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Annotation of /fract/mandelzoom.cgi

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Revision 1.10 - (hide annotations)
Tue Jun 26 12:43:34 2001 UTC (23 years, 5 months ago) by teddy
Branch: MAIN
CVS Tags: HEAD
Changes since 1.9: +19 -8 lines
Disable alarm inside signal handler.
Add some comments throughout.

1 teddy 1.1 #!/usr/bin/python
2    
3 teddy 1.9 import cgi, Image, ImageDraw, sys, math, signal, errno, os
4 teddy 1.2 from string import atoi, atof
5    
6 teddy 1.9 def handler(signum, frame):
7 teddy 1.10 signal.alarm(0)
8 teddy 1.9 raise os.error, (errno.ETIME, "Timer expired")
9    
10     signal.alarm(55)
11     signal.signal(signal.SIGALRM, handler)
12    
13 teddy 1.3 # This is to get backtrace output
14 teddy 1.2 sys.stderr = sys.stdout
15 teddy 1.1
16 teddy 1.3 # Uncomment this to get the backtrace more readable
17     #print "Content-Type: text/plain"
18     #print ""
19    
20 teddy 1.1 form= cgi.FieldStorage()
21    
22     # Image size
23     if form.has_key('width'):
24 teddy 1.2 width= atoi(form['width'].value)
25 teddy 1.1 else:
26 teddy 1.3 width= 480
27 teddy 1.1 if form.has_key('height'):
28 teddy 1.2 height= atoi(form['height'].value)
29 teddy 1.1 else:
30 teddy 1.3 height= 480
31 teddy 1.1
32     xmax, ymax = width-1, height-1 # Coordinate maximums
33    
34 teddy 1.2 # Complex number in center of image is (cx+cy*j)
35     if form.has_key('cx'):
36     cx= atof(form['cx'].value)
37     else:
38 teddy 1.6 cx= 0.0
39 teddy 1.2
40     if form.has_key('cy'):
41     cy= atof(form['cy'].value)
42     else:
43 teddy 1.6 cy= 0.0
44 teddy 1.2
45 teddy 1.10 # The length of the diagonal line from corner to corner.
46     # Used as a measure of image size independent of aspect ratio.
47 teddy 1.2 if form.has_key('diag'):
48     diag= atof(form['diag'].value)
49     else:
50 teddy 1.5 diag= math.sqrt(32) # sqrt(4**2 + 4**2)
51 teddy 1.2
52 teddy 1.1 debug= form.has_key('debug')
53    
54     if form.has_key('iter'):
55 teddy 1.2 maxiter= atoi(form['iter'].value)
56 teddy 1.1 else:
57 teddy 1.5 maxiter= 270
58 teddy 1.1
59 teddy 1.2 # If type!=image, then output an HTML page, not an image
60     if not (form.has_key('type') and form['type'].value == "image"):
61 teddy 1.1 print """Content-Type: text/html
62    
63     <!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML 2.0//EN">
64     <HTML><HEAD>
65 teddy 1.6 <TITLE>Mandelbrot Set Zoomer</TITLE>
66 teddy 1.1 </HEAD>
67     <BODY>
68 teddy 1.6 <H1>Mandelbrot Set Zoomer</H1>
69 teddy 1.1
70     <FORM ACTION="mandelzoom.cgi" METHOD=GET>
71    
72 teddy 1.2 <!-- implies TYPE=SUBMIT -->"""
73     print '<INPUT TYPE=IMAGE NAME="image"',
74     print 'WIDTH="%s"' % (str(width)),
75     print 'HEIGHT="%s"' % (str(height)),
76     if debug:
77     ds="&debug=on"
78     else:
79     ds=""
80 teddy 1.10 # If the user has selected a specific point on the image
81 teddy 1.6 if form.has_key('image.x') and form.has_key('image.y'):
82     # Adjust cx and cy
83 teddy 1.10 ix= atof(form['image.x'].value) # Intermediate value
84     iy= atof(form['image.y'].value) # Intermediate value
85 teddy 1.6 owidth= atof(form['owidth'].value)
86     oheight= atof(form['oheight'].value)
87 teddy 1.10 diagp= math.sqrt(owidth**2 + oheight**2) # Intermediate value
88     scale= diagp/diag # Intermediate value
89 teddy 1.7 cx= (ix/scale) + (cx - (owidth / (scale*2)))
90     cy= ((oheight-iy)/scale) + (cy - (oheight / (scale*2)))
91 teddy 1.2 if form.has_key('zoom'):
92 teddy 1.5 zoom=atof(form['zoom'].value)
93 teddy 1.2 diag=diag/zoom
94     else:
95 teddy 1.10 # If no zoom provided, don't actually zoom, but keep the
96     # default of ×2 zoom.
97 teddy 1.6 zoom= 2.0
98 teddy 1.2 print 'SRC="mandelzoom.cgi?type=image&width=%s&height=%s&iter=%s%s&diag=%s&cx=%s&cy=%s"' % (str(width), str(height), str(maxiter), ds, str(diag), str(cx), str(cy)),
99     print 'ALIGN=BOTTOM HEIGHT="%s"' % (str(height)),
100     print 'WIDTH="%s"><P>' % (str(width))
101     print 'Zoom: <SELECT NAME="zoom">'
102 teddy 1.5 for zv in [1.0/5, 1.0/3, 1.0/2, 1.0/1.5, 1.0, 1.5, 2.0, 3.0, 5.0]:
103 teddy 1.2 print '<OPTION',
104 teddy 1.5 if str(zv)==str(zoom):
105 teddy 1.2 print 'SELECTED',
106     print 'VALUE="%s"' % (str(zv))
107 teddy 1.3 if zv == 1:
108     print '>Pan'
109     elif zv < 1:
110 teddy 1.6 print '>Out ÷%s' % (str(1/zv))
111 teddy 1.2 else:
112 teddy 1.3 print '>In ×%s' % (str(zv))
113 teddy 1.2 print '</SELECT>'
114     print """Width: <INPUT TYPE=TEXT NAME="width" MAXLENGTH="4" SIZE="3"
115     VALUE="%s">
116     Height: <INPUT TYPE=TEXT NAME="height" MAXLENGTH="4" SIZE="3"
117     VALUE="%s">
118 teddy 1.1 Iterations: <INPUT TYPE=TEXT NAME="iter" MAXLENGTH="4" SIZE="3"
119     VALUE="%s">
120 teddy 1.3 Debug mode: <INPUT TYPE=CHECKBOX NAME="debug" """ % (str(width), str(height), str(maxiter)),
121 teddy 1.2 if debug:
122     print 'CHECKED>'
123     else:
124     print '>'
125 teddy 1.3 print '<INPUT TYPE=SUBMIT VALUE="Apply">'
126 teddy 1.6 for var in (("diag", diag), ("cx", cx), ("cy", cy), ("owidth", width),
127     ("oheight", height)):
128 teddy 1.5 print '<INPUT TYPE=HIDDEN NAME="%s" VALUE="%s">' % var
129 teddy 1.2 print '<INPUT TYPE=HIDDEN NAME=type VALUE="html">'
130 teddy 1.1
131 teddy 1.8 print """</FORM><P>
132     After changing any settings, don't forget to change the "Zoom" setting
133     to "Pan" if you don't want to zoom when applying them.
134 teddy 1.1 </BODY></HTML>"""
135 teddy 1.10 # Just exit, don't calculate an image.
136 teddy 1.1 sys.exit(0)
137    
138 teddy 1.10 # c1 and c2 are the coordinates of two opposite corners.
139 teddy 1.5 # Figure out c1 and c2 from width, height, diag, cx, and cy.
140 teddy 1.10
141 teddy 1.5 # Diagonal in pixels
142     diagp= math.sqrt(width**2 + height**2)
143     # Scale between pixels and coordinates
144     scale= diagp/diag
145 teddy 1.10 # half the width/height in real numbers; intermediate values
146 teddy 1.5 x= (width/2.0)/scale
147     y= (height/2.0)/scale
148    
149 teddy 1.10 # The coordinates of two opposite corners
150 teddy 1.6 c1= cx - x + (cy - y) * (0+1j)
151     c2= cx + x + (cy + y) * (0+1j)
152 teddy 1.5
153     #print width, height, diag, cx, cy, diagp, scale, x, y, c1, c2
154     #sys.exit(0)
155    
156 teddy 1.1 # Force c1 to be upper left and c2 to be lower right
157     c1, c2= complex(min(c1.real, c2.real), max(c1.imag, c2.imag)), \
158     complex(max(c1.real, c2.real), min(c1.imag, c2.imag))
159    
160 teddy 1.10 # New image object
161 teddy 1.1 mandel= Image.new("L", (width, height))
162 teddy 1.10 # shortcut to the "Draw" method on the image object
163 teddy 1.1 draw= ImageDraw.Draw(mandel)
164    
165     def drawrect((x1, y1), (x2, y2)):
166     "Draw a rectangle defined by the corners (x1, y1) and (x2, y2)."
167     color= plot(x1, y1) # Plot the upper left corner
168     # Should we cut this rectangle and recurse into the pieces?
169     cut= 0
170     ## Plot the edges and at the same time check if they are all the
171     ## same color.
172     # Upper edge (left to right)
173     x, y= x1+1, y1
174     while x<=x2:
175     if color<>plot(x, y):
176     cut= 1
177     x= x+1
178     # Right edge (top to bottom)
179     x, y= x2, y1+1
180     while y<=y2:
181     if color<>plot(x, y):
182     cut= 1
183     y= y+1
184     # Bottom edge (right to left)
185     x, y= x2-1, y2
186     while x>=x1:
187     if color<>plot(x, y):
188     cut= 1
189     x= x-1
190     # Left edge (bottom to top)
191     x, y= x1, y2-1
192     while y>y1:
193     if color<>plot(x, y):
194     cut= 1
195     y= y-1
196     # If our rectangle is too small to have an inside, we have now
197     # plotted every pixel in it.
198     if x2-x1<=1 or y2-y1<=1:
199     return
200     if cut: # If we're cutting the rectangle
201     if x2-x1 > y2-y1: # If it's wider than high
202     # Cut vertically
203     xc= ((x2-x1)/2)+x1
204     drawrect((x1, y1), (xc, y2))
205     drawrect((xc, y1), (x2, y2))
206     else: # if it's higher than wide
207     # Cut horizontally
208     yc= ((y2-y1)/2)+y1
209     drawrect((x1, y1), (x2, yc))
210     drawrect((x1, yc), (x2, y2))
211     else:
212     # If we're not cutting, it was the same color along the edge
213     if not debug:
214     # Fill in the rectangle
215     draw.rectangle([x1, y1, x2, y2], fill= color)
216     if yorig >= 0: # The x axis is visible on image
217     # Fill in the mirror rectangle
218     # Mirror y1 and y2 over yorig, but keep within image
219     y1m= max(0, min(2*yorig-y1, ymax))
220     y2m= max(0, min(2*yorig-y2, ymax))
221     draw.rectangle([x1, y1m, x2, y2m], fill= color)
222    
223     def constant(x, y):
224 teddy 1.10 "Return complex number from pixel coordinates x and y."
225 teddy 1.1 creal= (float(x)/xmax)*(c2.real - c1.real)+c1.real
226     cimag= (float(y)/ymax)*(c2.imag - c1.imag)+c1.imag
227     return complex(creal, cimag)
228    
229     def plot(x, y):
230     c= constant(x, y)
231     z= i= 0
232     color= mandel.getpixel((x, y))
233     if color<>0:
234     return color
235     while i<maxiter and abs(z)<2:
236     z= z**2+c
237     i= i+1
238     color= 16*i%256
239     if i>=maxiter or color==0:
240     if debug:
241     color= 255
242     else:
243     color= 1
244     try:
245     mandel.putpixel((x, y), color)
246     if yorig >= 0: # The x axis is visible on image
247     ym= 2*yorig-y # ym is y mirrored over yorig
248     if ym >= 0 and ym <= ymax:
249     # ym is on the image
250     mandel.putpixel((x, ym), color)
251     except IndexError, the_error:
252     print "coord", x, y, xm, ym
253     raise IndexError, the_error
254     return color
255    
256     # Initial default values
257     yfrom= 0
258     yto= ymax
259     yorig= -1 # The pixel coordinate of the x axis; negative means not on image
260    
261     # Check if we should do mirroring
262     if c1.imag > 0 and c2.imag < 0: # the x axis is visible
263     yorig= int((-c1.imag/(c2.imag-c1.imag))*height) # pixel pos. of x axis
264     if c1.imag < abs(c2.imag): # the x axis is closer to top than bottom
265     yfrom= yorig # Begin at x axis
266     else:
267     yto= yorig # End at x axis
268    
269 teddy 1.9 try:
270     drawrect((0, yfrom), (xmax, yto))
271     except os.error, the_error:
272     if the_error[0] != errno.ETIME:
273     raise os.error, the_error
274 teddy 1.10
275 teddy 1.9 signal.alarm(0)
276 teddy 1.1
277     print "Content-type: image/png"
278     print
279     mandel.save(sys.stdout, "PNG")

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