Math Challenge: A Lathe Problem

[Aaron Hill]

Ah, thanks for the answers.  I have Foley's Introduction
to Computer Graphics (the 1994 re-printed and updated
version of Computer Graphics: Principles and Practice,
1990)  :)

I figured NURBS could do it, because it is a rational
based spline.  However, the circle is actually a SQUARE-
ROOT based curve.  X^2 + Y^2 = R^2 ; Y = SQR(R^2 - X^2).
But this is only in "function" form, and only one half
of the curve can be shown.  This form is easily converted
to the parametric (via rect->polar).  Then the form is
XT=R*COS(T); YT=R*SIN(T), where T=[0,2PI].  (I remember
doing this in Calc class... was NOT any fun!)

But the torus would ONLY work if the "circle"'s center
was on the same side of the axis relative to the arc.
For instance, the example I stated before could not be
done with a torus.  However, if you want to lathe a
circle where the center is above the axis, well then you
HAVE a torus.  Good thinking though.

====
Aaron Hill (Redmond, WA)
E-Mail: SeracOhw24 at msn.com
IRC-Nick: Serac (EF-Net) (was SeracOhw)