cvs/fract/mandelzoom.cgi

#!/usr/bin/python

import cgi, Image, ImageDraw, sys, math, signal, errno, os
from string import atoi, atof

def handler(signum, frame):
    signal.alarm(0)
    raise os.error, (errno.ETIME, "Timer expired")

signal.alarm(55)
signal.signal(signal.SIGALRM, handler)

# This is to get backtrace output
sys.stderr = sys.stdout

# Uncomment this to get the backtrace more readable
#print "Content-Type: text/plain"
#print ""

form= cgi.FieldStorage()

# Image size
if form.has_key('width'):
    width= atoi(form['width'].value)
else:
    width= 480
if form.has_key('height'):
    height= atoi(form['height'].value)
else:
    height= 480

xmax, ymax = width-1, height-1          # Coordinate maximums

# Complex number in center of image is (cx+cy*j)
if form.has_key('cx'):
    cx= atof(form['cx'].value)
else:
    cx= 0.0

if form.has_key('cy'):
    cy= atof(form['cy'].value)
else:
    cy= 0.0

# The length of the diagonal line from corner to corner.
# Used as a measure of image size independent of aspect ratio.
if form.has_key('diag'):
    diag= atof(form['diag'].value)
else:
    diag= math.sqrt(32) # sqrt(4**2 + 4**2)

debug= form.has_key('debug')

if form.has_key('iter'):
    maxiter= atoi(form['iter'].value)
else:
    maxiter= 270

# If type!=image, then output an HTML page, not an image
if not (form.has_key('type') and form['type'].value == "image"):
    print """Content-Type: text/html

<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML 2.0//EN">
<HTML><HEAD>
<TITLE>Mandelbrot Set Zoomer</TITLE>
</HEAD>
<BODY>
<H1>Mandelbrot Set Zoomer</H1>

<FORM ACTION="mandelzoom.cgi" METHOD=GET>

<!-- implies TYPE=SUBMIT -->"""
    print '<INPUT TYPE=IMAGE NAME="image"',
    print 'WIDTH="%s"' % (str(width)),
    print 'HEIGHT="%s"' % (str(height)),
    if debug:
        ds="&debug=on"
    else:
        ds=""
    # If the user has selected a specific point on the image
    if form.has_key('image.x') and form.has_key('image.y'):
        # Adjust cx and cy
        ix= atof(form['image.x'].value) # Intermediate value
        iy= atof(form['image.y'].value) # Intermediate value
        owidth= atof(form['owidth'].value)
        oheight= atof(form['oheight'].value)
        diagp= math.sqrt(owidth**2 + oheight**2) # Intermediate value
        scale= diagp/diag               # Intermediate value
        cx= (ix/scale) + (cx - (owidth / (scale*2)))
        cy= ((oheight-iy)/scale) + (cy - (oheight / (scale*2)))
    if form.has_key('zoom'):
        zoom=atof(form['zoom'].value)
        diag=diag/zoom
    else:
        # If no zoom provided, don't actually zoom, but keep the
        # default of �2 zoom.
        zoom= 2.0
    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)),
    print 'ALIGN=BOTTOM HEIGHT="%s"' % (str(height)),
    print 'WIDTH="%s"><P>' % (str(width))
    print 'Zoom: <SELECT NAME="zoom">'
    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]:
        print '<OPTION',
        if str(zv)==str(zoom):
            print 'SELECTED',
        print 'VALUE="%s"' % (str(zv))
        if zv == 1:
            print '>Pan'
        elif zv < 1:
            print '>Out �%s' % (str(1/zv))
        else:
            print '>In �%s' % (str(zv))
    print '</SELECT>'
    print """Width: <INPUT TYPE=TEXT NAME="width" MAXLENGTH="4" SIZE="3"
    VALUE="%s">
    Height: <INPUT TYPE=TEXT NAME="height" MAXLENGTH="4" SIZE="3"
    VALUE="%s">
    Iterations: <INPUT TYPE=TEXT NAME="iter" MAXLENGTH="4" SIZE="3"
    VALUE="%s">
    Debug mode: <INPUT TYPE=CHECKBOX NAME="debug" """ % (str(width), str(height), str(maxiter)),
    if debug:
        print 'CHECKED>'
    else:
        print '>'
    print '<INPUT TYPE=SUBMIT VALUE="Apply">'
    for var in (("diag", diag), ("cx", cx), ("cy", cy), ("owidth", width),
                ("oheight", height)):
        print '<INPUT TYPE=HIDDEN NAME="%s" VALUE="%s">' % var
    print '<INPUT TYPE=HIDDEN NAME=type VALUE="html">'

    print """</FORM><P>
After changing any settings, don't forget to change the "Zoom" setting
to "Pan" if you don't want to zoom when applying them.
</BODY></HTML>"""
    # Just exit, don't calculate an image.
    sys.exit(0)

# c1 and c2 are the coordinates of two opposite corners.
# Figure out c1 and c2 from width, height, diag, cx, and cy.

# Diagonal in pixels
diagp= math.sqrt(width**2 + height**2)
# Scale between pixels and coordinates
scale= diagp/diag
# half the width/height in real numbers; intermediate values
x= (width/2.0)/scale
y= (height/2.0)/scale

# The coordinates of two opposite corners
c1= cx - x + (cy - y) * (0+1j)
c2= cx + x + (cy + y) * (0+1j)

#print width, height, diag, cx, cy, diagp, scale, x, y, c1, c2
#sys.exit(0)

# Force c1 to be upper left and c2 to be lower right
c1, c2= complex(min(c1.real, c2.real), max(c1.imag, c2.imag)), \
        complex(max(c1.real, c2.real), min(c1.imag, c2.imag))

# New image object
mandel= Image.new("L", (width, height))
# shortcut to the "Draw" method on the image object
draw= ImageDraw.Draw(mandel)

def drawrect((x1, y1), (x2, y2)):
    "Draw a rectangle defined by the corners (x1, y1) and (x2, y2)."
    color= plot(x1, y1) # Plot the upper left corner
    # Should we cut this rectangle and recurse into the pieces?
    cut= 0
    ## Plot the edges and at the same time check if they are all the
    ## same color.
    # Upper edge (left to right)
    x, y= x1+1, y1
    while x<=x2:
        if color<>plot(x, y):
            cut= 1
        x= x+1
    # Right edge (top to bottom)
    x, y= x2, y1+1
    while y<=y2:
        if color<>plot(x, y):
            cut= 1
        y= y+1
    # Bottom edge (right to left)
    x, y= x2-1, y2
    while x>=x1:
        if color<>plot(x, y):
            cut= 1
        x= x-1
    # Left edge (bottom to top)
    x, y= x1, y2-1
    while y>y1:
        if color<>plot(x, y):
            cut= 1
        y= y-1
    # If our rectangle is too small to have an inside, we have now
    # plotted every pixel in it.
    if x2-x1<=1 or y2-y1<=1:
        return
    if cut:                             # If we're cutting the rectangle
        if x2-x1 > y2-y1:               # If it's wider than high
            # Cut vertically
            xc= ((x2-x1)/2)+x1
            drawrect((x1, y1), (xc, y2))
            drawrect((xc, y1), (x2, y2))
        else:                           # if it's higher than wide
            # Cut horizontally
            yc= ((y2-y1)/2)+y1
            drawrect((x1, y1), (x2, yc))
            drawrect((x1, yc), (x2, y2))
    else:
        # If we're not cutting, it was the same color along the edge
        if not debug:
            # Fill in the rectangle
            draw.rectangle([x1, y1, x2, y2], fill= color)
            if yorig >= 0: # The x axis is visible on image
                # Fill in the mirror rectangle
                # Mirror y1 and y2 over yorig, but keep within image
                y1m= max(0, min(2*yorig-y1, ymax))
                y2m= max(0, min(2*yorig-y2, ymax))
                draw.rectangle([x1, y1m, x2, y2m], fill= color)

def constant(x, y):
    "Return complex number from pixel coordinates x and y."
    creal= (float(x)/xmax)*(c2.real - c1.real)+c1.real
    cimag= (float(y)/ymax)*(c2.imag - c1.imag)+c1.imag
    return complex(creal, cimag)

def plot(x, y):
    c= constant(x, y)
    z= i= 0
    color= mandel.getpixel((x, y))
    if color<>0:
        return color
    while i<maxiter and abs(z)<2:
        z= z**2+c
        i= i+1
    color= 16*i%256
    if i>=maxiter or color==0:
        if debug:
            color= 255
        else:
            color= 1
    try:
        mandel.putpixel((x, y), color)
        if yorig >= 0: # The x axis is visible on image
            ym= 2*yorig-y   # ym is y mirrored over yorig
            if ym >= 0 and ym <= ymax:
                # ym is on the image
                mandel.putpixel((x, ym), color)
    except IndexError, the_error:
        print "coord", x, y, xm, ym
        raise IndexError, the_error
    return color

# Initial default values
yfrom= 0
yto= ymax
yorig= -1 # The pixel coordinate of the x axis; negative means not on image

# Check if we should do mirroring
if c1.imag > 0 and c2.imag < 0: # the x axis is visible
    yorig= int((-c1.imag/(c2.imag-c1.imag))*height) # pixel pos. of x axis
    if c1.imag < abs(c2.imag): # the x axis is closer to top than bottom
        yfrom= yorig # Begin at x axis
    else:
        yto= yorig # End at x axis

try:
    drawrect((0, yfrom), (xmax, yto))
except os.error, the_error:
    if the_error[0] != errno.ETIME:
        raise os.error, the_error

signal.alarm(0)

print "Content-type: image/png"
print
mandel.save(sys.stdout, "PNG")
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(42 + 42)
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(owidth2 + oheight2) # 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(width2 + height2)
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")