File: x27.py

package info (click to toggle)
plplot 5.15.0%2Bdfsg-19
  • links: PTS, VCS
  • area: main
  • in suites: bullseye
  • size: 31,312 kB
  • sloc: ansic: 79,707; xml: 28,583; cpp: 20,033; ada: 19,456; tcl: 12,081; f90: 11,431; ml: 7,276; java: 6,863; python: 6,792; sh: 3,274; perl: 828; lisp: 75; makefile: 50; sed: 34; fortran: 5
file content (160 lines) | stat: -rw-r--r-- 4,569 bytes parent folder | download | duplicates (4)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
#  Copyright (C) 2007 Arjen Markus
#  Copyright (C) 2008 Andrew Ross
#  Copyright (C) 2007-2016 Alan W. Irwin

#  Drawing "spirograph" curves - epitrochoids, cycolids, roulettes

#  This file is part of PLplot.
#
#  PLplot is free software; you can redistribute it and/or modify
#  it under the terms of the GNU Library General Public License as published
#  by the Free Software Foundation; either version 2 of the License, or
#  (at your option) any later version.
#
#  PLplot is distributed in the hope that it will be useful,
#  but WITHOUT ANY WARRANTY; without even the implied warranty of
#  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#  GNU Library General Public License for more details.
#
#  You should have received a copy of the GNU Library General Public License
#  along with PLplot; if not, write to the Free Software
#  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
#

from numpy import *
import types

# main
#
# Generates two kinds of plots:
#   - construction of a cycloid (animated)
#   - series of epitrochoids and hypotrochoids

def main(w):

    # R, r, p, N
    # R and r should be integers to give correct termination of the
    # angle loop using gcd.
    # N.B. N is just a place holder since it is no longer used
    # (because we now have proper termination of the angle loop).
    params = [ [21.0,  7.0,  7.0,  3.0],  # Deltoid
               [21.0,  7.0, 10.0,  3.0],
               [21.0, -7.0, 10.0,  3.0],
               [20.0,  3.0,  7.0, 20.0],
               [20.0,  3.0, 10.0, 20.0],
               [20.0, -3.0, 10.0, 20.0],
               [20.0, 13.0,  7.0, 20.0],
               [20.0, 13.0, 20.0, 20.0],
               [20.0,-13.0, 20.0, 20.0] ]

    # Illustrate the construction of a cycloid

    # TODO
    #cycloid()

    # Loop over the various curves
    # First an overview, then all curves one by one
    w.pladv(0)
    w.plssub(3, 3)  # Three by three window

    for i in range(9) :
        w.pladv(0)
        w.plvpor( 0.0, 1.0, 0.0, 1.0 )
        spiro( w, params[i], 0 )

    w.pladv(0)
    w.plssub(1, 1)  # One window per curve

    for i in range(9):
        w.pladv(0)
        w.plvpor( 0.0, 1.0, 0.0, 1.0 )
        spiro( w, params[i], 0 )

    # Fill the curves.
    w.pladv(0)
    w.plssub(1, 1)  # One window per curve

    for i in range(9):
        w.pladv(0)
        w.plvpor( 0.0, 1.0, 0.0, 1.0 )
        spiro( w, params[i], 1 )

    arcs(w)

    # Restore defaults
    w.plssub(1, 1)
    w.pleop()

    # Must be done independently because otherwise this changes output files
    # and destroys agreement with C examples.
    #w.plcol0(1)

def gcd(a, b):
    if not isinstance(a, int) and isinstance(b, int):
        raise RuntimeError("gcd arguments must be integers")
    a = abs(a);
    b = abs(b);
    while(b != 0):
        t = b
        b = a % b
        a = t
    return a

def spiro(w, params, fill):
    # Fill the coordinates
    NPNT = 2000

    # Proper termination of the angle loop very near the beginning
    # point, see
    # http://mathforum.org/mathimages/index.php/Hypotrochoid.
    windings = int(abs(params[1])/gcd(int(params[0]), int(params[1])))
    steps    = int(NPNT/windings)
    dphi     = 2.0*pi/float(steps)

    phi = arange(windings*steps+1)*dphi
    phiw      = (params[0]-params[1])/params[1]*phi
    xcoord = (params[0]-params[1])*cos(phi) + params[2]*cos(phiw)
    ycoord = (params[0]-params[1])*sin(phi) - params[2]*sin(phiw)
    xmin = min(xcoord)
    xmax = max(xcoord)
    ymin = min(ycoord)
    ymax = max(ycoord)

    xrange_adjust = 0.15 * (xmax - xmin)
    xmin -= xrange_adjust
    xmax += xrange_adjust
    yrange_adjust = 0.15 * (ymax - ymin)
    ymin -= yrange_adjust
    ymax += yrange_adjust

    w.plwind( xmin, xmax, ymin, ymax )

    w.plcol0(1)
    if fill:
        w.plfill( xcoord, ycoord )
    else:
        w.plline( xcoord, ycoord )

def arcs(w) :
    NSEG = 8

    theta = 0.0
    dtheta = 360.0 / NSEG
    w.plenv( -10.0, 10.0, -10.0, 10.0, 1, 0 )

    # Plot segments of circle in different colors
    for i in range (NSEG) :
        w.plcol0( i%2 + 1 )
        w.plarc(0.0, 0.0, 8.0, 8.0, theta, theta + dtheta, 0.0, 0)
        theta = theta + dtheta


    # Draw several filled ellipses inside the circle at different
    # angles.
    a = 3.0
    b = a * tan( (dtheta/180.0*pi)/2.0 )
    theta = dtheta/2.0
    for i in range(NSEG):
        w.plcol0( 2 - i%2 )
        w.plarc( a*cos(theta/180.0*pi), a*sin(theta/180.0*pi), a, b, 0.0, 360.0, theta, 1)
        theta = theta + dtheta