def cik_to_v(cik, xyc=None, inverse=False):
"""
Calculate v-format ellipse descriptor from 2x2 'covariance matrix'^-1 cik
Args:
:cik:
| 'Nx2x2' (covariance matrix)^-1
:inverse:
| If True: input is inverse of cik.
Returns:
:v:
| (Nx5) np.ndarray
| ellipse parameters [Rmax,Rmin,xc,yc,theta]
Notes:
| cik is not actually the inverse covariance matrix,
| only for a Gaussian or normal distribution!
"""
if cik.ndim < 3:
cik = cik[None, ...]
if inverse == True:
for i in range(cik.shape[0]):
cik[i, :, :] = np.linalg.inv(cik[i, :, :])
g11 = cik[:, 0, 0]
g22 = cik[:, 1, 1]
g12 = cik[:, 0, 1]
theta = 0.5 * np.arctan2(2 * g12, (g11 - g22)) + (np.pi / 2) * (g12 < 0)
#theta = theta2 + (np.pi/2)*(g12<0)
#theta2 = theta
cottheta = np.cos(theta) / np.sin(theta) #np.cot(theta)
cottheta[np.isinf(cottheta)] = 0
a = 1 / np.sqrt((g22 + g12 * cottheta))
b = 1 / np.sqrt((g11 - g12 * cottheta))
# ensure largest ellipse axis is first (correct angle):
c = b > a
a[c], b[c], theta[c] = b[c], a[c], theta[c] + np.pi / 2
v = np.vstack((a, b, np.zeros(a.shape), np.zeros(a.shape), theta)).T
# add center coordinates:
if xyc is not None:
v[:, 2:4] = xyc
return v
def cik_to_v(cik, xyc=None, inverse=False):
"""
Calculate v-format ellipse descriptor from 2x2 'covariance matrix'^-1 cik
Args:
:cik:
'2x2xN' (covariance matrix)^-1
Returns:
:v:
| (Nx5) np.ndarray
| ellipse parameters [Rmax,Rmin,xc,yc,theta]
Notes:
| cik is not actually the inverse covariance matrix,
| only for a Gaussian or normal distribution!
"""
if inverse == True:
for i in np.arange(cik.shape[0]):
cik[i, :, :] = np.linalg.inv(cik[i, :, :])
g11 = cik[:, 0, 0]
g22 = cik[:, 1, 1]
g12 = cik[:, 0, 1]
theta2 = 1 / 2 * np.arctan2(2 * g12, (g11 - g22))
theta = theta2 + (np.pi / 2) * (g12 < 0)
theta2 = theta
cottheta = np.cos(theta) / np.sin(theta) #np.cot(theta)
cottheta[np.isinf(cottheta)] = 0
a = 1 / np.sqrt((g22 + g12 * cottheta))
b = 1 / np.sqrt((g11 - g12 * cottheta))
v = np.vstack((a, b, np.zeros(a.shape), np.zeros(a.shape), theta)).T
# add center coordinates:
if xyc is not None:
v[:, 2:4] = xyc
return v
def plot_chromaticity_diagram_colors(diagram_samples = 256, diagram_opacity = 1.0, diagram_lightness = 0.25,\
cieobs = _CIEOBS, cspace = 'Yxy', cspace_pars = {},\
show = True, axh = None,\
show_grid = True, label_fontname = 'Times New Roman', label_fontsize = 12,\
**kwargs):
"""
Plot the chromaticity diagram colors.
Args:
:diagram_samples:
| 256, optional
| Sampling resolution of color space.
:diagram_opacity:
| 1.0, optional
| Sets opacity of chromaticity diagram
:diagram_lightness:
| 0.25, optional
| Sets lightness of chromaticity diagram
:axh:
| None or axes handle, optional
| Determines axes to plot data in.
| None: make new figure.
:show:
| True or False, optional
| Invoke matplotlib.pyplot.show() right after plotting
:cieobs:
| luxpy._CIEOBS or str, optional
| Determines CMF set to calculate spectrum locus or other.
:cspace:
| luxpy._CSPACE or str, optional
| Determines color space / chromaticity diagram to plot data in.
| Note that data is expected to be in specified :cspace:
:cspace_pars:
| {} or dict, optional
| Dict with parameters required by color space specified in :cspace:
| (for use with luxpy.colortf())
:show_grid:
| True, optional
| Show grid (True) or not (False)
:label_fontname:
| 'Times New Roman', optional
| Sets font type of axis labels.
:label_fontsize:
| 12, optional
| Sets font size of axis labels.
:kwargs:
| additional keyword arguments for use with matplotlib.pyplot.
Returns:
"""
offset = _EPS
ii, jj = np.meshgrid(np.linspace(offset, 1 + offset, diagram_samples), np.linspace(1+offset, offset, diagram_samples))
ij = np.dstack((ii, jj))
SL = _CMF[cieobs]['bar'][1:4].T
SL = np.vstack((SL,SL[0]))
SL = 100.0*SL/SL[:,1,None]
SL = colortf(SL, tf = cspace, tfa0 = cspace_pars)
Y,x,y = asplit(SL)
SL = np.vstack((x,y)).T
ij2D = ij.reshape((diagram_samples**2,2))
ij2D = np.hstack((diagram_lightness*100*np.ones((ij2D.shape[0],1)), ij2D))
xyz = colortf(ij2D, tf = cspace + '>xyz', tfa0 = cspace_pars)
xyz[xyz < 0] = 0
xyz[np.isinf(xyz.sum(axis=1)),:] = np.nan
xyz[np.isnan(xyz.sum(axis=1)),:] = offset
srgb = xyz_to_srgb(xyz)
srgb = srgb/srgb.max()
srgb = srgb.reshape((diagram_samples,diagram_samples,3))
if show == True:
if axh is None:
fig = plt.figure()
axh = fig.add_subplot(111)
polygon = Polygon(SL, facecolor='none', edgecolor='none')
axh.add_patch(polygon)
image = axh.imshow(
srgb,
interpolation='bilinear',
extent = (0.0, 1, -0.05, 1),
clip_path=None,
alpha=diagram_opacity)
image.set_clip_path(polygon)
plt.plot(x,y, color = 'darkgray')
if cspace == 'Yxy':
plt.xlim([0,1])
plt.ylim([0,1])
elif cspace == 'Yuv':
plt.xlim([0,0.6])
plt.ylim([0,0.6])
if (cspace is not None):
xlabel = _CSPACE_AXES[cspace][1]
ylabel = _CSPACE_AXES[cspace][2]
if (label_fontname is not None) & (label_fontsize is not None):
plt.xlabel(xlabel, fontname = label_fontname, fontsize = label_fontsize)
plt.ylabel(ylabel, fontname = label_fontname, fontsize = label_fontsize)
if show_grid == True:
plt.grid()
#plt.show()
return axh
else:
return None