def mercator2ortho(mercator_image_size, latitude, angular_width, out_width):
phi0 = latitude #latitude and longitude of the
sin_phi0 = sin(phi0)
cos_phi0 = cos(phi0)
z0 = cos_phi0
x0 = sin_phi0
#y0 = 0
#Absolute coordinate of the point on the sphere
swidth, sheight = mercator_image_size
out_height = int(sheight / swidth * out_width)
y_merc0 = asinh(tan(phi0))
def ortho2merc_tfm(xp, yp):
r2 = xp**2 + yp**2
if r2 > 1: return None #Out of domain
zp = sqrt(1 - r2)
#XYZ are coordinates in the rotated coordinate system
#Rotate them by phi (perpendicular to equator), in the xz plane
x,z = zp * cos_phi0 - yp * sin_phi0, \
zp * sin_phi0 + yp * cos_phi0
y = xp
#now (x, y, z) are global coordinates of the projected point on a sphere
#Convert them back to angles...
r_xy = sqrt(x**2 + y**2)
#phi2 = atan2( z, r_xy )
if r_xy == 0:
return None
return (
atan2(y, x), #lambda2
asinh(z / r_xy) - y_merc0) #asinh(tan(phi2))
#angular size of 1 pixel
src_pixel_size = angular_width / swidth
#Determine the size of the projected map piece, in the units where Earth radius = 1.
projection_width = orthogonal_projection_width(mercator_image_size,
latitude, angular_width)
#
dst_pixel_size = angular_width / out_width
dst_pixel_size = projection_width / out_width
scaled_ortho2merc_tfm = compose(
translate_tfm(swidth * 0.5, sheight * 0.5),
scale_tfm(-1.0 / src_pixel_size), ortho2merc_tfm,
scale_tfm(-dst_pixel_size),
translate_tfm(-out_width * 0.5, -out_height * 0.5))
return (out_width, out_height), scaled_ortho2merc_tfm, dst_pixel_size
def inv_logpolar_transform(image_size, y0, out_width, out_height, alpha0 = 0):
"""Inverse log polar transform
"""
xc = out_width/2
yc = out_height/2
center = (xc,yc)
swidth, sheight = image_size
log_rmax = log(xc**2+yc**2)*0.5
#source image scale (pixels per unit)
# image width must be 2PI units
source_scale = (swidth-1)/2/pi
def logz(xf,yf):
if xf == 0 and yf == 0:
return 0, 1e-2
else:
return atan2(yf, xf), log(xf*xf+yf*yf)*0.5
tfm_func1 = compose(
#without translate, min y is: -log_rmax*source_scale. It must be y0.
translate_tfm( source_scale*pi, log_rmax*source_scale+y0 ),
scale_tfm( source_scale, -source_scale ),
logz,
translate_tfm(-xc, -yc)
)
return tfm_func1
def logpolar_transform(image_size, center, out_width=None, out_height=None, alpha0 = 0):
swidth, sheight = image_size
if center is None:
center = (swidth/2, sheight/2)
if out_width is None:
#Automatically determine output width
#Should be enough for mostly loseless transform
out_width = (swidth+sheight)*2
x0,y0 = center
min_log = log(0.5)
max_log = log(max(x0, swidth-x0)**2 + max(y0,sheight-y0)**2)*0.5
#Determine appropriate height of the output image, requiring that whole original
# image fits into it, and highest zoom levels is single pixel.
if out_height is None:
out_height = int(out_width / (2*pi) * (max_log-min_log))
out_size = (out_width, out_height)
out_scale = 2*pi/out_width
def expz(xf,yf):
ey = exp(yf)
return cos(xf)*ey, sin(xf)*ey
tfm_func1 = compose(
translate_tfm(x0, y0),
expz,
translate_tfm( alpha0, max_log ),
scale_tfm( out_scale, -out_scale)
)
def tfm_func(x,y):
xf = x*out_scale + alpha0
yf = max_log-y*out_scale #Put highest resolution at the top
ey = exp(yf)
yfs = sin(xf)*ey
xfs = cos(xf)*ey
return xfs + x0, yfs + y0
return (out_width, out_height), tfm_func
def logpolar_transform(image_size,
center,
out_width=None,
out_height=None,
alpha0=0):
swidth, sheight = image_size
if center is None:
center = (swidth / 2, sheight / 2)
if out_width is None:
#Automatically determine output width
#Should be enough for mostly loseless transform
out_width = (swidth + sheight) * 2
x0, y0 = center
min_log = log(0.5)
max_log = log(max(x0, swidth - x0)**2 + max(y0, sheight - y0)**2) * 0.5
#Determine appropriate height of the output image, requiring that whole original
# image fits into it, and highest zoom levels is single pixel.
if out_height is None:
out_height = int(out_width / (2 * pi) * (max_log - min_log))
out_size = (out_width, out_height)
out_scale = 2 * pi / out_width
def expz(xf, yf):
ey = exp(yf)
return cos(xf) * ey, sin(xf) * ey
tfm_func1 = compose(translate_tfm(x0, y0), expz,
translate_tfm(alpha0, max_log),
scale_tfm(out_scale, -out_scale))
def tfm_func(x, y):
xf = x * out_scale + alpha0
yf = max_log - y * out_scale #Put highest resolution at the top
ey = exp(yf)
yfs = sin(xf) * ey
xfs = cos(xf) * ey
return xfs + x0, yfs + y0
return (out_width, out_height), tfm_func
def download_and_glue(coordinates,
zoom_range=(0, 19),
fragment_size=(512, 512),
out_width=1024,
alpha_gradient_size=10,
map_type="roadmap",
mercator_to_ortho=True,
mesh_step=8,
scale=2,
margins=(0, 0, 0, 0)):
#Increasing zoom by one level offsets image by this amount in the logarithmic view
zoom_level_offset = (0.5 * log(2) / pi) * out_width
fragment_size_scaled = tuple(s * scale for s in fragment_size)
#Prepare alpha
alpha = make_alpha(fragment_size_scaled, alpha_gradient_size, margins)
z0, z1 = zoom_range
out_height = int(zoom_level_offset * (z1 - z0 + 1))
print("Output image size: {out_width}x{out_height}".format(**locals()))
out_image = Image.new("RGBA", (out_width, out_height))
dy_base = None
for zoom in range(z0, z1 + 1):
print("Downloading fragment, zoom={zoom}... ".format(**locals()),
end='',
flush=True)
fragment = get_map_cached(coordinates, zoom, fragment_size, map_type,
scale)
fragment.putalpha(alpha)
print("done, downloaded size: {fragment.size}".format(**locals()))
if not mercator_to_ortho:
dy = (zoom - z0) * zoom_level_offset
_, tfm = logpolar_transform(fragment.size,
scale_tfm(0.5)(*fragment.size),
out_width=out_width)
else:
longitude_extent = (2 * pi) * fragment.size[0] / 256 / scale * (
0.5)**zoom
#Make a transform from mercator to orthogonal
out_ortho_size, merc2otrho_tfm, ortho_pix_size = mercator2ortho(
fragment.size,
coordinates[0] / 180 * pi, #latitude
longitude_extent,
out_width)
_, log_tfm = logpolar_transform(
out_ortho_size,
center=scale_tfm(0.5)(*out_ortho_size),
out_width=out_width)
if dy_base is None:
dy_base = (0.5 / pi * log(ortho_pix_size)) * out_width
dy = 0
else:
dy = dy_base - (0.5 / pi * log(ortho_pix_size)) * out_width
tfm = compose(merc2otrho_tfm, log_tfm)
transformed_size = (out_width, int(zoom_level_offset * 3))
#Put transformed image to the output
print(" Transforming fragment...", end='', flush=True)
transformed = transform_image(fragment,
tfm,
transformed_size,
mesh_step=mesh_step)
print("Done, created {transformed.size} image.".format(**locals()))
paste_with_alpha(out_image, transformed, (0, int(dy)))
print("Done")
return out_image
def download_and_glue(coordinates,
zoom_range=(0,19),
fragment_size=(512,512),
out_width = 1024,
alpha_gradient_size=10,
map_type="roadmap",
mercator_to_ortho=True,
mesh_step=8,
scale=2,
margins=(0,0,0,0)):
#Increasing zoom by one level offsets image by this amount in the logarithmic view
zoom_level_offset = (0.5*log(2)/pi)*out_width
fragment_size_scaled = tuple(s*scale for s in fragment_size)
#Prepare alpha
alpha = make_alpha(fragment_size_scaled, alpha_gradient_size, margins)
z0, z1 = zoom_range
out_height = int(zoom_level_offset * (z1-z0+1))
print ("Output image size: {out_width}x{out_height}".format(**locals()))
out_image = Image.new("RGBA",(out_width, out_height))
dy_base = None
for zoom in range(z0,z1+1):
print ("Downloading fragment, zoom={zoom}... ".format(**locals()), end='', flush=True)
fragment = get_map_cached(coordinates, zoom, fragment_size, map_type, scale)
fragment.putalpha(alpha)
print ("done, downloaded size: {fragment.size}".format(**locals()))
if not mercator_to_ortho:
dy = (zoom-z0) * zoom_level_offset
_, tfm = logpolar_transform(
fragment.size,
scale_tfm(0.5)(*fragment.size),
out_width=out_width)
else:
longitude_extent = (2*pi)*fragment.size[0]/256/scale*(0.5)**zoom
#Make a transform from mercator to orthogonal
out_ortho_size, merc2otrho_tfm, ortho_pix_size = mercator2ortho(
fragment.size,
coordinates[0]/180*pi, #latitude
longitude_extent,
out_width
)
_, log_tfm = logpolar_transform(
out_ortho_size,
center = scale_tfm(0.5)(*out_ortho_size),
out_width=out_width
)
if dy_base is None:
dy_base = (0.5/pi*log(ortho_pix_size))*out_width
dy = 0
else:
dy = dy_base - (0.5/pi*log(ortho_pix_size))*out_width
tfm = compose( merc2otrho_tfm, log_tfm )
transformed_size = (out_width, int(zoom_level_offset*3))
#Put transformed image to the output
print(" Transforming fragment...", end='', flush=True)
transformed=transform_image(fragment, tfm, transformed_size, mesh_step=mesh_step)
print("Done, created {transformed.size} image.".format(**locals()))
paste_with_alpha(out_image,
transformed,
(0, int(dy)))
print ("Done")
return out_image
def main():
from optparse import OptionParser
parser = OptionParser(usage = "%prog [options] INPUT_IMAGE OUTPUT_IMAGE\n"
"Log-Polar image transform. Generated image always have RGBA format")
parser.add_option("-c", "--center", dest="center",
help="Center point position, x:y", metavar="X:Y")
parser.add_option("-A", "--angle", dest="angle", type=float, default=0.0,
help="Angle, corresponding left side of the transformed image, in graduses. 0 is horizontal, left to right.", metavar="ANGLE")
parser.add_option("-w", "--width", dest="width", type=int,
help="Width of the output image. Default is auto-detect, based on the source inmage dimensions (the size is usually quite big)", metavar="PIXELS")
parser.add_option("-H", "--height", dest="height", type=int,
help="Height of the output image. Default is auto-detect, based on width", metavar="PIXELS")
parser.add_option("", "--mesh-step", dest="mesh_step", type=int, default=8,
help="Step of the output mesh. Default is 8", metavar="PIXELS")
parser.add_option("", "--mercator2ortho", dest="mercator2ortho",
help="Treat source image as a piece of the map in Mercator projection. Map in converted to orthogonal projection regarding the point in the center of the map.", metavar="CENTER_LAT:LNG_WIDTH")
(options, args) = parser.parse_args()
if len(args) < 1:
parser.error("No input file specified")
input =args[0]
if len(args) >= 2:
output = args[1]
else:
output = None
if options.mercator2ortho:
if options.center:
parser.error("Center not supported in mercator map pieces. It is always at the center of the image")
try:
lat_center_s, lng_extent_s = options.mercator2ortho.split(":",2)
mercator2ortho_options = {
"center_lat": float(lat_center_s)/180*pi,
"lng_extent": float(lng_extent_s)/180*pi
}
except Exception as err:
parser.error("Error parsing mercator projection options: {0}".format(err))
else:
mercator2ortho_options = None
if options.center is None:
center = None
else:
center = tuple(map(int, options.center.split(":",2)))
img = Image.open(input)
#Image conversions
# SOurce image can be one of:
# - RGB
# - RGBA - has alpha
# - I - may have alpha
# - L
# - 1
# Target image:
# always have alpha.
if img.mode != "RGBA":
img =img.convert("RGBA")
if mercator2ortho_options:
from mercator2ortho import mercator2ortho
out_ortho_size, merc2otrho_tfm, _ = mercator2ortho(img.size,
mercator2ortho_options["center_lat"],
mercator2ortho_options["lng_extent"],
max(img.size)
)
out_size, ortho2log_tfm = logpolar_transform(out_ortho_size,
center=scale_tfm(0.5)(*out_ortho_size),
out_width = options.width,
alpha0 = options.angle/180*pi)
#Create composite transform: first convert Mercator map to orthogonal projection, then apply log-transform to it.
transform = compose(
merc2otrho_tfm,
ortho2log_tfm )
else:
out_size, transform = logpolar_transform(img.size,
center=center,
out_width = options.width,
alpha0 = options.angle/180*pi)
img = transform_image(img, transform, out_size, mesh_step=options.mesh_step)
if output:
img.save(output)
else:
img.show()
def main():
from optparse import OptionParser
parser = OptionParser(
usage="%prog [options] INPUT_IMAGE OUTPUT_IMAGE\n"
"Log-Polar image transform. Generated image always have RGBA format")
parser.add_option("-c",
"--center",
dest="center",
help="Center point position, x:y",
metavar="X:Y")
parser.add_option(
"-A",
"--angle",
dest="angle",
type=float,
default=0.0,
help=
"Angle, corresponding left side of the transformed image, in graduses. 0 is horizontal, left to right.",
metavar="ANGLE")
parser.add_option(
"-w",
"--width",
dest="width",
type=int,
help=
"Width of the output image. Default is auto-detect, based on the source inmage dimensions (the size is usually quite big)",
metavar="PIXELS")
parser.add_option(
"-H",
"--height",
dest="height",
type=int,
help=
"Height of the output image. Default is auto-detect, based on width",
metavar="PIXELS")
parser.add_option("",
"--mesh-step",
dest="mesh_step",
type=int,
default=8,
help="Step of the output mesh. Default is 8",
metavar="PIXELS")
parser.add_option(
"",
"--mercator2ortho",
dest="mercator2ortho",
help=
"Treat source image as a piece of the map in Mercator projection. Map in converted to orthogonal projection regarding the point in the center of the map.",
metavar="CENTER_LAT:LNG_WIDTH")
(options, args) = parser.parse_args()
if len(args) < 1:
parser.error("No input file specified")
input = args[0]
if len(args) >= 2:
output = args[1]
else:
output = None
if options.mercator2ortho:
if options.center:
parser.error(
"Center not supported in mercator map pieces. It is always at the center of the image"
)
try:
lat_center_s, lng_extent_s = options.mercator2ortho.split(":", 2)
mercator2ortho_options = {
"center_lat": float(lat_center_s) / 180 * pi,
"lng_extent": float(lng_extent_s) / 180 * pi
}
except Exception as err:
parser.error(
"Error parsing mercator projection options: {0}".format(err))
else:
mercator2ortho_options = None
if options.center is None:
center = None
else:
center = tuple(map(int, options.center.split(":", 2)))
img = Image.open(input)
#Image conversions
# SOurce image can be one of:
# - RGB
# - RGBA - has alpha
# - I - may have alpha
# - L
# - 1
# Target image:
# always have alpha.
if img.mode != "RGBA":
img = img.convert("RGBA")
if mercator2ortho_options:
from mercator2ortho import mercator2ortho
out_ortho_size, merc2otrho_tfm, _ = mercator2ortho(
img.size, mercator2ortho_options["center_lat"],
mercator2ortho_options["lng_extent"], max(img.size))
out_size, ortho2log_tfm = logpolar_transform(
out_ortho_size,
center=scale_tfm(0.5)(*out_ortho_size),
out_width=options.width,
alpha0=options.angle / 180 * pi)
#Create composite transform: first convert Mercator map to orthogonal projection, then apply log-transform to it.
transform = compose(merc2otrho_tfm, ortho2log_tfm)
else:
out_size, transform = logpolar_transform(img.size,
center=center,
out_width=options.width,
alpha0=options.angle / 180 *
pi)
img = transform_image(img,
transform,
out_size,
mesh_step=options.mesh_step)
if output:
img.save(output)
else:
img.show()