def _adv_superbee(vel, var, mask, dx, axis, cost, cosu, dt_tracer):
velfac = 1
if axis == 0:
sm1, s, sp1, sp2 = ((slice(1 + n, -2 + n or None), slice(2, -2), slice(None))
for n in range(-1, 3))
dx = cost[bh.newaxis, 2:-2, bh.newaxis] * \
dx[1:-2, bh.newaxis, bh.newaxis]
elif axis == 1:
sm1, s, sp1, sp2 = ((slice(2, -2), slice(1 + n, -2 + n or None), slice(None))
for n in range(-1, 3))
dx = (cost * dx)[bh.newaxis, 1:-2, bh.newaxis]
velfac = cosu[bh.newaxis, 1:-2, bh.newaxis]
elif axis == 2:
vel, var, mask = (pad_z_edges(a) for a in (vel, var, mask))
sm1, s, sp1, sp2 = ((slice(2, -2), slice(2, -2), slice(1 + n, -2 + n or None))
for n in range(-1, 3))
dx = dx[bh.newaxis, bh.newaxis, :-1]
else:
raise ValueError('axis must be 0, 1, or 2')
uCFL = bh.abs(velfac * vel[s] * dt_tracer / dx)
rjp = (var[sp2] - var[sp1]) * mask[sp1]
rj = (var[sp1] - var[s]) * mask[s]
rjm = (var[s] - var[sm1]) * mask[sm1]
cr = limiter(_calc_cr(rjp, rj, rjm, vel[s]))
return velfac * vel[s] * (var[sp1] + var[s]) * 0.5 - bh.abs(velfac * vel[s]) * ((1. - cr) + uCFL * cr) * rj * 0.5
def marble(size=(256,256),xPeriod=3.0,yPeriod=10.0,turbPower=0.8,turbSize=None,seed=None):
"""
Generate a marble texture akin to blender and others
:param xPeriod: defines repetition of marble lines in x direction
:param yPeriod: defines repetition of marble lines in y direction
:param turbPower: add twists and swirls (when turbPower==0 it becomes a normal sine pattern)
:param turbSize: initial size of the turbulence default is max(w,h)/10
NOTE:
xPeriod and yPeriod together define the angle of the lines
xPeriod and yPeriod both 0 then it becomes a normal clouds or turbulence pattern
Optimized version of:
https://lodev.org/cgtutor/randomnoise.html
"""
w,h=size
turb=turbulence(size,turbSize,seed=seed)*turbPower
# determine where the pixels will cycle
cycleValue=np.ndarray((w,h))
for y in range(h):
for x in range(w):
cycleValue[x,y]=(x*xPeriod/w)+(y*yPeriod/h)
# add in the turbulence and then last of all, make it a sinewave
img=np.abs(np.sin((cycleValue+turb)*math.pi))
return img
def normalMapFromHeightMap(heightmap):
"""
Create a normal map from a height map (sometimes called a bumpmap)
:param heightmap: height map to convert
Comes from:
http://www.juhanalankinen.com/calculating-normalmaps-with-python-and-numpy/
"""
heightmap = numpyArray(heightmap)
heightmap = normalize(heightmap)
matI = np.identity(heightmap.shape[0] + 1)
matNeg = -1 * matI[0:-1, 1:]
matNeg[0, -1] = -1
matI = matI[1:, 0:-1]
matI[-1, 0] = 1
matI += matNeg
matGradX = (matI.dot(heightmap.T)).T
matGradY = matI.dot(heightmap)
matNormal = np.zeros([heightmap.shape[0], heightmap.shape[1], 3])
matNormal[:, :, 0] = -matGradX
matNormal[:, :, 1] = matGradY
matNormal[:, :, 2] = 1.0
fNormMax = np.max(np.abs(matNormal))
matNormal = ((matNormal / fNormMax) + 1.0) / 2.0
return matNormal
def selectHighContrast(image):
"""
get mask based on very bright or very dark areas
returns b&w image where white=interesting, black=uninteresting
NOTE: since we are using a color-weighted grayscale conversion,
this does account somewhat for color discrimination of human vision.
"""
image = grayscale(image, method='BT.709')
a = np.average(image)
return normalize(np.abs(image - a))
def woodRings(size=(256,256),xyPeriod=12.0,turbPower=0.15,turbSize=32.0,seed=None):
"""
Draw wood rings
:param xyPeriod: number of rings
:param turbPower: makes twists
:param turbSize: # initial size of the turbulence
Optimized version of:
https://lodev.org/cgtutor/randomnoise.html
"""
turb=turbulence(size,turbSize,seed=seed)*turbPower
dc=normalize(deltaC(size,magnitude=True))
img = np.abs(np.sin(xyPeriod * (dc+turb) * math.pi))
return normalize(img)
def clock2(size=(256,256),waveform="sine",frequency=(10,10),noise=0.2,noiseBasis="perlin",
noiseOctaves=4,noiseSoften=0.0,direction=0,invert=False,seed=None):
"""
a rotary clockface gradient
"""
noiseSize=max(size)/8 # TODO: pass this value in somehow
turb=turbulence(size,noiseSize,seed=seed)*noise
#points=np.ndarray((int(size[0]),int(size[1])))
angle=0.75-direction/360.0
dc=deltaC(size)
img=np.arctan2(dc[:,:,0],dc[:,:,1])/math.pi
img=np.abs(np.sin((((normalize(img)+angle)%1.0)+turb)*math.pi))
img=normalize(img)
if invert:
img=1.0-img
return img
def imageDifference(img1, img2) -> Union[float, None]:
"""
returns an image difference as a decimal percent (1.0 = 100%)
images can be a pil image, rgb numpy array, url, or filename
NOTE: returns None if images are incomparable
(including being a different size)
"""
if img1 is None or img2 is None:
return None
img1, img2 = makeSameMode([defaultLoader(img1), defaultLoader(img2)])
img1, img2 = numpyArray(img1), numpyArray(img2)
if img1.shape != img2.shape:
# if they're not even the same size, never mind, then
return None
return np.abs(img1 - img2).sum() / (img1.shape[0] * img1.shape[1])
def waveImage(size=(256,256),repeats=2,angle=0,wave='sine',radial=False):
"""
create an image based on a sine, saw, or triangle wave function
"""
ret=np.zeros(size)
if radial:
raise NotImplementedError() # TODO: Implement radial wave images
else:
twopi=2*pi
thetas=np.arange(size[0])*float(repeats)/size[0]*twopi
if wave=='sine':
ret[:,:]=0.5+0.5*np.sin(thetas)
elif wave=='saw':
n=np.round(thetas/twopi)
thetas-=n*twopi
ret[:,:]=np.where(thetas<0,thetas+twopi,thetas)/twopi
elif wave=='triangle':
ret[:,:]=1.0-2.0*np.abs(np.floor((thetas*(1.0/twopi))+0.5)-(thetas*(1.0/twopi)))
return ret
def weighted_line(r0, c0, r1, c1, w, rmin=0, rmax=np.inf):
# The algorithm below works fine if c1 >= c0 and c1-c0 >= abs(r1-r0).
# If either of these cases are violated, do some switches.
if abs(c1-c0) < abs(r1-r0):
# Switch x and y, and switch again when returning.
xx, yy, val = weighted_line(c0, r0, c1, r1, w, rmin=rmin, rmax=rmax)
return (yy, xx, val)
# At this point we know that the distance in columns (x) is greater
# than that in rows (y). Possibly one more switch if c0 > c1.
if c0 > c1:
return weighted_line(r1, c1, r0, c0, w, rmin=rmin, rmax=rmax)
# The following is now always < 1 in abs
num=r1-r0
denom=c1-c0
slope = np.divide(num,denom,out=np.zeros_like(denom), where=denom!=0)
# Adjust weight by the slope
w *= np.sqrt(1+np.abs(slope)) / 2
# We write y as a function of x, because the slope is always <= 1
# (in absolute value)
x = np.arange(c0, c1+1, dtype=float)
y = x * slope + (c1*r0-c0*r1) / (c1-c0)
# Now instead of 2 values for y, we have 2*np.ceil(w/2).
# All values are 1 except the upmost and bottommost.
thickness = np.ceil(w/2)
yy = (np.floor(y).reshape(-1,1) + np.arange(-thickness-1,thickness+2).reshape(1,-1))
xx = np.repeat(x, yy.shape[1])
vals = trapez(yy, y.reshape(-1,1), w).flatten()
yy = yy.flatten()
# Exclude useless parts and those outside of the interval
# to avoid parts outside of the picture
mask = np.logical_and.reduce((yy >= rmin, yy < rmax, vals > 0))
return (yy[mask].astype(int), xx[mask].astype(int), vals[mask])
def _calc_cr(rjp, rj, rjm, vel):
"""
Calculates cr value used in superbee advection scheme
"""
eps = 1e-20 # prevent division by 0
return where(vel > 0., rjm, rjp) / where(bh.abs(rj) < eps, eps, rj)
def sin(x):
return np.abs(np.sin(x*math.pi))
def _difference(bottom, top):
return np.abs(bottom - top)
def selectByColor(img,
color,
tolerance=0,
soften=10,
smartSoften=True,
colorspace='RGB'):
"""
Select all pixels of a given color
:param img: can be a pil image, numpy array, etc
:param color: (in colorspace units) can be anything that pickColor returns:
a color int array
a color string to decode
a color range (colorLow,colorHigh)
an array of any of these
:param tolerance: how close the selection must be
:param soften: apply a soften radius to the edges of the selection
:param smartSoften: multiply the soften radius by how near the pixel is to the selection color
:param colorspace: change the given img (assumed to be RGB) into another corlorspace before matching
:returns: black and white image in a numpy array (usable as a selection or a mask)
"""
from . import colorSpaces
img = numpyArray(img)
img = colorSpaces.changeColorspace(img, colorspace)
if (isinstance(color, list)
and isinstance(color[0], list)) or (isinstance(color, np.ndarray)
and len(color.shape) > 1):
# there are multiple colors, so select them all one at a time
# TODO: this could possibly be made faster with array operations??
ret = None
for c in color:
if ret is None:
ret = selectByColor(img, c, tolerance, soften, smartSoften)
else:
ret = ret + selectByColor(img, c, tolerance, soften,
smartSoften)
ret = clampImage(ret)
elif isinstance(color, tuple):
# color range - select all colors "between" these two in the given color space
color = (matchColorToImage(color[0],
img), matchColorToImage(color[1], img))
matches = np.logical_and(img >= color[0], img <= color[1])
ret = np.where(matches.all(axis=2), 1.0, 0.0)
else:
# a single color (or a series of colors that have been averaged down to one)
color = matchColorToImage(color, img)
if isFloat(color):
imax = 1.0
imin = 0.0
else:
imax = 255
imin = 0
numColors = img.shape[-1]
avgDelta = np.sum(np.abs(img[:, :] - color), axis=-1) / numColors
ret = np.where(avgDelta <= tolerance, imax, imin)
if soften > 0:
ret = gaussianBlur(ret, soften)
if smartSoften:
ret = np.minimum(imax, ret / avgDelta)
return ret
def dm_taper(sx):
"""
tapering function for isopycnal slopes
"""
return 0.5 * (1. + bh.tanh((-bh.abs(sx) + iso_slopec) / iso_dslope))
def isoneutral_diffusion_pre(maskT, maskU, maskV, maskW, dxt, dxu, dyt, dyu,
dzt, dzw, cost, cosu, salt, temp, zt, K_iso, K_11,
K_22, K_33, Ai_ez, Ai_nz, Ai_bx, Ai_by):
"""
Isopycnal diffusion for tracer
following functional formulation by Griffies et al
Code adopted from MOM2.1
"""
epsln = 1e-20
iso_slopec = 1e-3
iso_dslope = 1e-3
K_iso_steep = 50.
tau = 0
dTdx = bh.zeros_like(K_11)
dSdx = bh.zeros_like(K_11)
dTdy = bh.zeros_like(K_11)
dSdy = bh.zeros_like(K_11)
dTdz = bh.zeros_like(K_11)
dSdz = bh.zeros_like(K_11)
"""
drho_dt and drho_ds at centers of T cells
"""
drdT = maskT * get_drhodT(salt[:, :, :, tau], temp[:, :, :, tau],
bh.abs(zt))
drdS = maskT * get_drhodS(salt[:, :, :, tau], temp[:, :, :, tau],
bh.abs(zt))
"""
gradients at top face of T cells
"""
dTdz[:, :, :-1] = maskW[:, :, :-1] * \
(temp[:, :, 1:, tau] - temp[:, :, :-1, tau]) / \
dzw[bh.newaxis, bh.newaxis, :-1]
dSdz[:, :, :-1] = maskW[:, :, :-1] * \
(salt[:, :, 1:, tau] - salt[:, :, :-1, tau]) / \
dzw[bh.newaxis, bh.newaxis, :-1]
"""
gradients at eastern face of T cells
"""
dTdx[:-1, :, :] = maskU[:-1, :, :] * (temp[1:, :, :, tau] - temp[:-1, :, :, tau]) \
/ (dxu[:-1, bh.newaxis, bh.newaxis] * cost[bh.newaxis, :, bh.newaxis])
dSdx[:-1, :, :] = maskU[:-1, :, :] * (salt[1:, :, :, tau] - salt[:-1, :, :, tau]) \
/ (dxu[:-1, bh.newaxis, bh.newaxis] * cost[bh.newaxis, :, bh.newaxis])
"""
gradients at northern face of T cells
"""
dTdy[:, :-1, :] = maskV[:, :-1, :] * \
(temp[:, 1:, :, tau] - temp[:, :-1, :, tau]) \
/ dyu[bh.newaxis, :-1, bh.newaxis]
dSdy[:, :-1, :] = maskV[:, :-1, :] * \
(salt[:, 1:, :, tau] - salt[:, :-1, :, tau]) \
/ dyu[bh.newaxis, :-1, bh.newaxis]
def dm_taper(sx):
"""
tapering function for isopycnal slopes
"""
return 0.5 * (1. + bh.tanh((-bh.abs(sx) + iso_slopec) / iso_dslope))
"""
Compute Ai_ez and K11 on center of east face of T cell.
"""
diffloc = bh.zeros_like(K_11)
diffloc[1:-2, 2:-2,
1:] = 0.25 * (K_iso[1:-2, 2:-2, 1:] + K_iso[1:-2, 2:-2, :-1] +
K_iso[2:-1, 2:-2, 1:] + K_iso[2:-1, 2:-2, :-1])
diffloc[1:-2, 2:-2, 0] = 0.5 * \
(K_iso[1:-2, 2:-2, 0] + K_iso[2:-1, 2:-2, 0])
sumz = bh.zeros_like(K_11)[1:-2, 2:-2]
for kr in range(2):
ki = 0 if kr == 1 else 1
for ip in range(2):
drodxe = drdT[1 + ip:-2 + ip, 2:-2, ki:] * dTdx[1:-2, 2:-2, ki:] \
+ drdS[1 + ip:-2 + ip, 2:-2, ki:] * dSdx[1:-2, 2:-2, ki:]
drodze = drdT[1 + ip:-2 + ip, 2:-2, ki:] * dTdz[1 + ip:-2 + ip, 2:-2, :-1 + kr or None] \
+ drdS[1 + ip:-2 + ip, 2:-2, ki:] * \
dSdz[1 + ip:-2 + ip, 2:-2, :-1 + kr or None]
sxe = -drodxe / (bh.minimum(0., drodze) - epsln)
taper = dm_taper(sxe)
sumz[:, :, ki:] += dzw[bh.newaxis, bh.newaxis, :-1 + kr or None] * maskU[1:-2, 2:-2, ki:] \
* bh.maximum(K_iso_steep, diffloc[1:-2, 2:-2, ki:] * taper)
Ai_ez[1:-2, 2:-2, ki:, ip, kr] = taper * \
sxe * maskU[1:-2, 2:-2, ki:]
K_11[1:-2, 2:-2, :] = sumz / (4. * dzt[bh.newaxis, bh.newaxis, :])
"""
Compute Ai_nz and K_22 on center of north face of T cell.
"""
diffloc[...] = 0
diffloc[2:-2, 1:-2,
1:] = 0.25 * (K_iso[2:-2, 1:-2, 1:] + K_iso[2:-2, 1:-2, :-1] +
K_iso[2:-2, 2:-1, 1:] + K_iso[2:-2, 2:-1, :-1])
diffloc[2:-2, 1:-2, 0] = 0.5 * \
(K_iso[2:-2, 1:-2, 0] + K_iso[2:-2, 2:-1, 0])
sumz = bh.zeros_like(K_11)[2:-2, 1:-2]
for kr in range(2):
ki = 0 if kr == 1 else 1
for jp in range(2):
drodyn = drdT[2:-2, 1 + jp:-2 + jp, ki:] * dTdy[2:-2, 1:-2, ki:] + \
drdS[2:-2, 1 + jp:-2 + jp, ki:] * dSdy[2:-2, 1:-2, ki:]
drodzn = drdT[2:-2, 1 + jp:-2 + jp, ki:] * dTdz[2:-2, 1 + jp:-2 + jp, :-1 + kr or None] \
+ drdS[2:-2, 1 + jp:-2 + jp, ki:] * \
dSdz[2:-2, 1 + jp:-2 + jp, :-1 + kr or None]
syn = -drodyn / (bh.minimum(0., drodzn) - epsln)
taper = dm_taper(syn)
sumz[:, :, ki:] += dzw[bh.newaxis, bh.newaxis, :-1 + kr or None] \
* maskV[2:-2, 1:-2, ki:] * bh.maximum(K_iso_steep, diffloc[2:-2, 1:-2, ki:] * taper)
Ai_nz[2:-2, 1:-2, ki:, jp, kr] = taper * \
syn * maskV[2:-2, 1:-2, ki:]
K_22[2:-2, 1:-2, :] = sumz / (4. * dzt[bh.newaxis, bh.newaxis, :])
"""
compute Ai_bx, Ai_by and K33 on top face of T cell.
"""
sumx = bh.zeros_like(K_11)[2:-2, 2:-2, :-1]
sumy = bh.zeros_like(K_11)[2:-2, 2:-2, :-1]
for kr in range(2):
drodzb = drdT[2:-2, 2:-2, kr:-1 + kr or None] * dTdz[2:-2, 2:-2, :-1] \
+ drdS[2:-2, 2:-2, kr:-1 + kr or None] * dSdz[2:-2, 2:-2, :-1]
# eastward slopes at the top of T cells
for ip in range(2):
drodxb = drdT[2:-2, 2:-2, kr:-1 + kr or None] * dTdx[1 + ip:-3 + ip, 2:-2, kr:-1 + kr or None] \
+ drdS[2:-2, 2:-2, kr:-1 + kr or None] * \
dSdx[1 + ip:-3 + ip, 2:-2, kr:-1 + kr or None]
sxb = -drodxb / (bh.minimum(0., drodzb) - epsln)
taper = dm_taper(sxb)
sumx += dxu[1 + ip:-3 + ip, bh.newaxis, bh.newaxis] * \
K_iso[2:-2, 2:-2, :-1] * taper * \
sxb**2 * maskW[2:-2, 2:-2, :-1]
Ai_bx[2:-2, 2:-2, :-1, ip, kr] = taper * \
sxb * maskW[2:-2, 2:-2, :-1]
# northward slopes at the top of T cells
for jp in range(2):
facty = cosu[1 + jp:-3 + jp] * dyu[1 + jp:-3 + jp]
drodyb = drdT[2:-2, 2:-2, kr:-1 + kr or None] * dTdy[2:-2, 1 + jp:-3 + jp, kr:-1 + kr or None] \
+ drdS[2:-2, 2:-2, kr:-1 + kr or None] * \
dSdy[2:-2, 1 + jp:-3 + jp, kr:-1 + kr or None]
syb = -drodyb / (bh.minimum(0., drodzb) - epsln)
taper = dm_taper(syb)
sumy += facty[bh.newaxis, :, bh.newaxis] * K_iso[2:-2, 2:-2, :-1] \
* taper * syb**2 * maskW[2:-2, 2:-2, :-1]
Ai_by[2:-2, 2:-2, :-1, jp, kr] = taper * \
syb * maskW[2:-2, 2:-2, :-1]
K_33[2:-2, 2:-2, :-1] = sumx / (4 * dxt[2:-2, bh.newaxis, bh.newaxis]) + \
sumy / (4 * dyt[bh.newaxis, 2:-2, bh.newaxis]
* cost[bh.newaxis, 2:-2, bh.newaxis])
K_33[2:-2, 2:-2, -1] = 0.
