link curves
March 25, 2002; Ralph E. Griswold
This file is in the public domain.
This file links procedure files that generate traces of points on various
plain curves.
The first two parameters determine the defining position of the
curve:
x x coordinate
y y coordinate
The meaning of "definition position" depends on the curve. In some
cases it is the position at which plotting starts. In others, it
is a "center" for the curve.
The next arguments vary and generally refer to parameters of the
curve. There is no practical way to describe these here. If they
are not obvious, the best reference is
A Catalog of Special Plane Curves, J. Dennis Lawrence,
Dover Publications, Inc., New York, 1972.
This book, which is in print at the time of this writing, is a
marvelous source of information about plane curves and is inexpensive
as well.
The trailing parameters give the number of steps and the end points
(generally in angles) of the curves:
steps number of points, default varies
lo beginning of plotting range, default varies
hi end of plotting range, default varies
Because of floating-point roundoff, the number of steps
may not be exactly the number specified.
Note: Some of the curves may be "upside down" when plotted on
coordinate systems in which the y axis increases in a downward direction.
Caution: Some of these procedures generate very large values
in portions of their ranges. These may cause run-time errors when
used in versions of Icon prior to 8.10. One work-around is to
turn on error conversion in such cases.
Warning: The procedures that follow have not been tested thoroughly.
Corrections and additions are most welcome.
These procedures are, in fact, probably most useful for the parametric
equations they contain.