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Diffstat (limited to 'ipl/procs/curves.icn')
| -rw-r--r-- | ipl/procs/curves.icn | 520 |
1 files changed, 520 insertions, 0 deletions
diff --git a/ipl/procs/curves.icn b/ipl/procs/curves.icn new file mode 100644 index 0000000..a3a3a2a --- /dev/null +++ b/ipl/procs/curves.icn @@ -0,0 +1,520 @@ +############################################################################ +# +# File: curves.icn +# +# Subject: Procedures to generate points on plain curves +# +# Author: Ralph E. Griswold +# +# Date: March 25, 2002 +# +############################################################################ +# +# 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. +# +############################################################################ +# +# Links: gobject, math, step +# +############################################################################ + +link gobject +link math +link step + +procedure bullet_nose(x, y, a, b, steps, lo, hi) + local incr, theta + + /steps := 300 + lo := dtor(\lo) | -&pi + hi := dtor(\hi) | &pi + incr := (hi - lo) / steps + + every theta := step(lo, hi, incr) do + suspend Point( + x + a * cos(theta), + y + b * tan(&pi / 2 - theta), + 0 + ) + +end + +procedure cardioid(x, y, a, steps, lo, hi) + local incr, theta, fact + + /steps := 300 + lo := dtor(\lo) | -&pi + hi := dtor(\hi) | &pi + incr := (hi - lo) / steps + + every theta := step(lo, hi, incr) do { + fact := 2 * a * (1 + cos(theta)) + suspend Point( + x + cos(theta) * fact, + y + sin(theta) * fact, + 0 + ) + } + +end + +procedure cissoid_diocles(x, y, a, steps, lo, hi) + local incr, theta, radius + + /steps := 300 + lo := dtor(\lo) | (-2 * &pi) + hi := dtor(\hi) | (2 * &pi) + incr := (hi - lo) / steps + + every theta := step(lo, hi, incr) do { + radius := a * sin(theta) * cos(theta) + suspend Point( + x + radius * cos(theta), + y + radius * sin(theta), + 0 + ) + } + +end + +procedure cross_curve(x, y, a, b, steps, lo, hi) + local incr, theta + + /steps := 300 + lo := dtor(\lo) | -&pi + hi := dtor(\hi) | &pi + incr := (hi - lo) / steps + + every theta := step(lo, hi, incr) do + suspend Point( + x + a / cos(theta), + y + b / sin(theta), + 0 + ) + +end + +procedure cycloid(x, y, a, b, steps, lo, hi) + local incr, theta + + /steps := 100 + lo := dtor(\lo) | 0 + hi := dtor(\hi) | (8 * &pi) + incr := (hi - lo) / steps + + every theta := step(lo, hi, incr) do + suspend Point( + x + a * theta - b * sin(theta), + y + a - b * cos(theta), + 0 + ) + +end + +procedure deltoid(x, y, a, steps, lo, hi) + local incr, theta + + /steps := 300 + lo := dtor(\lo) | -&pi + hi := dtor(\hi) | &pi + incr := (hi - lo) / steps + + every theta := step(lo, hi, incr) do + suspend Point( + x + a * (2 * cos(theta) + cos(2 * theta)), + y + a * (2 * sin(theta) - sin(2 * theta)), + 0 + ) + +end + +procedure ellipse(x, y, a, b, steps, lo, hi) + local incr, theta + + /steps := 300 + lo := dtor(\lo) | -&pi + hi := dtor(\hi) | &pi + incr := (hi - lo) / steps + + every theta := step(lo, hi, incr) do + suspend Point( + x + a * cos(theta), + y + b * sin(theta), + 0 + ) + +end + +procedure ellipse_evolute(x, y, a, b, steps, lo, hi) + local incr, theta + + /steps := 300 + lo := dtor(\lo) | -&pi + hi := dtor(\hi) | &pi + incr := (hi - lo) / steps + + every theta := step(lo, hi, incr) do + suspend Point( + x + a * cos(theta) ^ 3, + y + b * sin(theta) ^ 3, + 0 + ) + +end + +procedure epitrochoid(x, y, a, b, h, steps, lo, hi) + local incr, theta, sum, fact + + /steps := 300 + lo := dtor(\lo) | -&pi + hi := dtor(\hi) | &pi + incr := (hi - lo) / steps + + sum := a + b + fact := sum / b + + every theta := step(lo, hi, incr) do + suspend Point( + x + sum * cos(theta) - h * cos(fact * theta), + y + sum * sin(theta) - h * sin(fact * theta), + 0 + ) + +end + +procedure folium(x, y, a, b, steps, lo, hi) + local incr, theta, radius + + /steps := 300 + lo := dtor(\lo) | -&pi + hi := dtor(\hi) | &pi + incr := (hi - lo) / steps + + every theta := step(lo, hi, incr) do { + radius := (3 * a * sin(theta) * cos(theta)) / + (sin(theta) ^ 2 + cos(theta) ^ 2) + suspend Point( + x + radius * cos(theta), + y + radius * sin(theta), + 0 + ) + } + +end + +procedure hippopede(x, y, a, b, steps, lo, hi) + local incr, theta, mul + + /steps := 300 + lo := dtor(\lo) | -&pi + hi := dtor(\hi) | &pi + incr := (hi - lo) / steps + + every theta := step(lo, hi, incr) do { + mul := a * b - b ^ 2 * sin(theta) ^ 2 + if mul < 0 then next + mul := 2 * sqrt(mul) + suspend Point( + x + mul * cos(theta), + y + mul *sin(theta), + 0 + ) + } + +end + +procedure kampyle_exodus(x, y, a, b, steps, lo, hi) + local incr, theta, fact + + /steps := 300 + lo := dtor(\lo) | (-&pi / 2) + hi := dtor(\hi) | (3 * &pi / 2) + incr := (hi - lo) / steps + + every theta := step(lo, hi, incr) do { + fact := a / cos(theta) + suspend Point( + x + fact, + y + fact * tan(theta), + 0 + ) + } + +end + +procedure kappa(x, y, a, b, steps, lo, hi) + local incr, theta, fact + + /steps := 300 + lo := dtor(\lo) | 0 + hi := dtor(\hi) | (2 * &pi) + incr := (hi - lo) / steps + + every theta := step(lo, hi, incr) do { + fact := a * cos(theta) + suspend Point( + x + fact / (0 ~= tan(theta)), + y + fact, + 0 + ) + } + +end + +procedure lemniscate_bernoulli(x, y, a, steps, lo, hi) + local incr, theta, fact + + /steps := 300 + lo := dtor(\lo) | -&pi + hi := dtor(\hi) | &pi + incr := (hi - lo) / steps + + every theta := step(lo, hi, incr) do { + fact := a * cos(theta) / (1 + sin(theta) ^ 2) + suspend Point( + x + fact, + y + fact * sin(theta), + 0 + ) + } + +end + +procedure lemniscate_gerono(x, y, a, b, steps, lo, hi) + local incr, theta, fact + + /steps := 300 + lo := dtor(\lo) | -&pi + hi := dtor(\hi) | &pi + incr := (hi - lo) / steps + + every theta := step(lo, hi, incr) do { + fact := a * cos(theta) + suspend Point( + x + fact, + y + sin(theta) * fact, + 0 + ) + } + +end + +procedure limacon_pascal(x, y, a, b, steps, lo, hi) + local incr, theta, fact + + /steps := 300 + lo := dtor(\lo) | -&pi + hi := dtor(\hi) | &pi + incr := (hi - lo) / steps + + every theta := step(lo, hi, incr) do { + fact := b + 2 * a * cos(theta) + suspend Point( + x + fact * cos(theta), + y + fact * sin(theta), + 0 + ) + } + +end + +procedure line(x, y, x1, y1, steps) + local xincr, yincr + + /steps := 100 + + xincr := (x1 - x) / (steps - 1) + yincr := (y1 - y) / (steps - 1) + + every 1 to steps do { + suspend Point(x, y, 0) + x +:= xincr + y +:= yincr + } + +end + +procedure lissajous(x, y, a, b, r, delta, steps, lo, hi) + local incr, theta + + /steps := 300 + lo := dtor(\lo) | 0 + hi := dtor(\hi) | (16 * &pi) + incr := (hi - lo) / steps + + r := dtor(r) + + every theta := step(lo, hi, incr) do + suspend Point( + x + a * sin(r * theta + delta), + y + b * sin(theta), + 0 + ) + +end + +procedure nephroid(x, y, a, steps, lo, hi) + local incr, theta + + /steps := 300 + lo := dtor(\lo) | -&pi + hi := dtor(\hi) | &pi + incr := (hi - lo) / steps + + every theta := step(lo, hi, incr) do + suspend Point( + x + a * (3 * cos(theta) - cos(3 * theta)), + y + a * (3 * sin(theta) - sin(3 * theta)), + 0 + ) + +end + +# Needs to be checked out + +procedure parabola(x, y, a, steps, lo, hi) + local incr, theta, denom, radius + + /steps := 300 + lo := dtor(\lo) | -&pi + hi := dtor(\hi) | &pi + incr := (hi - lo) / steps + + every theta := step(lo, hi, incr) do { + denom := 1 - cos(theta) + if denom = 0 then next + radius := 2 * a / denom + suspend Point( + radius * cos(theta), + radius * sin(theta), + 0 + ) + } + +end + +procedure piriform(x, y, a, b, steps, lo, hi) + local incr, theta, fact + + /steps := 300 + lo := dtor(\lo) | (-&pi / 2) + hi := dtor(\hi) | (3 * &pi / 2) + incr := (hi - lo) / steps + + every theta := step(lo, hi, incr) do { + fact := 1 + sin(theta) + suspend Point( + x + a * fact, + y + b * cos(theta) * fact, + 0 + ) + } + +end + +procedure trisectrix_catalan(x, y, a, steps, lo, hi) + local incr, theta, radius + + /steps := 300 + lo := dtor(\lo) | (-2 * &pi) + hi := dtor(\hi) | (2 * &pi) + incr := (hi - lo) / steps + + every theta := step(lo, hi, incr) do { + radius := a / cos(theta / 3) ^ 3 + suspend Point( + x + radius * cos(theta), + y + radius * sin(theta), + 0 + ) + } + +end + +procedure trisectrix_maclaurin(x, y, a, b, steps, lo, hi) + local incr, theta, fact + + /steps := 300 + lo := dtor(\lo) | (-&pi / 2) + hi := dtor(\hi) | (&pi / 2) + incr := (hi - lo) / steps + + every theta := step(lo, hi, incr) do { + fact := a * (1 - 4 * cos(theta) ^ 2) + suspend Point( + x + fact, + y + fact * tan(theta), + 0 + ) + } + +end + +procedure witch_agnesi(x, y, a, steps, lo, hi) + local incr, theta, fact + + /steps := 300 + lo := dtor(\lo) | (-&pi /2) + hi := dtor(\hi) | (&pi / 2) + incr := (hi - lo) / steps + + fact := 2 * a + + every theta := step(lo, hi, incr) do + suspend Point( + x + fact * tan(theta), + y - fact * cos(theta) ^ 2, + 0 + ) + +end |