[comp.graphics] Parametric Representation of General Conic Curve

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.

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	      ->  Even aliens think The Three Stooges are funny.  <-
   Jack Ritter, S/W Eng. Versatec, 2710 Walsh Av, Santa Clara, CA 95051
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rustcat@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