cvs/fract/mandelzoom.cgi

#!/usr/bin/python

import cgi, Image, ImageDraw, sys, math
from string import atoi, atof

# 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

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 form.has_key('image.x') and form.has_key('image.y'):
        # Adjust cx and cy
        ix= atof(form['image.x'].value)
        iy= atof(form['image.y'].value)
        owidth= atof(form['owidth'].value)
        oheight= atof(form['oheight'].value)
        diagp= math.sqrt(owidth**2 + oheight**2)
        scale= diagp/diag
        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
        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>
</BODY></HTML>"""
    sys.exit(0)

# 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
x= (width/2.0)/scale
y= (height/2.0)/scale

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)

#c1, c2 = (-2+2j), (2-2j)                # Corner coordinates

# 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))

mandel= Image.new("L", (width, height))
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):
    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

drawrect((0, yfrom), (xmax, yto))

print "Content-type: image/png"
print
mandel.save(sys.stdout, "PNG")
1	#!/usr/bin/python
2
3	import cgi, Image, ImageDraw, sys, math
4	from string import atoi, atof
5
6	# This is to get backtrace output
7	sys.stderr = sys.stdout
8
9	# Uncomment this to get the backtrace more readable
10	#print "Content-Type: text/plain"
11	#print ""
12
13	form= cgi.FieldStorage()
14
15	# Image size
16	if form.has_key('width'):
17	width= atoi(form['width'].value)
18	else:
19	width= 480
20	if form.has_key('height'):
21	height= atoi(form['height'].value)
22	else:
23	height= 480
24
25	xmax, ymax = width-1, height-1 # Coordinate maximums
26
27	# Complex number in center of image is (cx+cy*j)
28	if form.has_key('cx'):
29	cx= atof(form['cx'].value)
30	else:
31	cx= 0.0
32
33	if form.has_key('cy'):
34	cy= atof(form['cy'].value)
35	else:
36	cy= 0.0
37
38	if form.has_key('diag'):
39	diag= atof(form['diag'].value)
40	else:
41	diag= math.sqrt(32) # sqrt(42 + 42)
42
43	debug= form.has_key('debug')
44
45	if form.has_key('iter'):
46	maxiter= atoi(form['iter'].value)
47	else:
48	maxiter= 270
49
50	# If type!=image, then output an HTML page, not an image
51	if not (form.has_key('type') and form['type'].value == "image"):
52	print """Content-Type: text/html
53
54	<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML 2.0//EN">
55	<HTML><HEAD>
56	<TITLE>Mandelbrot Set Zoomer</TITLE>
57	</HEAD>
58	<BODY>
59	<H1>Mandelbrot Set Zoomer</H1>
60
61	<FORM ACTION="mandelzoom.cgi" METHOD=GET>
62
63	<!-- implies TYPE=SUBMIT -->"""
64	print '<INPUT TYPE=IMAGE NAME="image"',
65	print 'WIDTH="%s"' % (str(width)),
66	print 'HEIGHT="%s"' % (str(height)),
67	if debug:
68	ds="&debug=on"
69	else:
70	ds=""
71	if form.has_key('image.x') and form.has_key('image.y'):
72	# Adjust cx and cy
73	ix= atof(form['image.x'].value)
74	iy= atof(form['image.y'].value)
75	owidth= atof(form['owidth'].value)
76	oheight= atof(form['oheight'].value)
77	diagp= math.sqrt(owidth2 + oheight2)
78	scale= diagp/diag
79	cx= (ix/scale) + (cx - (owidth / (scale*2)))
80	cy= ((oheight-iy)/scale) + (cy - (oheight / (scale*2)))
81	if form.has_key('zoom'):
82	zoom=atof(form['zoom'].value)
83	diag=diag/zoom
84	else:
85	# If no zoom provided, don't actually zoom
86	zoom= 2.0
87	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)),
88	print 'ALIGN=BOTTOM HEIGHT="%s"' % (str(height)),
89	print 'WIDTH="%s"><P>' % (str(width))
90	print 'Zoom: <SELECT NAME="zoom">'
91	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]:
92	print '<OPTION',
93	if str(zv)==str(zoom):
94	print 'SELECTED',
95	print 'VALUE="%s"' % (str(zv))
96	if zv == 1:
97	print '>Pan'
98	elif zv < 1:
99	print '>Out �%s' % (str(1/zv))
100	else:
101	print '>In �%s' % (str(zv))
102	print '</SELECT>'
103	print """Width: <INPUT TYPE=TEXT NAME="width" MAXLENGTH="4" SIZE="3"
104	VALUE="%s">
105	Height: <INPUT TYPE=TEXT NAME="height" MAXLENGTH="4" SIZE="3"
106	VALUE="%s">
107	Iterations: <INPUT TYPE=TEXT NAME="iter" MAXLENGTH="4" SIZE="3"
108	VALUE="%s">
109	Debug mode: <INPUT TYPE=CHECKBOX NAME="debug" """ % (str(width), str(height), str(maxiter)),
110	if debug:
111	print 'CHECKED>'
112	else:
113	print '>'
114	print '<INPUT TYPE=SUBMIT VALUE="Apply">'
115	for var in (("diag", diag), ("cx", cx), ("cy", cy), ("owidth", width),
116	("oheight", height)):
117	print '<INPUT TYPE=HIDDEN NAME="%s" VALUE="%s">' % var
118	print '<INPUT TYPE=HIDDEN NAME=type VALUE="html">'
119
120	print """</FORM>
121	</BODY></HTML>"""
122	sys.exit(0)
123
124	# Figure out c1 and c2 from width, height, diag, cx, and cy.
125	# Diagonal in pixels
126	diagp= math.sqrt(width2 + height2)
127	# Scale between pixels and coordinates
128	scale= diagp/diag
129	x= (width/2.0)/scale
130	y= (height/2.0)/scale
131
132	c1= cx - x + (cy - y) * (0+1j)
133	c2= cx + x + (cy + y) * (0+1j)
134
135	#print width, height, diag, cx, cy, diagp, scale, x, y, c1, c2
136	#sys.exit(0)
137
138	#c1, c2 = (-2+2j), (2-2j) # Corner coordinates
139
140	# Force c1 to be upper left and c2 to be lower right
141	c1, c2= complex(min(c1.real, c2.real), max(c1.imag, c2.imag)), \
142	complex(max(c1.real, c2.real), min(c1.imag, c2.imag))
143
144	mandel= Image.new("L", (width, height))
145	draw= ImageDraw.Draw(mandel)
146
147	def drawrect((x1, y1), (x2, y2)):
148	"Draw a rectangle defined by the corners (x1, y1) and (x2, y2)."
149	color= plot(x1, y1) # Plot the upper left corner
150	# Should we cut this rectangle and recurse into the pieces?
151	cut= 0
152	## Plot the edges and at the same time check if they are all the
153	## same color.
154	# Upper edge (left to right)
155	x, y= x1+1, y1
156	while x<=x2:
157	if color<>plot(x, y):
158	cut= 1
159	x= x+1
160	# Right edge (top to bottom)
161	x, y= x2, y1+1
162	while y<=y2:
163	if color<>plot(x, y):
164	cut= 1
165	y= y+1
166	# Bottom edge (right to left)
167	x, y= x2-1, y2
168	while x>=x1:
169	if color<>plot(x, y):
170	cut= 1
171	x= x-1
172	# Left edge (bottom to top)
173	x, y= x1, y2-1
174	while y>y1:
175	if color<>plot(x, y):
176	cut= 1
177	y= y-1
178	# If our rectangle is too small to have an inside, we have now
179	# plotted every pixel in it.
180	if x2-x1<=1 or y2-y1<=1:
181	return
182	if cut: # If we're cutting the rectangle
183	if x2-x1 > y2-y1: # If it's wider than high
184	# Cut vertically
185	xc= ((x2-x1)/2)+x1
186	drawrect((x1, y1), (xc, y2))
187	drawrect((xc, y1), (x2, y2))
188	else: # if it's higher than wide
189	# Cut horizontally
190	yc= ((y2-y1)/2)+y1
191	drawrect((x1, y1), (x2, yc))
192	drawrect((x1, yc), (x2, y2))
193	else:
194	# If we're not cutting, it was the same color along the edge
195	if not debug:
196	# Fill in the rectangle
197	draw.rectangle([x1, y1, x2, y2], fill= color)
198	if yorig >= 0: # The x axis is visible on image
199	# Fill in the mirror rectangle
200	# Mirror y1 and y2 over yorig, but keep within image
201	y1m= max(0, min(2*yorig-y1, ymax))
202	y2m= max(0, min(2*yorig-y2, ymax))
203	draw.rectangle([x1, y1m, x2, y2m], fill= color)
204
205	def constant(x, y):
206	creal= (float(x)/xmax)*(c2.real - c1.real)+c1.real
207	cimag= (float(y)/ymax)*(c2.imag - c1.imag)+c1.imag
208	return complex(creal, cimag)
209
210	def plot(x, y):
211	c= constant(x, y)
212	z= i= 0
213	color= mandel.getpixel((x, y))
214	if color<>0:
215	return color
216	while i<maxiter and abs(z)<2:
217	z= z**2+c
218	i= i+1
219	color= 16*i%256
220	if i>=maxiter or color==0:
221	if debug:
222	color= 255
223	else:
224	color= 1
225	try:
226	mandel.putpixel((x, y), color)
227	if yorig >= 0: # The x axis is visible on image
228	ym= 2*yorig-y # ym is y mirrored over yorig
229	if ym >= 0 and ym <= ymax:
230	# ym is on the image
231	mandel.putpixel((x, ym), color)
232	except IndexError, the_error:
233	print "coord", x, y, xm, ym
234	raise IndexError, the_error
235	return color
236
237	# Initial default values
238	yfrom= 0
239	yto= ymax
240	yorig= -1 # The pixel coordinate of the x axis; negative means not on image
241
242	# Check if we should do mirroring
243	if c1.imag > 0 and c2.imag < 0: # the x axis is visible
244	yorig= int((-c1.imag/(c2.imag-c1.imag))*height) # pixel pos. of x axis
245	if c1.imag < abs(c2.imag): # the x axis is closer to top than bottom
246	yfrom= yorig # Begin at x axis
247	else:
248	yto= yorig # End at x axis
249
250	drawrect((0, yfrom), (xmax, yto))
251
252	print "Content-type: image/png"
253	print
254	mandel.save(sys.stdout, "PNG")