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- epicycle - draws a point moving around a circle which
- moves around a cicle which...
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- 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]
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- 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.
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- -\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
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- default, best, mono, monochrome, gray, grey,
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- color, staticgray, staticcolor, truecolor,
- grayscale, greyscale, pseudocolor, directcolor,
- _\bn_\bu_\bm_\bb_\be_\br
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- 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.
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- -\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.
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- -\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.
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-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
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- 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.
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- 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.
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-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.
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-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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