b$ .

--> draw3d(color=red, parametric(t,t^2,t^3,t,-2,2))

We can draw a twisted cubic curve as the intersection of the two cylinders

and

for $-2 \le x \le 2$ , $0 \le y \le 4$ and $-8 \le z \le 8$ .

--> draw3d(color=blue, parametric_surface(x,x^2,z,x,-2,2,z,-8,8),
       color=green, parametric_surface(x,y,x^3,x,-2,2,y,0,4),
       surface_hide = true);

Axes labels. The x-axis and y-axis are given by "right-hand rule," and the customized labels can be displayed alongside the boundary on the direction of the respective axes.

--> draw3d(xlabel="x-axis", ylabel="y-axis",
           color=red, parametric(t,t^2,t^3,t,-2,2))

The following wxm file has some of the even-numbered exercises assigned in the class.

exercise13-1.wxm