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#!/usr/bin/python |
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|
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import cgi, Image, ImageDraw, sys, math, signal, errno, os |
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from string import atoi, atof |
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|
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def handler(signum, frame): |
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signal.alarm(0) |
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raise os.error, (errno.ETIME, "Timer expired") |
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|
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signal.alarm(55) |
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signal.signal(signal.SIGALRM, handler) |
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|
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# This is to get backtrace output |
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sys.stderr = sys.stdout |
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|
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# Uncomment this to get the backtrace more readable |
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#print "Content-Type: text/plain" |
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#print "" |
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|
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form= cgi.FieldStorage() |
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|
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# Image size |
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if form.has_key('width'): |
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width= atoi(form['width'].value) |
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else: |
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width= 480 |
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if form.has_key('height'): |
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height= atoi(form['height'].value) |
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else: |
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height= 480 |
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|
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xmax, ymax = width-1, height-1 # Coordinate maximums |
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|
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# Complex number in center of image is (cx+cy*j) |
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if form.has_key('cx'): |
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cx= atof(form['cx'].value) |
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else: |
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cx= 0.0 |
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|
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if form.has_key('cy'): |
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cy= atof(form['cy'].value) |
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else: |
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cy= 0.0 |
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|
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# The length of the diagonal line from corner to corner. |
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# Used as a measure of image size independent of aspect ratio. |
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if form.has_key('diag'): |
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diag= atof(form['diag'].value) |
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else: |
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diag= math.sqrt(32) # sqrt(4**2 + 4**2) |
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|
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debug= form.has_key('debug') |
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|
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if form.has_key('iter'): |
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maxiter= atoi(form['iter'].value) |
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else: |
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maxiter= 270 |
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|
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# If type!=image, then output an HTML page, not an image |
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if not (form.has_key('type') and form['type'].value == "image"): |
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print """Content-Type: text/html |
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|
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<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML 2.0//EN"> |
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<HTML><HEAD> |
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<TITLE>Mandelbrot Set Zoomer</TITLE> |
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</HEAD> |
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<BODY> |
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<H1>Mandelbrot Set Zoomer</H1> |
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|
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<FORM ACTION="mandelzoom.cgi" METHOD=GET> |
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|
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<!-- implies TYPE=SUBMIT -->""" |
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print '<INPUT TYPE=IMAGE NAME="image"', |
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print 'WIDTH="%s"' % (str(width)), |
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print 'HEIGHT="%s"' % (str(height)), |
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if debug: |
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ds="&debug=on" |
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else: |
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ds="" |
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# If the user has selected a specific point on the image |
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if form.has_key('image.x') and form.has_key('image.y'): |
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# Adjust cx and cy |
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ix= atof(form['image.x'].value) # Intermediate value |
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iy= atof(form['image.y'].value) # Intermediate value |
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owidth= atof(form['owidth'].value) |
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oheight= atof(form['oheight'].value) |
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diagp= math.sqrt(owidth**2 + oheight**2) # Intermediate value |
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scale= diagp/diag # Intermediate value |
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cx= (ix/scale) + (cx - (owidth / (scale*2))) |
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cy= ((oheight-iy)/scale) + (cy - (oheight / (scale*2))) |
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if form.has_key('zoom'): |
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zoom=atof(form['zoom'].value) |
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diag=diag/zoom |
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else: |
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# If no zoom provided, don't actually zoom, but keep the |
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# default of ×2 zoom. |
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zoom= 2.0 |
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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)), |
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print 'ALIGN=BOTTOM HEIGHT="%s"' % (str(height)), |
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print 'WIDTH="%s"><P>' % (str(width)) |
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print 'Zoom: <SELECT NAME="zoom">' |
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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]: |
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print '<OPTION', |
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if str(zv)==str(zoom): |
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print 'SELECTED', |
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print 'VALUE="%s"' % (str(zv)) |
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if zv == 1: |
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print '>Pan' |
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elif zv < 1: |
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print '>Out ÷%s' % (str(1/zv)) |
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else: |
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print '>In ×%s' % (str(zv)) |
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print '</SELECT>' |
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print """Width: <INPUT TYPE=TEXT NAME="width" MAXLENGTH="4" SIZE="3" |
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VALUE="%s"> |
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Height: <INPUT TYPE=TEXT NAME="height" MAXLENGTH="4" SIZE="3" |
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VALUE="%s"> |
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Iterations: <INPUT TYPE=TEXT NAME="iter" MAXLENGTH="4" SIZE="3" |
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VALUE="%s"> |
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Debug mode: <INPUT TYPE=CHECKBOX NAME="debug" """ % (str(width), str(height), str(maxiter)), |
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if debug: |
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print 'CHECKED>' |
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else: |
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print '>' |
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print '<INPUT TYPE=SUBMIT VALUE="Apply">' |
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for var in (("diag", diag), ("cx", cx), ("cy", cy), ("owidth", width), |
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("oheight", height)): |
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print '<INPUT TYPE=HIDDEN NAME="%s" VALUE="%s">' % var |
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print '<INPUT TYPE=HIDDEN NAME=type VALUE="html">' |
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|
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print """</FORM><P> |
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After changing any settings, don't forget to change the "Zoom" setting |
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to "Pan" if you don't want to zoom when applying them. |
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</BODY></HTML>""" |
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# Just exit, don't calculate an image. |
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sys.exit(0) |
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|
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# c1 and c2 are the coordinates of two opposite corners. |
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# Figure out c1 and c2 from width, height, diag, cx, and cy. |
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|
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# Diagonal in pixels |
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diagp= math.sqrt(width**2 + height**2) |
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# Scale between pixels and coordinates |
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scale= diagp/diag |
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# half the width/height in real numbers; intermediate values |
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x= (width/2.0)/scale |
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y= (height/2.0)/scale |
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|
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# The coordinates of two opposite corners |
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c1= cx - x + (cy - y) * (0+1j) |
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c2= cx + x + (cy + y) * (0+1j) |
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|
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#print width, height, diag, cx, cy, diagp, scale, x, y, c1, c2 |
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#sys.exit(0) |
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|
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# Force c1 to be upper left and c2 to be lower right |
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c1, c2= complex(min(c1.real, c2.real), max(c1.imag, c2.imag)), \ |
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complex(max(c1.real, c2.real), min(c1.imag, c2.imag)) |
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|
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# New image object |
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mandel= Image.new("L", (width, height)) |
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# shortcut to the "Draw" method on the image object |
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draw= ImageDraw.Draw(mandel) |
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|
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def drawrect((x1, y1), (x2, y2)): |
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"Draw a rectangle defined by the corners (x1, y1) and (x2, y2)." |
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color= plot(x1, y1) # Plot the upper left corner |
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# Should we cut this rectangle and recurse into the pieces? |
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cut= 0 |
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## Plot the edges and at the same time check if they are all the |
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## same color. |
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# Upper edge (left to right) |
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x, y= x1+1, y1 |
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while x<=x2: |
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if color<>plot(x, y): |
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cut= 1 |
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x= x+1 |
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# Right edge (top to bottom) |
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x, y= x2, y1+1 |
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while y<=y2: |
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if color<>plot(x, y): |
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cut= 1 |
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y= y+1 |
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# Bottom edge (right to left) |
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x, y= x2-1, y2 |
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while x>=x1: |
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if color<>plot(x, y): |
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cut= 1 |
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x= x-1 |
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# Left edge (bottom to top) |
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x, y= x1, y2-1 |
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while y>y1: |
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if color<>plot(x, y): |
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cut= 1 |
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y= y-1 |
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# If our rectangle is too small to have an inside, we have now |
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# plotted every pixel in it. |
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if x2-x1<=1 or y2-y1<=1: |
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return |
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if cut: # If we're cutting the rectangle |
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if x2-x1 > y2-y1: # If it's wider than high |
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# Cut vertically |
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xc= ((x2-x1)/2)+x1 |
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drawrect((x1, y1), (xc, y2)) |
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drawrect((xc, y1), (x2, y2)) |
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else: # if it's higher than wide |
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# Cut horizontally |
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yc= ((y2-y1)/2)+y1 |
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drawrect((x1, y1), (x2, yc)) |
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drawrect((x1, yc), (x2, y2)) |
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else: |
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# If we're not cutting, it was the same color along the edge |
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if not debug: |
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# Fill in the rectangle |
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draw.rectangle([x1, y1, x2, y2], fill= color) |
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if yorig >= 0: # The x axis is visible on image |
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# Fill in the mirror rectangle |
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# Mirror y1 and y2 over yorig, but keep within image |
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y1m= max(0, min(2*yorig-y1, ymax)) |
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y2m= max(0, min(2*yorig-y2, ymax)) |
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draw.rectangle([x1, y1m, x2, y2m], fill= color) |
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|
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def constant(x, y): |
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"Return complex number from pixel coordinates x and y." |
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creal= (float(x)/xmax)*(c2.real - c1.real)+c1.real |
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cimag= (float(y)/ymax)*(c2.imag - c1.imag)+c1.imag |
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return complex(creal, cimag) |
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|
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def plot(x, y): |
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c= constant(x, y) |
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z= i= 0 |
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color= mandel.getpixel((x, y)) |
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if color<>0: |
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return color |
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while i<maxiter and abs(z)<2: |
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z= z**2+c |
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i= i+1 |
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color= 16*i%256 |
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if i>=maxiter or color==0: |
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if debug: |
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color= 255 |
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else: |
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color= 1 |
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try: |
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mandel.putpixel((x, y), color) |
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if yorig >= 0: # The x axis is visible on image |
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ym= 2*yorig-y # ym is y mirrored over yorig |
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if ym >= 0 and ym <= ymax: |
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# ym is on the image |
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mandel.putpixel((x, ym), color) |
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except IndexError, the_error: |
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print "coord", x, y, xm, ym |
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raise IndexError, the_error |
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return color |
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|
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# Initial default values |
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yfrom= 0 |
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yto= ymax |
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yorig= -1 # The pixel coordinate of the x axis; negative means not on image |
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|
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# Check if we should do mirroring |
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if c1.imag > 0 and c2.imag < 0: # the x axis is visible |
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yorig= int((-c1.imag/(c2.imag-c1.imag))*height) # pixel pos. of x axis |
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if c1.imag < abs(c2.imag): # the x axis is closer to top than bottom |
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yfrom= yorig # Begin at x axis |
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else: |
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yto= yorig # End at x axis |
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|
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try: |
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drawrect((0, yfrom), (xmax, yto)) |
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except os.error, the_error: |
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if the_error[0] != errno.ETIME: |
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raise os.error, the_error |
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|
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signal.alarm(0) |
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|
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print "Content-type: image/png" |
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print |
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mandel.save(sys.stdout, "PNG") |
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