/[cvs]/fract/mandelzoom.cgi
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Contents of /fract/mandelzoom.cgi

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Revision 1.10 - (show annotations)
Tue Jun 26 12:43:34 2001 UTC (22 years, 9 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 #!/usr/bin/python
2
3 import cgi, Image, ImageDraw, sys, math, signal, errno, os
4 from string import atoi, atof
5
6 def handler(signum, frame):
7 signal.alarm(0)
8 raise os.error, (errno.ETIME, "Timer expired")
9
10 signal.alarm(55)
11 signal.signal(signal.SIGALRM, handler)
12
13 # This is to get backtrace output
14 sys.stderr = sys.stdout
15
16 # Uncomment this to get the backtrace more readable
17 #print "Content-Type: text/plain"
18 #print ""
19
20 form= cgi.FieldStorage()
21
22 # Image size
23 if form.has_key('width'):
24 width= atoi(form['width'].value)
25 else:
26 width= 480
27 if form.has_key('height'):
28 height= atoi(form['height'].value)
29 else:
30 height= 480
31
32 xmax, ymax = width-1, height-1 # Coordinate maximums
33
34 # 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 cx= 0.0
39
40 if form.has_key('cy'):
41 cy= atof(form['cy'].value)
42 else:
43 cy= 0.0
44
45 # The length of the diagonal line from corner to corner.
46 # Used as a measure of image size independent of aspect ratio.
47 if form.has_key('diag'):
48 diag= atof(form['diag'].value)
49 else:
50 diag= math.sqrt(32) # sqrt(4**2 + 4**2)
51
52 debug= form.has_key('debug')
53
54 if form.has_key('iter'):
55 maxiter= atoi(form['iter'].value)
56 else:
57 maxiter= 270
58
59 # If type!=image, then output an HTML page, not an image
60 if not (form.has_key('type') and form['type'].value == "image"):
61 print """Content-Type: text/html
62
63 <!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML 2.0//EN">
64 <HTML><HEAD>
65 <TITLE>Mandelbrot Set Zoomer</TITLE>
66 </HEAD>
67 <BODY>
68 <H1>Mandelbrot Set Zoomer</H1>
69
70 <FORM ACTION="mandelzoom.cgi" METHOD=GET>
71
72 <!-- 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 # If the user has selected a specific point on the image
81 if form.has_key('image.x') and form.has_key('image.y'):
82 # Adjust cx and cy
83 ix= atof(form['image.x'].value) # Intermediate value
84 iy= atof(form['image.y'].value) # Intermediate value
85 owidth= atof(form['owidth'].value)
86 oheight= atof(form['oheight'].value)
87 diagp= math.sqrt(owidth**2 + oheight**2) # Intermediate value
88 scale= diagp/diag # Intermediate value
89 cx= (ix/scale) + (cx - (owidth / (scale*2)))
90 cy= ((oheight-iy)/scale) + (cy - (oheight / (scale*2)))
91 if form.has_key('zoom'):
92 zoom=atof(form['zoom'].value)
93 diag=diag/zoom
94 else:
95 # If no zoom provided, don't actually zoom, but keep the
96 # default of ×2 zoom.
97 zoom= 2.0
98 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 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 print '<OPTION',
104 if str(zv)==str(zoom):
105 print 'SELECTED',
106 print 'VALUE="%s"' % (str(zv))
107 if zv == 1:
108 print '>Pan'
109 elif zv < 1:
110 print '>Out ÷%s' % (str(1/zv))
111 else:
112 print '>In ×%s' % (str(zv))
113 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 Iterations: <INPUT TYPE=TEXT NAME="iter" MAXLENGTH="4" SIZE="3"
119 VALUE="%s">
120 Debug mode: <INPUT TYPE=CHECKBOX NAME="debug" """ % (str(width), str(height), str(maxiter)),
121 if debug:
122 print 'CHECKED>'
123 else:
124 print '>'
125 print '<INPUT TYPE=SUBMIT VALUE="Apply">'
126 for var in (("diag", diag), ("cx", cx), ("cy", cy), ("owidth", width),
127 ("oheight", height)):
128 print '<INPUT TYPE=HIDDEN NAME="%s" VALUE="%s">' % var
129 print '<INPUT TYPE=HIDDEN NAME=type VALUE="html">'
130
131 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 </BODY></HTML>"""
135 # Just exit, don't calculate an image.
136 sys.exit(0)
137
138 # c1 and c2 are the coordinates of two opposite corners.
139 # Figure out c1 and c2 from width, height, diag, cx, and cy.
140
141 # Diagonal in pixels
142 diagp= math.sqrt(width**2 + height**2)
143 # Scale between pixels and coordinates
144 scale= diagp/diag
145 # half the width/height in real numbers; intermediate values
146 x= (width/2.0)/scale
147 y= (height/2.0)/scale
148
149 # The coordinates of two opposite corners
150 c1= cx - x + (cy - y) * (0+1j)
151 c2= cx + x + (cy + y) * (0+1j)
152
153 #print width, height, diag, cx, cy, diagp, scale, x, y, c1, c2
154 #sys.exit(0)
155
156 # 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 # New image object
161 mandel= Image.new("L", (width, height))
162 # shortcut to the "Draw" method on the image object
163 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 "Return complex number from pixel coordinates x and y."
225 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 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
275 signal.alarm(0)
276
277 print "Content-type: image/png"
278 print
279 mandel.save(sys.stdout, "PNG")

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