ritter@versatc.UUCP (Jack Ritter) (02/23/89)
I want to find a parametric representation of
the general (2 dimensional) conic curve:
a*X**2 + b*X*Y + c*Y**2 + d*X + e*Y + f = 0.
Note, this is a general, rotated conic; it could
be an ellipse, parabola, or hyperbola (or line(s)).
What I want are 2 parametric functions representing
the above locus: X=G(t) & Y=H(t), so the curve
can be rendered.
Boundary points on the curve would determine start
and end values for t.
--
-> Even aliens think The Three Stooges are funny. <-
Jack Ritter, S/W Eng. Versatec, 2710 Walsh Av, Santa Clara, CA 95051
Mail Stop 1-7. (408)982-4332, or (408)988-2800 X 5743
UUCP: {pyramid,mips,vsi1,arisia}!versatc!ritterrustcat@csli.STANFORD.EDU (Vallury Prabhakar) (02/24/89)
In article <15517@versatc.UUCP> ritter@versatc.UUCP (Jack Ritter) writes:
#
# I want to find a parametric representation of
# the general (2 dimensional) conic curve:
#
# a*X**2 + b*X*Y + c*Y**2 + d*X + e*Y + f = 0.
#
# Note, this is a general, rotated conic; it could
# be an ellipse, parabola, or hyperbola (or line(s)).
#
# What I want are 2 parametric functions representing
# the above locus: X=G(t) & Y=H(t), so the curve
# can be rendered.
#
# Boundary points on the curve would determine start
# and end values for t.
This is completely explained in the section about Conics in "Geometric
Modelling" by Michael E. Mortenson. (Chapter 2, Section 11, Pages 79-91)
-- Vallury Prabhakar