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+ epicycle - draws a point moving around a circle which
+ moves around a cicle which...
+
+S\bSY\bYN\bNO\bOP\bPS\bSI\bIS\bS
+ e\bep\bpi\bic\bcy\byc\bcl\ble\be [-display _\bh_\bo_\bs_\bt_\b:_\bd_\bi_\bs_\bp_\bl_\ba_\by_\b._\bs_\bc_\br_\be_\be_\bn] [-root] [-window]
+ [-mono] [-install] [-noinstall] [-visual _\bv_\bi_\bz] [-colors _\bN]
+ [-foreground _\bn_\ba_\bm_\be] [-color-shift _\bN] [-delay _\bm_\bi_\bc_\br_\bo_\bs_\be_\bc_\bo_\bn_\bd_\bs]
+ [-holdtime _\bs_\be_\bc_\bo_\bn_\bd_\bs] [-linewidth _\bN] [-min_circles _\bN]
+ [-max_circles _\bN] [-min_speed _\bn_\bu_\bm_\bb_\be_\br] [-max_speed _\bn_\bu_\bm_\bb_\be_\br]
+ [-harmonics _\bN] [-timestep _\bn_\bu_\bm_\bb_\be_\br] [-divisor_poisson _\bp_\br_\bo_\bb_\ba_\b-
+ _\bb_\bi_\bl_\bi_\bt_\by] [-size_factor_min _\bn_\bu_\bm_\bb_\be_\br] [-size_factor_max _\bn_\bu_\bm_\b-
+ _\bb_\be_\br]
+
+D\bDE\bES\bSC\bCR\bRI\bIP\bPT\bTI\bIO\bON\bN
+ The epicycle program draws the path traced out by a point
+ on the edge of a circle. That circle rotates around a
+ point on the rim of another circle, and so on, several
+ times. The random curves produced can be simple or com-
+ plex, convex or concave, but they are always closed curves
+ (they never go in indefinitely).
+
+ You can configure both the way the curves are drawn and
+ the way in which the random sequence of circles is gener-
+ ated, either with command-line options or X resources.
+
+O\bOP\bPT\bTI\bIO\bON\bNS\bS
+ -\b-d\bdi\bis\bsp\bpl\bla\bay\by _\bh_\bo_\bs_\bt_\b:_\bd_\bi_\bs_\bp_\bl_\ba_\by_\b._\bs_\bc_\br_\be_\be_\bn
+ Specifies which X display we should use (see the
+ section DISPLAY NAMES in X\bX(1) for more information
+ about this option).
+
+ -\b-r\bro\boo\bot\bt Draw on the root window.
+
+ -\b-w\bwi\bin\bnd\bdo\bow\bw Draw on a newly-created window. This is the
+ default.
+
+ -\b-m\bmo\bon\bno\bo If on a color display, pretend we're on a
+ monochrome display. If we're on a mono display,
+ we have no choice.
+
+ -\b-i\bin\bns\bst\bta\bal\bll\bl
+ Install a private colormap for the window.
+
+ -\b-n\bno\boi\bin\bns\bst\bta\bal\bll\bl
+ Don't install a private colormap for the window.
+
+ -\b-v\bvi\bis\bsu\bua\bal\bl _\bv_\bi_\bz
+ Specify which visual to use. Legal values are the
+ name of a visual class, or the id number (decimal
+ or hex) of a specific visual. Possible choices
+ include
+
+ default, best, mono, monochrome, gray, grey,
+
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+ color, staticgray, staticcolor, truecolor,
+ grayscale, greyscale, pseudocolor, directcolor,
+ _\bn_\bu_\bm_\bb_\be_\br
+
+ If a decimal or hexadecimal number is used,
+ X\bXG\bGe\bet\btV\bVi\bis\bsu\bua\bal\blI\bIn\bnf\bfo\bo(3X) is consulted to obtain the
+ required visual.
+
+ -\b-c\bco\bol\blo\bor\brs\bs _\bN
+ How many colors should be used (if possible). The
+ colors are chosen randomly.
+
+ -\b-f\bfo\bor\bre\beg\bgr\bro\bou\bun\bnd\bd _\bn_\ba_\bm_\be
+ With -\b-m\bmo\bon\bno\bo, this option selects the foreground
+ colour.
+
+ -\b-d\bde\bel\bla\bay\by _\bm_\bi_\bc_\br_\bo_\bs_\be_\bc_\bo_\bn_\bd_\bs
+ Specifies the delay between drawing successive
+ line segments of the path. If you do not specify
+ -\b-s\bsy\byn\bnc\bc, some X servers may batch up several drawing
+ operations together, producing a less smooth
+ effect. This is more likely to happen in
+ monochrome mode (on monochrome servers or when
+ -\b-m\bmo\bon\bno\bo is specified).
+
+ -\b-h\bho\bol\bld\bdt\bti\bim\bme\be _\bs_\be_\bc_\bo_\bn_\bd_\bs
+ When the figure is complete, _\be_\bp_\bi_\bc_\by_\bc_\bl_\be pauses this
+ number of seconds.
+
+ -\b-l\bli\bin\bne\bew\bwi\bid\bdt\bth\bh _\bN
+ Width in pixels of the body's track. Specifying
+ values greater than one may cause slower drawing.
+ The fastest value is usually zero, meaning one
+ pixel.
+
+ -\b-m\bmi\bin\bn_\b_c\bci\bir\brc\bcl\ble\bes\bs _\bN
+ Smallest number of epicycles in the figure.
+
+ -\b-m\bma\bax\bx_\b_c\bci\bir\brc\bcl\ble\bes\bs _\bN
+ Largest number of epicycles in the figure.
+
+ -\b-m\bmi\bin\bn_\b_s\bsp\bpe\bee\bed\bd _\bn_\bu_\bm_\bb_\be_\br
+ Smallest possible value for the base speed of rev-
+ olution of the epicycles. The actual speeds of
+ the epicycles vary from this down to _\bm_\bi_\bn_\b__\bs_\bp_\be_\be_\bd _\b/
+ _\bh_\ba_\br_\bm_\bo_\bn_\bi_\bc_\bs.\b.
+
+ -\b-m\bma\bax\bx_\b_s\bsp\bpe\bee\bed\bd _\bn_\bu_\bm_\bb_\be_\br
+ Smallest possible value for the base speed of rev-
+ olution of the epicycles.
+
+ -\b-h\bha\bar\brm\bmo\bon\bni\bic\bcs\bs _\bN
+ Number of possible harmonics; the larger this
+ value is, the greater the possible variety of
+
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+ possible speeds of epicycle.
+
+ -\b-t\bti\bim\bme\bes\bst\bte\bep\bp _\bn_\bu_\bm_\bb_\be_\br
+ Decreasing this value will reduce the distance the
+ body moves for each line segment, possibly produc-
+ ing a smoother figure. Increasing it may produce
+ faster results.
+
+ -\b-d\bdi\biv\bvi\bis\bso\bor\br_\b_p\bpo\boi\bis\bss\bso\bon\bn _\bp_\br_\bo_\bb_\ba_\bb_\bi_\bl_\bi_\bt_\by
+ Each epicycle rotates at a rate which is a factor
+ of the base speed. The speed of each epicycle is
+ the base speed divided by some integer between 1
+ and the value of the -\b-h\bha\bar\brm\bmo\bon\bni\bic\bcs\bs option. This
+ integer is decided by starting at 1 and tossing a
+ biased coin. For each consecutive head, the value
+ is incremented by one. The integer will not be
+ incremented above the value of the -\b-h\bha\bar\brm\bmo\bon\bni\bic\bcs\bs
+ option. The argument of this option decides the
+ bias of the coin; it is the probability that that
+ coin will produce a head at any given toss.
+
+ -\b-s\bsi\biz\bze\be_\b_f\bfa\bac\bct\bto\bor\br_\b_m\bmi\bin\bn _\bn_\bu_\bm_\bb_\be_\br
+ Epicycles are always at least this factor smaller
+ than their parents.
+
+ -\b-s\bsi\biz\bze\be_\b_f\bfa\bac\bct\bto\bor\br_\b_m\bma\bax\bx _\bn_\bu_\bm_\bb_\be_\br
+ Epicycles are never more than this factor smaller
+ than their parents.
+
+R\bRE\bES\bSO\bOU\bUR\bRC\bCE\bES\bS
+ Option Resource Default Value
+ ------ -------- -------------
+ -colors .colors 100
+ -delay .delay 1000
+ -holdtime .holdtime 2
+ -linewidth .lineWidth 4
+ -min_circles .minCircles 2
+ -max_circles .maxCircles 10
+ -min_speed .minSpeed 0.003
+ -max_speed .maxSpeed 0.005
+ -harmonics .harmonics 8
+ -timestep .timestep 1.0
+ -divisor_poisson .divisorPoisson 0.4
+ -size_factor_min .sizeFactorMin 1.05
+ -size_factor_max .sizeFactorMax 2.05
+ .timestepCoarseFactor 1.0
+
+ Before the drawing of the figure is begun, a preliminary
+ calculation of the path is done in order to scale the
+ radii of the epicycles so as to fit the figure on the
+ screen or window. For the sake of speed, This calculation
+ is done with a larger timestep than the actual drawing.
+ The time-step used is the value of the -\b-t\bti\bim\bme\bes\bst\bte\bep\bp option
+ multiplied by the timestepCoarseFactor resource. The
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+ default value of 1 will almost always work fast enough and
+ so this resource is not available as a command-line
+ option.
+
+U\bUS\bSE\bER\bR I\bIN\bNT\bTE\bER\bRF\bFA\bAC\bCE\bE
+ The program runs mostly without user interaction. When
+ running on the root window, no input is accepted. When
+ running in its own window, the program will exit if mouse
+ button 3 is pressed. If any other mouse button is
+ pressed, the current figure will be abandoned and another
+ will be started.
+
+H\bHI\bIS\bST\bTO\bOR\bRY\bY
+ The geometry of epicycles was perfected by Hipparchus of
+ Rhodes at some time around 125 B.C., 185 years after the
+ birth of Aristarchus of Samos, the inventor of the helio-
+ centric universe model. Hipparchus applied epicycles to
+ the Sun and the Moon. Ptolemy of Alexandria went on to
+ apply them to what was then the known universe, at around
+ 150 A.D. Copernicus went on to apply them to the helio-
+ centric model at the beginning of the sixteenth century.
+ Johannes Kepler discovered that the planets actually move
+ in elliptical orbits in about 1602. The inverse-square
+ law of gravity was suggested by Boulliau in 1645. Isaac
+ Newton's _\bP_\br_\bi_\bn_\bc_\bi_\bp_\bi_\ba _\bM_\ba_\bt_\bh_\be_\bm_\ba_\bt_\bi_\bc_\ba was published in 1687, and
+ proved that Kepler's laws derived from Newtonian gravita-
+ tion.
+
+B\bBU\bUG\bGS\bS
+ The colour selection is re-done for every figure. This
+ may generate too much network traffic for this program to
+ work well over slow or long links.
+
+C\bCO\bOP\bPY\bYR\bRI\bIG\bGH\bHT\bT
+ Copyright (C) 1998, James Youngman. Permission to use,
+ copy, modify, distribute, and sell this software and its
+ documentation for any purpose is hereby granted without
+ fee, provided that the above copyright notice appear in
+ all copies and that both that copyright notice and this
+ permission notice appear in supporting documentation. No
+ representations are made about the suitability of this
+ software for any purpose. It is provided "as is" without
+ express or implied warranty.
+
+A\bAU\bUT\bTH\bHO\bOR\bR
+ James Youngman <jay@gnu.org>, April 1998.
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