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From: rustcat@csli.STANFORD.EDU (Vallury Prabhakar)
Newsgroups: comp.graphics,sci.math,sci.math.symbolic
Subject: Re: Parametric Representation of General Conic Curve
Message-ID: <7735@csli.STANFORD.EDU>
Date: 24 Feb 89 04:39:12 GMT
References: <15517@versatc.UUCP>
Reply-To: rustcat@csli.stanford.edu (Vallury Prabhakar)
Organization: Stanford University
Lines: 21

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