def findBoundary(data, points): """ use convex hull algorithm to find the boundary of the image and make the pixels that are used to construct the polygon in convex hull. :param data: 2 d array of image :param points: corresponding coordinates of the pixels that are black (0) :return: modified 2-d array """ hull = ConvexHull(points) plt.plot(points[:, 0], points[:, 1], 'o') for simplex in hull.simplices: plt.plot(points[simplex, 0], points[simplex, 1], 'k-') p1 = points[simplex] p2 = points[simplex] data[p1[0][0]][p1[0][1]] = 1 data[p1[1][0]][p1[1][1]] = 1 data[p2[0][0]][p2[0][1]] = 1 data[p2[1][0]][p2[1][1]] = 1 ### display the convexHull result # toimage(data).show() # plt.show() hull.close() return data
def getDelaunayEdges(points):
"""Return the list of edges between points without fake neighbors"""
delau = Delaunay(points)
hull = ConvexHull(points)
hull = path.Path(points[hull.vertices])
hull = expandPath(hull,1.2)
allEdges = list()
badEdges = list()
for simplex in [x.tolist() for x in delau.simplices]:
for edge in [[x, simplex[simplex.index(x)-1]] for x in simplex]:
addCoupleToList(allEdges, edge)
circumCircleCenter = getCircumCircleCenter(points[simplex])
if(hull.contains_point(circumCircleCenter) == False):
simplexPoints = points[simplex]
edge0 = dist(simplexPoints[0], simplexPoints[1])
edge1 = dist(simplexPoints[1], simplexPoints[2])
edge2 = dist(simplexPoints[2], simplexPoints[0])
largestEdge = max(edge0, edge1, edge2)
if(edge0 == largestEdge):
addCoupleToList(badEdges, [simplex[0], simplex[1]])
elif(edge1 == largestEdge):
addCoupleToList(badEdges, [simplex[1], simplex[2]])
elif(edge2 == largestEdge):
addCoupleToList(badEdges, [simplex[2], simplex[0]])
return [x for x in allEdges if checkCoupleInList(badEdges, x) == False]
def compute(self):
"""ABC API"""
self.id = "CH({})".format(self._qhull_options)
scipy_ConvexHull.__init__(self,
self._points,
self._incremental,
self._qhull_options)
def __init__(self, points):
"""A customized constructor.
"""
ConvexHull.__init__(self, points)
indices = self.vertices
points = self.points
# Customize
self.anchors = points[indices]
def r( self, c, gpos, mpos=0.0):
"""
Calculates the virtual distances between grid point locations and
microphone locations or the origin. These virtual distances correspond
to travel times of the sound along a ray that is traced through the
medium.
Parameters
----------
c : float
The speed of sound to use for the calculation.
gpos : array of floats of shape (3, N)
The locations of points in the beamforming map grid in 3D cartesian
co-ordinates.
mpos : array of floats of shape (3, M), optional
The locations of microphones in 3D cartesian co-ordinates. If not
given, then only one microphone at the origin (0, 0, 0) is
considered.
Returns
-------
array of floats
The distances in a twodimensional (N, M) array of floats. If M==1,
then only a onedimensional array is returned.
"""
if isscalar(mpos):
mpos = array((0, 0, 0), dtype = float32)[:, newaxis]
# the DE system
def f1(t, y, v):
x = y[0:3]
s = y[3:6]
vv, dv = v(x)
sa = sqrt(s[0]*s[0]+s[1]*s[1]+s[2]*s[2])
x = empty(6)
x[0:3] = c*s/sa - vv # time reversal
x[3:6] = dot(s, -dv.T) # time reversal
return x
# integration along a single ray
def fr(x0, n0, rmax, dt, v, xyz, t):
s0 = n0 / (c+dot(v(x0)[0], n0))
y0 = hstack((x0, s0))
oo = ode(f1)
oo.set_f_params(v)
oo.set_integrator('vode',
rtol=1e-4, # accuracy !
max_step=1e-4*rmax) # for thin shear layer
oo.set_initial_value(y0, 0)
while oo.successful():
xyz.append(oo.y[0:3])
t.append(oo.t)
if norm(oo.y[0:3]-x0)>rmax:
break
oo.integrate(oo.t+dt)
gs2 = gpos.shape[-1]
gt = empty((gs2, mpos.shape[-1]))
vv = self.ff.v
NN = int(sqrt(self.N))
for micnum, x0 in enumerate(mpos.T):
xe = gpos.mean(1) # center of grid
r = x0[:, newaxis]-gpos
rmax = sqrt((r*r).sum(0).max()) # maximum distance
nv = spiral_sphere(self.N, self.Om, b=xe-x0)
rstep = rmax/sqrt(self.N)
rmax += rstep
tstep = rstep/c
xyz = []
t = []
lastind = 0
for i, n0 in enumerate(nv.T):
fr(x0, n0, rmax, tstep, vv, xyz, t)
if i and i % NN == 0:
if not lastind:
dd = ConvexHull(vstack((gpos.T, xyz)), incremental=True)
else:
dd.add_points(xyz[lastind:], restart=True)
lastind = len(xyz)
# ConvexHull includes grid if no grid points on hull
if dd.simplices.min()>=gs2:
break
xyz = array(xyz)
t = array(t)
li = LinearNDInterpolator(xyz, t)
gt[:, micnum] = li(gpos.T)
if gt.shape[1] == 1:
gt = gt[:, 0]
return c*gt #return distance along ray
def per_drone_wind_multipliers(self, layer_wind_multiplier=0.9):
drone_position_matrix = np.asarray([[d.pos[0], d.pos[1]]
for d in self.drones])
wind_vec_orth = np.asarray([-self.wind_dev[1], self.wind_dev[0]])
no_drones_covered = 0
no_exposed_current_layer = 0
wind_fact = 1
drone_position_matrix = np.append(drone_position_matrix,
np.zeros(self.N).reshape(self.N, 1),
axis=1)
drone_position_matrix = np.append(drone_position_matrix,
np.arange(self.N).reshape(self.N, 1),
axis=1)
#print (self.wind_dev)
while (self.N - no_drones_covered) > 2:
reached_edges = [False, False]
exposed_hull = []
no_exposed_current_layer = 0
hull = ConvexHull(drone_position_matrix[:self.N -
no_drones_covered, 0:2])
projections = np.matmul(drone_position_matrix[hull.vertices, 0:2],
self.wind_dev[:2]) / np.linalg.norm(
self.wind_dev[:2])
projections_orth = np.matmul(
drone_position_matrix[hull.vertices, 0:2],
wind_vec_orth) / np.linalg.norm(wind_vec_orth)
sorted_proj_indexes = np.argsort(projections)
sorted_proj_orth_indexes = np.argsort(projections_orth)
for i in sorted_proj_indexes:
drone_position_matrix[hull.vertices[i], 2] = wind_fact
exposed_hull.append(i)
no_exposed_current_layer += 1
if hull.vertices[i] == hull.vertices[
sorted_proj_orth_indexes[0]]:
reached_edges[0] = True
elif hull.vertices[i] == hull.vertices[
sorted_proj_orth_indexes[-1]]:
reached_edges[1] = True
if reached_edges[0] and reached_edges[1]:
break
sorted_indexes = np.sort(hull.vertices[exposed_hull])
for i in range(1, no_exposed_current_layer + 1):
row = sorted_indexes[-i]
drone_position_matrix[[self.N - no_drones_covered - i,
row]] = drone_position_matrix[[
row, self.N - no_drones_covered - i
]]
no_drones_covered += no_exposed_current_layer
wind_fact = wind_fact * layer_wind_multiplier
# All that's left is to check if we have one or two points left and fill that with the next wind_fact
if (self.N - no_drones_covered) >= 1:
drone_position_matrix[0, 2] = wind_fact
if (self.N - no_drones_covered) == 2:
drone_position_matrix[1, 2] = wind_fact
return drone_position_matrix[np.argsort(drone_position_matrix[:,
3])][:,
2]
def nn_point(xp, yp, variable, grid_loc, tri, neighbors, triangle_info):
r"""Generate a natural neighbor interpolation of the observations to the given point.
This uses the Liang and Hale approach [Liang2010]_. The interpolation will fail if
the grid point has no natural neighbors.
Parameters
----------
xp: (N, ) ndarray
x-coordinates of observations
yp: (N, ) ndarray
y-coordinates of observations
variable: (N, ) ndarray
observation values associated with (xp, yp) pairs.
IE, variable[i] is a unique observation at (xp[i], yp[i])
grid_loc: (float, float)
Coordinates of the grid point at which to calculate the
interpolation.
tri: object
Delaunay triangulation of the observations.
neighbors: (N, ) ndarray
Simplex codes of the grid point's natural neighbors. The codes
will correspond to codes in the triangulation.
triangle_info: dictionary
Pre-calculated triangle attributes for quick look ups. Requires
items 'cc' (circumcenters) and 'r' (radii) to be associated with
each simplex code key from the delaunay triangulation.
Returns
-------
value: float
Interpolated value for the grid location
"""
edges = triangles.find_local_boundary(tri, neighbors)
edge_vertices = [segment[0] for segment in polygons.order_edges(edges)]
num_vertices = len(edge_vertices)
p1 = edge_vertices[0]
p2 = edge_vertices[1]
polygon = list()
c1 = triangles.circumcenter(grid_loc, tri.points[p1], tri.points[p2])
polygon.append(c1)
area_list = []
total_area = 0.0
for i in range(num_vertices):
p3 = edge_vertices[(i + 2) % num_vertices]
try:
c2 = triangles.circumcenter(grid_loc, tri.points[p3],
tri.points[p2])
polygon.append(c2)
for check_tri in neighbors:
if p2 in tri.simplices[check_tri]:
polygon.append(triangle_info[check_tri]['cc'])
pts = [polygon[i] for i in ConvexHull(polygon).vertices]
value = variable[(tri.points[p2][0] == xp)
& (tri.points[p2][1] == yp)]
cur_area = polygons.area(pts)
total_area += cur_area
area_list.append(cur_area * value[0])
except (ZeroDivisionError, qhull.QhullError) as e:
message = ('Error during processing of a grid. '
'Interpolation will continue but be mindful '
'of errors in output. ') + str(e)
log.warning(message)
return np.nan
polygon = list()
polygon.append(c2)
p2 = p3
return sum(x / total_area for x in area_list)
def _get_hull_in_nph_nphi_space(self, entries):
"""
Generates convex hull of pourbaix diagram entries in composition,
npH, and nphi space. This enables filtering of multi-entries
such that only compositionally stable combinations of entries
are included.
Args:
entries ([PourbaixEntry]): list of PourbaixEntries to construct
the convex hull
Returns: list of entries and stable facets corresponding to that
list of entries
"""
ion_entries = [entry for entry in entries if entry.phase_type == "Ion"]
solid_entries = [
entry for entry in entries if entry.phase_type == "Solid"
]
# Pre-filter solids based on min at each composition
logger.debug("Pre-filtering solids by min energy at each composition")
sorted_entries = sorted(
solid_entries,
key=lambda x:
(x.composition.reduced_composition, x.entry.energy_per_atom))
grouped_by_composition = itertools.groupby(
sorted_entries, key=lambda x: x.composition.reduced_composition)
min_entries = [
list(grouped_entries)[0]
for comp, grouped_entries in grouped_by_composition
]
min_entries += ion_entries
logger.debug("Constructing nph-nphi-composition points for qhull")
vecs = self._convert_entries_to_points(min_entries)
maxes = np.max(vecs[:, :3], axis=0)
extra_point = np.concatenate(
[maxes, np.ones(self.dim) / self.dim], axis=0)
# Add padding for extra point
pad = 1000
extra_point[2] += pad
points = np.concatenate([vecs, np.array([extra_point])], axis=0)
logger.debug("Constructing convex hull in nph-nphi-composition space")
hull = ConvexHull(points, qhull_options="QJ i")
# Create facets and remove top
facets = [
facet for facet in hull.simplices if not len(points) - 1 in facet
]
if self.dim > 1:
logger.debug("Filtering facets by pourbaix composition")
valid_facets = []
for facet in facets:
comps = vecs[facet][:, 3:]
full_comps = np.concatenate(
[comps, 1 - np.sum(comps, axis=1).reshape(len(comps), 1)],
axis=1)
# Ensure an compositional interior point exists in the simplex
if np.linalg.matrix_rank(full_comps) > self.dim:
valid_facets.append(facet)
else:
valid_facets = facets
return min_entries, valid_facets
def encircle(x, y, ax, **kw):
p = np.c_[x, y]
hull = ConvexHull(p)
poly = Polygon(p[hull.vertices, :], **kw)
ax.add_patch(poly)
def reader(cube, inPath):
image = cv2.imread(inPath, -1)
filtered = filterImage(image)
# Detect all contours
contours, hierarchy = cv2.findContours(filtered, cv2.RETR_TREE,
cv2.CHAIN_APPROX_NONE)
facelets = getFacelets(contours)
# Cluster facelets based on angle
clusters = clusterFacelets(facelets)
if clusters == None:
return 'E'
# Filter the 3 clusters to 9 facelets each
filterClusters(clusters)
# Label colors
for i, cluster in enumerate(clusters):
for j, facelet in enumerate(cluster):
hull = cv2.convexHull(facelet[0])
mask = np.zeros(image.shape, np.uint8)
cv2.fillConvexPoly(mask, hull, (255, 255, 255))
masked = cv2.bitwise_and(image, mask)
color = identifyColor(masked)
clusters[i][j].append(color)
# Find center pieces
centers = []
for cluster in clusters:
# Find CM
sum = [0, 0]
for facelet in cluster:
sum[0] += facelet[3][0]
sum[1] += facelet[3][1]
mid = [sum[0] / 9, sum[1] / 9]
# Find closest to CM. This is center piece
c = cluster[0]
minD = 1000000
for facelet in cluster:
dX = facelet[3][0] - mid[0]
dY = facelet[3][1] - mid[1]
d = dX * dX + dY * dY
if d < minD:
minD = d
c = facelet
centers.append(c)
# Identify each face. White/yellow is x, and y and z are cw from there
hull = ConvexHull([center[3] for center in centers])
centers = [centers[i] for i in hull.vertices]
clusters = [clusters[i] for i in hull.vertices]
whiteYellowIndex = 0
for i, center in enumerate(centers):
if center[4] == 'w' or center[4] == 'y':
whiteYellowIndex = i
break
# Roll array so that first is x, second is y, third is z
if whiteYellowIndex == 1:
centers = [centers[i] for i in [1, 2, 0]]
clusters = [clusters[i] for i in [1, 2, 0]]
if whiteYellowIndex == 2:
centers = [centers[i] for i in [2, 0, 1]]
clusters = [clusters[i] for i in [2, 0, 1]]
# For AB_C, clusters on the C face from A and B face perp bisector
# In order: XY_X XZ_X XY_Y YZ_Y XZ_Z YZ_Z
facePositions = [
clusterWithBisector(centers[0][3], centers[1][3], clusters[0]),
clusterWithBisector(centers[0][3], centers[2][3], clusters[0]),
clusterWithBisector(centers[0][3], centers[1][3], clusters[1]),
clusterWithBisector(centers[1][3], centers[2][3], clusters[1]),
clusterWithBisector(centers[0][3], centers[2][3], clusters[2]),
clusterWithBisector(centers[1][3], centers[2][3], clusters[2])
]
# Save colors in cube
orientation = centers[0][4] + centers[1][4]
saveColors(cube, facePositions, clusters, orientation)
def triangulateSphereIdx(pts):
hull = ConvexHull(pts)
return hull.simplices
import matplotlib.pyplot as plt from scipy.spatial import ConvexHull, convex_hull_plot_2d # The convex hull of a random set of points: points = np.random.rand(30, 2) hull = ConvexHull(points) # Plot it: _ = convex_hull_plot_2d(hull) plt.show()
def _start_pts_noisy_filter(self, plotAll=False):
startPoints = self._trajDataFeatures[["trajIndex", "startX", "startY"]]
startCoordinates = startPoints[["startX", "startY"]].values
corePointFlag = []
# Fit Nearest Neighbors of start points dataset.
neigh = NearestNeighbors(n_neighbors=self._startMinSamples, n_jobs=1)
neigh.fit(startCoordinates)
totalNums = len(startCoordinates)
# Confirm core point flag and assign cluster labels for each data point.
for ind, pts in enumerate(startCoordinates):
print("Total is {}, now is {}.".format(totalNums, ind + 1))
pts = pts.reshape(1, -1)
distance, indices = neigh.kneighbors(pts)
if distance[:, -1] <= self._startEps:
corePointFlag.append(1)
else:
corePointFlag.append(0)
startPoints["corePointFlag"] = np.array(corePointFlag)
startPoints["labels"] = self.__assign_cluster_label(
startCoordinates,
eps=self._startEps,
minSamples=self._startMinSamples)
self._trajDataFeatures["startZone"] = startPoints["labels"].values
# Calculate core density for each cluster.
self._start = pd.DataFrame(None,
columns=[
"clusterId", "clusterPointNums",
"convexHullArea", "density", "signal"
])
uniqueLabels = list(
startPoints[startPoints["labels"] != -1]["labels"].unique())
clusterId = []
clusterPointNums = []
clusterCorePointNums = []
covexHullArea = []
density = []
for i in uniqueLabels:
clusterId.append(i)
clusterTmp = startPoints[startPoints["labels"] == i]
clusterPointNums.append(len(clusterTmp))
clusterCorePointNums.append(
len(clusterTmp[clusterTmp["corePointFlag"] == 1]))
clusterTmp = clusterTmp[clusterTmp["corePointFlag"] == 1]
clusterTmp.drop(["corePointFlag", "labels", "trajIndex"],
axis=1,
inplace=True)
corePtsTmp = clusterTmp.values
hull = ConvexHull(corePtsTmp)
covexHullArea.append(hull.area)
density.append(clusterCorePointNums[-1] / hull.area)
self._start = {
"clusterId": clusterId,
"clusterCorePointNums": clusterCorePointNums,
"clusterPointNums": clusterPointNums,
"convexHullArea": covexHullArea,
"density": density
}
self._start = pd.DataFrame(self._start)
self._startAverageDensity = self._startAlpha * self._start[
"density"].mean()
self._start["signal"] = self._start[
"density"].values > self._startAverageDensity
noisyCluster = self._start["clusterId"][
self._start["signal"] != True].values
# Step 1: remove all non core points
self._trajDataFeatures["startBrokenFlag"] = startPoints[
"corePointFlag"] == False
# Step 2: remove all points which are noisy points for DBSCAN
self._trajDataFeatures["startBrokenFlag"] = self._trajDataFeatures[
"startBrokenFlag"] | (startPoints["labels"] == -1)
for ind in noisyCluster:
self._trajDataFeatures["startBrokenFlag"] = self._trajDataFeatures[
"startBrokenFlag"] | (startPoints["labels"] == ind)
# Plot and save all results
if plotAll == True:
convexHullPts = startPoints[(startPoints["corePointFlag"] == 1)
& (startPoints["labels"] != -1)][[
"startX", "startY"
]].values
uniqueLabels = list(
startPoints[startPoints["labels"] != -1]["labels"].unique())
labels = startPoints[(startPoints["corePointFlag"] == 1) & (
startPoints["labels"] != -1)]["labels"].values
plt.figure()
plt.imshow(background)
density = []
for ind, item in enumerate(uniqueLabels):
index = labels == item
tmp = convexHullPts[index]
hull = ConvexHull(tmp)
for simplex in hull.simplices:
plt.plot(tmp[simplex, 0],
tmp[simplex, 1],
'k-',
linewidth=0.9)
plt.plot(convexHullPts[index, 0],
convexHullPts[index, 1],
'+',
markersize=0.3,
color="red") #RGB[ind])
pos = convexHullPts[index][2] - 40
d = len(convexHullPts[index, 0]) / hull.area
d = round(d, 3)
density.append(d)
#plt.text(pos[0], pos[1], str(ind) + "_" + str(density[ind]), fontsize=10, color='red') #str(density)
cond = [round(sum(density) * self._startAlpha / (ind + 1))]
plt.title("Entry core points clusters")
plt.savefig("..//Plots//EntryCorePointsClusteringResults.pdf",
dpi=700,
bbox_inches='tight')
plt.figure()
plt.plot(self._start["clusterId"].astype(int).values,
self._start["density"].values, 'k-s')
x = np.linspace(-1, 7, 2000)
y = np.array(cond * 2000, dtype='float64')
plt.plot(x, y, 'b--')
plt.title("Entry points average density")
plt.legend(["density", "threshold"])
plt.xlabel("clusterID")
plt.ylabel("Core area")
plt.xlim(self._start["clusterId"].min() - 0.1,
self._start["clusterId"].max() + 0.1)
plt.ylim(self._start["density"].min() - 0.5,
self._start["density"].max() + 0.5)
plt.savefig("..//Plots//EntryCorePointsDensityPlots.pdf",
dpi=700,
bbox_inches='tight')
plt.close("all")
plt.figure()
plt.imshow(background)
normalPts = self._trajDataFeatures[
self._trajDataFeatures["startBrokenFlag"] == False][[
"startX", "startY"
]].values
plt.plot(normalPts[:, 0],
normalPts[:, 1],
'+',
markersize=0.3,
color="red")
plt.title("Start clusters after filtering")
plt.savefig("..//Plots//EntryCorePointsAfterFiltering.pdf",
dpi=700,
bbox_inches='tight')
return self._start
def scipy_convexify_polyhedron(hrep):
points = np.array(cdd.Polyhedron(hrep).get_generators())[:, 1:]
ch = ConvexHull(points, qhull_options='QbB')
return ch.points
num_corners = 100 dst = cv2.goodFeaturesToTrack(gray, num_corners, 0.01, 10) dst = np.int0(dst) blue = img[:,:,0] img[:,:,0] = img[:,:,2] img[:,:,2] = blue # Uncomment to see the corners # for corner in dst: # x,y = corner.ravel() # cv2.circle(img,(x,y), 10, [0,255,0], -1) corners = np.array([corner.ravel() for corner in dst]) hull = ConvexHull(corners) # for simplex in hull.simplices: # first_corner = tuple(corners[simplex, 0].tolist()) # second_corner = tuple(corners[simplex, 1].tolist()) # if first_corner in points_dict: # points_dict[first_corner].append(second_corner) # else: # points_dict[first_corner] = [second_corner] # # if second_corner in points_dict: # points_dict[second_corner].append(first_corner) # else: # points_dict[second_corner] = [first_corner] # # plt.plot(first_corner, second_corner, 'k-', c='r') # plt.show()
def generate_guess(vdc, pr_vec, show_plots=False):
"""
Given a single unfolded loop and centroid return the intial guess for the fitting.
We generate most of the guesses by looking at the loop centroid and looking
at the nearest intersection points with the loop, which is a polygon.
Parameters
-----------
vdc : 1D numpy array
DC offsets
pr_vec : 1D numpy array
Piezoresponse or unfolded loop
show_plots : Boolean (Optional. Default = False)
Whether or not the plot the convex hull, centroid, intersection points
Returns
-----------------
init_guess_coef_vec : 1D Numpy array
Fit guess coefficient vector
"""
points = np.transpose(np.array([np.squeeze(vdc), pr_vec])) # [points,axis]
geom_centroid, geom_area = calculate_loop_centroid(points[:, 0], points[:,
1])
hull = ConvexHull(points)
"""
Now we need to find the intersection points on the N,S,E,W
the simplex of the complex hull is essentially a set of line equations.
We need to find the two lines (top and bottom) or (left and right) that
interect with the vertical / horizontal lines passing through the geometric centroid
"""
def find_intersection(A, B, C, D):
"""
Finds the coordinates where two line segments intersect
Parameters
------------
A, B, C, D : Tuple or 1D list or 1D numpy array
(x,y) coordinates of the points that define the two line segments AB and CD
Returns
----------
obj : None or tuple
None if not intersecting. (x,y) coordinates of intersection
"""
def ccw(A, B, C):
"""Credit - StackOverflow"""
return (C[1] - A[1]) * (B[0] - A[0]) > (B[1] - A[1]) * (C[0] -
A[0])
def line(p1, p2):
"""Credit - StackOverflow"""
A = (p1[1] - p2[1])
B = (p2[0] - p1[0])
C = (p1[0] * p2[1] - p2[0] * p1[1])
return A, B, -C
def intersection(L1, L2):
"""
Finds the intersection of two lines (NOT line segments).
Credit - StackOverflow
"""
D = L1[0] * L2[1] - L1[1] * L2[0]
Dx = L1[2] * L2[1] - L1[1] * L2[2]
Dy = L1[0] * L2[2] - L1[2] * L2[0]
if D != 0:
x = Dx / D
y = Dy / D
return x, y
else:
return None
if ((ccw(A, C, D) is not ccw(B, C, D)) and
(ccw(A, B, C) is not ccw(A, B, D))) is False:
return None
else:
return intersection(line(A, B), line(C, D))
# start and end coordinates of each line segment defining the convex hull
outline_1 = np.zeros((hull.simplices.shape[0], 2), dtype=np.float)
outline_2 = np.zeros((hull.simplices.shape[0], 2), dtype=np.float)
for index, pair in enumerate(hull.simplices):
outline_1[index, :] = points[pair[0]]
outline_2[index, :] = points[pair[1]]
"""Find the coordinates of the points where the vertical line through the
centroid intersects with the convex hull"""
y_intersections = []
for pair in range(outline_1.shape[0]):
x_pt = find_intersection(outline_1[pair], outline_2[pair],
[geom_centroid[0], hull.min_bound[1]],
[geom_centroid[0], hull.max_bound[1]])
if type(x_pt) != type(None):
y_intersections.append(x_pt)
'''
Find the coordinates of the points where the horizontal line through the
centroid intersects with the convex hull
'''
x_intersections = []
for pair in range(outline_1.shape[0]):
x_pt = find_intersection(outline_1[pair], outline_2[pair],
[hull.min_bound[0], geom_centroid[1]],
[hull.max_bound[0], geom_centroid[1]])
if type(x_pt) != type(None):
x_intersections.append(x_pt)
'''
Default values if not intersections can be found.
'''
if len(y_intersections) == 0:
min_y_intercept = min(pr_vec)
max_y_intercept = max(pr_vec)
else:
min_y_intercept = min(y_intersections[0][1], y_intersections[1][1])
max_y_intercept = max(y_intersections[0][1], y_intersections[1][1])
if len(x_intersections) == 0:
min_x_intercept = min(vdc) / 2.0
max_x_intercept = max(vdc) / 2.0
else:
min_x_intercept = min(x_intersections[0][0], x_intersections[1][0])
max_x_intercept = max(x_intersections[0][0], x_intersections[1][0])
# Only the first four parameters use the information from the intercepts
# a3, a4 are swapped in Stephen's figure. That was causing the branches to swap during fitting
# the a3, a4 are fixed now below:
init_guess_coef_vec = np.zeros(shape=9)
init_guess_coef_vec[0] = min_y_intercept
init_guess_coef_vec[1] = max_y_intercept - min_y_intercept
init_guess_coef_vec[2] = min_x_intercept
init_guess_coef_vec[3] = max_x_intercept
init_guess_coef_vec[4] = 0
init_guess_coef_vec[5] = 2 # 0.5
init_guess_coef_vec[6] = 2 # 0.2
init_guess_coef_vec[7] = 2 # 1.0
init_guess_coef_vec[8] = 2 # 0.2
if show_plots:
fig, ax = plt.subplots()
ax.plot(points[:, 0], points[:, 1], 'o')
ax.plot(geom_centroid[0], geom_centroid[1], 'r*')
ax.plot([geom_centroid[0], geom_centroid[0]],
[hull.max_bound[1], hull.min_bound[1]], 'g')
ax.plot([hull.min_bound[0], hull.max_bound[0]],
[geom_centroid[1], geom_centroid[1]], 'g')
for simplex in hull.simplices:
ax.plot(points[simplex, 0], points[simplex, 1], 'k')
ax.plot(x_intersections[0][0], x_intersections[0][1], 'r*')
ax.plot(x_intersections[1][0], x_intersections[1][1], 'r*')
ax.plot(y_intersections[0][0], y_intersections[0][1], 'r*')
ax.plot(y_intersections[1][0], y_intersections[1][1], 'r*')
ax.plot(vdc, loop_fit_function(vdc, init_guess_coef_vec))
return init_guess_coef_vec
# ################################################ #
# ##### MAIN ##### #
# ################################################ #
if __name__ == '__main__':
n = int(input())
m = int(input())
p = []
for i in range(n):
x, y = map(int, input().split())
p.append((x, y))
p = np.array(p)
p = p[ConvexHull(p).vertices]
print("Pol1:", *p, file=sys.stderr)
q = []
for i in range(m):
x, y = map(int, input().split())
q.append((x, y))
q = np.array(q)
q = q[ConvexHull(q).vertices]
print("Pol2:", *q, file=sys.stderr)
inter = convexIntersect(Polygon([Point(x, y) for (x, y) in p]),
Polygon([Point(x, y) for (x, y) in q]))
if inter:
inter.make_convex()
image_file = cbook.get_sample_data(f_name[0])
image = plt.imread(image_file)
ax1.imshow(image)
# edges = cv2.Canny(image,50,400)
im2, contours, hierarchy = cv2.findContours(im_bw, cv2.RETR_TREE,
cv2.CHAIN_APPROX_NONE)
for ii, cnt in enumerate(contours):
if cnt.shape[0] > 20:
cnt = np.reshape(cnt, (cnt.shape[0], cnt.shape[2]))
cnt_list = cnt.tolist()
X, Y = zip(*cnt_list)
# plt.plot(X,Y)
hull = ConvexHull(cnt)
# plt.plot(cnt[hull.vertices,0], cnt[hull.vertices,1], 'r--', lw=2)
shapely_points = [
shapely.geometry.shape({
"type": "Point",
"coordinates": (x, y)
}) for (x, y) in zip(X, Y)
]
concave_hull, edge_points = alpha_shape(shapely_points,
alpha=0.01)
# print edge_points
if isinstance(concave_hull, shapely.geometry.Polygon):
# plot_polygon(ax1,concave_hull)
def color_transfer(Is, It):
global pi, pt, Vt
H, W, _ = Is.shape
Ht, Wt, _ = It.shape
mink_norm = 5
sigma = 2
kappa = 10
# step 1:White-balancing and rotating
# Grey-Egde algorithm to estimate illuminations of the source and target
print('calculating the white balance')
[wRs, wGs, wBs] = weightedGE(Is, kappa, mink_norm, sigma)
WBs = np.array([wRs, wGs, wBs])
[wRt, wGt, wBt] = weightedGE(It, kappa, mink_norm, sigma)
WBt = np.array([wRt, wGt, wBt])
WBs = np.sqrt(3) * WBs / (np.sqrt(np.sum(WBs**2)) * 1.0)
WBt = np.sqrt(3) * WBt / (np.sqrt(np.sum(WBt**2)) * 1.0)
Is = Is.reshape(-1, 3, order='F').T
It = It.reshape(-1, 3, order='F').T
Is = np.diag(1.0 / WBs).dot(Is) # pass
It = np.diag(1.0 / WBt).dot(It) # pass
Is = rotate_to_Zaxis(Is, np.array([1, 1, 1])) # pass
It = rotate_to_Zaxis(It, np.array([1, 1, 1])) # pass
# Step 2: Luminance Matchingnce
print('matching the Luminance')
Is = Is.T
It = It.T
Is[:, 2] = normalizeIntensity(Is[:, 2], It[:, 2], H, W)
# Step 3: Color Gamut Aligning
print('Color Gamut Aligning')
Ms = np.mean(Is, 0)
Mt = np.mean(It, 0)
Is = Is - np.matlib.repmat(Ms, H * W, 1)
It = It - np.matlib.repmat(Mt, Ht * Wt, 1)
hull_s = ConvexHull(Is)
Chi = hull_s.simplices
hull_t = ConvexHull(It)
Cht = hull_t.simplices
Vt = hull_t.volume
idi = np.unique(Chi[:])
idt = np.unique(Cht[:])
pi = Is[idi - 1, :]
pt = It[idt - 1, :]
# compute the optimal matrix
x0 = np.array([0, 1, 1])
x = fmin_bfgs(myfunoptimal, x0, maxiter=50, disp=1)
T = np.array([[x[1] * np.cos(x[0]), -x[1] * np.sin(x[0]), 0],
[x[2] * np.sin(x[0]), x[2] * np.cos(x[0]), 0], [0, 0, 1]])
# Align two gamuts
Io = T.dot(Is.T)
Mt[2] = Ms[2]
Io = Io + np.matlib.repmat(Mt.reshape(1, 3).T, 1, H * W)
# STEP 4: Rotate back and undo white-balancing
print('Rotate back and undo white-balancing')
Io = rotate_back_from_Zaxis(Io, np.array([1, 1, 1]))
Io = np.diag(WBt).dot(Io)
Io[Io < 0] = 0
Io[Io > 1] = 1
Io = Io.T
Io_ = np.reshape(Io, (H, W, 3), order='F')
Io_2 = np.asarray(Io_ * 255, dtype=np.uint8)
Io_2 = cv2.cvtColor(Io_2, cv2.COLOR_RGB2BGR)
return Io_2
if __name__ == '__main__':
mpl.rc('text', usetex=True)
mpl.rcParams['mathtext.fontset'] = 'stix'
mpl.rcParams['font.family'] = 'STIXGeneral'
count = 20
random.seed(18.9654)
ref_point2d = [0.001, 0.001]
set2d = np.zeros((count, 2))
for i in range(count):
for u in range(2):
rand = random.random()
set2d[i, u] = rand if (rand > ref_point2d) or (
rand > 0.3) else random.random()
#hv_2d_calc = HyperVolumeCalculator(ref_point2d)
#pf = hv_2d_calc.extract_front(set2d)
hullraw = ConvexHull(set2d)
hull = [set2d[x] for x in hullraw.vertices]
hull.append(hull[0])
size = 0.48 * 5.8091048611149611602
fig = plt.figure(figsize=[size, 0.75 * size])
fig.set_size_inches(size, 0.7 * size)
ax = fig.add_subplot(111)
ax.set_axisbelow(True)
plt.axis([0, max(set2d[:, 0] + 0.07), 0.05, max(set2d[:, 1] * 1.1)])
plt.setp(ax.get_xticklabels(), fontsize=9)
plt.setp(ax.get_yticklabels(), fontsize=9)
pfx = [hull[i][0] for i in range(len(hull))]
pfy = [hull[u][1] for u in range(len(hull))]
plt.plot(set2d[:, 0], set2d[:, 1], 'bo', markersize=4)
plt.plot(pfx, pfy, 'ro', markersize=4)
def cluster_label_points(title, points, ax, eps, min_cluster, n_clusters,
clabel_size, words_only):
db = DBSCAN(eps=eps, min_samples=min_cluster).fit(points)
#clusterer = hdbscan.HDBSCAN(min_cluster_size=min_cluster)
#db = clusterer.fit(points)
labels = db.labels_
texts = []
bboxes = []
r = get_renderer(ax.get_figure())
for l in set(labels):
text_set = False
if l == -1:
continue
ind = np.argwhere(labels == l)[:, 0]
#print("\n##\nlabel: {}, {} documents".format(l,len(ind)))
lpoints = points[ind]
if len(ind) > min_cluster:
try:
hull = ConvexHull(lpoints)
except:
continue
cx = np.mean(hull.points[hull.vertices, 0])
cy = np.mean(hull.points[hull.vertices, 1])
c = [cx, cy]
if words_only:
title = title.split(",")[0].replace("{", "")
text = ax.annotate(title,
c,
fontsize=clabel_size,
ha="center",
va="center",
bbox={
'facecolor': "white",
'alpha': 0.4,
'pad': 0.2,
'boxstyle': 'round'
})
texts.append(text)
#return text
#break
else:
title = title.split(",")[0].replace("{", "")
x = []
y = []
for i, v in enumerate(lpoints[hull.vertices, :]):
p1 = extend_points(c, v)
#p2 = extend_points(c,v])
x.append(p1[0])
y.append(p1[1])
#x.append(p2[0])
#y.append(p2[1])
# plt.plot(
# [p1[0],p2[0]],
# [p1[1],p2[1]],
# 'k-',
# linewidth=0.5
# )
if not text_set:
if p1[0] > cx:
ha = "left"
else:
ha = "right"
pl = extend_points(c, p1)
texts.append(
ax.annotate(
title,
c,
#p1,
#xytext=pl,
va="center",
#ha=ha,
ha="center",
fontsize=clabel_size,
#arrowprops=dict(width=0.2,headwidth=0.1),
bbox={
'facecolor': "white",
'alpha': 0.4,
'pad': 0.2,
'boxstyle': 'round'
}))
text_set = True
orig_len = len(x)
x = x[-3:-1] + x + x[1:3]
y = y[-3:-1] + y + y[1:3]
t = np.arange(len(x))
ti = np.linspace(2, orig_len + 1, 10 * orig_len)
x2 = interp1d(t, x, kind='cubic')(ti)
y2 = interp1d(t, y, kind='cubic')(ti)
x = lpoints[hull.vertices, 0]
x = np.append(x, [x[:1]])
y = lpoints[hull.vertices, 1]
y = np.append(y, [y[:1]])
coords = np.array(list(zip(x, y)))
coords = chaikins_corner_cutting(coords)
x2 = coords[:, 0]
y2 = coords[:, 1]
#x2 = interpolate.BSpline(t, x, nt)
#y2 = interpolate.BSpline(t, y, nt)
plt.plot(x2, y2, 'k-', linewidth=0.8)
# break here, just do the biggest cluster
#break
if len(texts) == 0:
print(f"couldn't find a cluster for {title}")
return texts
print('finding nearest neighbours...\t\t\t{0:06.2f}%'.format(
i / len(vor.point_region) * 100),
end='\r')
nbrs_idx = kdt.query(points[i], k=n_neighbors)[1]
neighborhood_area = 0
neighborhood_probability = 0
for idx in nbrs_idx:
reg_idx = vor.point_region[idx]
indices = vor.regions[reg_idx]
prob = probs[idx]
if -1 in indices: # some regions may be open
neighborhood_area += np.inf
neighborhood_probability += prob
else:
neighborhood_area += ConvexHull(vor.vertices[indices]).volume
neighborhood_probability += prob
den[i] = neighborhood_probability / neighborhood_area
# normalised to central density = 1
den /= max(den)
# remove particles below given limit
den = np.ma.masked_where(den <= lower_limit, den).filled(0)
# normalize chosen colormap
colormap = copy.copy(cm.get_cmap('magma'))
colormap.set_bad(colormap(0))
mapper = cm.ScalarMappable(norm=LogNorm(vmax=max(den), vmin=lower_limit),
cmap=colormap)
def expand_cluster_convexhull(self, df_in_name, df_cluster_name,
df_cluster_expanded_name):
from scipy.spatial import ConvexHull
if len(self.df_dict[df_cluster_name]) < 1:
print('NO CLUSTERS EXIST:')
print(df_cluster_expanded_name)
self.df_dict[df_cluster_expanded_name] = pd.DataFrame(columns=[
'CLUSTER', self.sample_name_column, 'PERCENTILE',
'CLUSTER_COUNT', 'ORIGINAL_CLUSTER_COUNT', 'ORIGINAL_CLUSTER',
'CLUSTER_RATIO', 'CLUSTERED', 'EXPANDED'
])
return
print('CLUSTERS EXIST:')
print(df_cluster_expanded_name)
cluster_names_df = self.df_dict[df_cluster_name][[
'CLUSTER', self.sample_name_column, 'PERCENTILE', 'CLUSTER_COUNT'
]].drop_duplicates(subset=None, keep='first', inplace=False)
self.df_dict[df_cluster_expanded_name] = pd.DataFrame()
for index, row in cluster_names_df.iterrows():
# get the cluster
cluster_points_df_i = self.df_dict[df_cluster_name].loc[
(self.df_dict[df_cluster_name]['PERCENTILE'] ==
row['PERCENTILE'])
& (self.df_dict[df_cluster_name]['CLUSTER'] == row['CLUSTER'])
& (self.df_dict[df_cluster_name][self.sample_name_column]
== row[self.sample_name_column])][['X', 'Y']]
# convert DF to an array
cluster_points_array = cluster_points_df_i.values
# get the hull for the cluster
hull = ConvexHull(cluster_points_array)
# get the vertices of the hull
hull_vertices = cluster_points_array[hull.vertices]
# get points inside the hull vertices as a numpy array
contained_points = in_hull(
self.df_dict[df_in_name][['X', 'Y']].values, hull_vertices)
# contained_points
# convert back to dataframe
contained_points_df = pd.DataFrame(contained_points,
columns=['X', 'Y'])
# name the cluster, Sample name, percentile and oritinal clustercount
contained_points_df['CLUSTER'] = [row['CLUSTER']] * len(
contained_points_df.index)
contained_points_df[self.sample_name_column] = [
row[self.sample_name_column]
] * len(contained_points_df.index)
contained_points_df['PERCENTILE'] = [row['PERCENTILE']] * len(
contained_points_df.index)
contained_points_df['ORIGINAL_CLUSTER_COUNT'] = [
row['CLUSTER_COUNT']
] * len(contained_points_df.index)
# get the newly expanded cluster count
contained_points_df['CLUSTER_COUNT'] = contained_points_df.groupby(
'CLUSTER')['CLUSTER'].transform('count')
# Label the points that are part of the original cluster
# get the points of the original cluster
original_cluster_points_df_i = cluster_points_df_i[['X', 'Y']]
# label this data frame as the original
original_cluster_points_df_i['ORIGINAL_CLUSTER'] = [
'ORIGINAL'
] * len(original_cluster_points_df_i.index)
contained_points_df = contained_points_df.merge(
original_cluster_points_df_i, how='outer', on=['X', 'Y'])
# contained_points_df
self.df_dict[df_cluster_expanded_name] = pd.concat(
[self.df_dict[df_cluster_expanded_name], contained_points_df],
ignore_index=True)
self.df_dict[df_cluster_expanded_name].ORIGINAL_CLUSTER.fillna(
'EXPANDED', inplace=True)
self.df_dict[df_cluster_expanded_name]['CLUSTERED'] = [
'CLUSTERED'
] * len(self.df_dict[df_cluster_expanded_name].index)
self.df_dict[df_cluster_expanded_name]['CLUSTER_RATIO'] = round(
self.df_dict[df_cluster_expanded_name]['ORIGINAL_CLUSTER_COUNT'] /
self.df_dict[df_cluster_expanded_name]['CLUSTER_COUNT'], 2)
def filter(pts):
hull = ConvexHull(pts, qhull_options='Q12')
return [pts[i] for i in hull.vertices.tolist()]
def transform(self, X):
d = []
for _, row in X.iterrows():
df_x = row.iloc[np.arange(3, 33, 3).tolist()]
df_y = row.iloc[np.arange(4, 34, 3).tolist()]
df_z = row.iloc[np.arange(5, 35, 3).tolist()]
x = np.array(df_x[df_x.notnull()].tolist())
y = np.array(df_y[df_y.notnull()].tolist())
z = np.array(df_z[df_z.notnull()].tolist())
n = len(x)
digits = 4 # number of decimal places in calculations
pts = np.vstack((x, y, z)).T
# length of all lines to the origin
lengths = []
for pt in pts:
length = np.linalg.norm(pt)
lengths.append(length)
lengths = np.array(lengths)
# angles between all points and origin
# e.g. points a, b, c would give 3 angles: a-o-b, a-o-c, b-o-c
angles = []
areas = []
for ang in combinations(pts, 2):
# Calculate all 3 angles of triangle using 3 sides
O0 = np.array(ang[0])
O1 = np.array(ang[1])
cosine_angle = np.dot(O0, -1 * O1) / (np.linalg.norm(O0) *
np.linalg.norm(-1 * O1))
angle = np.arccos(cosine_angle)
if not np.isnan(angle):
angles.append(angle)
# Area
area = 0.5 * np.linalg.norm(np.cross(O1, -1 * O0))
areas.append(area)
# Determine conex hull of posture, including origin as a data point
pts = np.vstack((pts, np.array([0, 0, 0])))
hull = ConvexHull(pts)
# Centroid of convex hull
cx = np.mean(hull.points[hull.vertices, 0])
cy = np.mean(hull.points[hull.vertices, 1])
cz = np.mean(hull.points[hull.vertices, 2])
d.append({
'id': int(row.iloc[0]),
'class': int(row.iloc[1]),
'user': int(row.iloc[2]),
'n_markers': n,
'x_mean': np.mean(x).round(digits),
'x_std': np.std(x).round(digits),
'x_min': np.min(x).round(digits),
'x_max': np.max(x).round(digits),
'y_mean': np.mean(y).round(digits),
'y_std': np.std(y).round(digits),
'y_min': np.min(y).round(digits),
'y_max': np.max(y).round(digits),
'z_mean': np.mean(z).round(digits),
'z_std': np.std(z).round(digits),
'z_min': np.min(z).round(digits),
'z_max': np.max(z).round(digits),
'l_mean': np.mean(lengths).round(digits),
'l_std': np.std(lengths).round(digits),
'l_min': np.min(lengths).round(digits),
'l_max': np.max(lengths).round(digits),
'ang_mean': np.mean(angles).round(digits),
'ang_std': np.std(angles).round(digits),
'ang_min': np.min(angles).round(digits),
'ang_max': np.max(angles).round(digits),
'area_mean': np.mean(areas).round(digits),
'area_std': np.std(areas).round(digits),
'area_min': np.min(areas).round(digits),
'area_max': np.max(areas).round(digits),
'conv_hull_vol': np.round(hull.volume, digits),
'conv_hull_cx': np.round(cx, digits),
'conv_hull_cy': np.round(cy, digits),
'conv_hull_cz': np.round(cz, digits)
})
df = pd.DataFrame(d)
X = df[[
'id', 'class', 'user', 'n_markers', 'x_mean', 'x_std', 'x_min',
'x_max', 'y_mean', 'y_std', 'y_min', 'y_max', 'z_mean', 'z_std',
'z_min', 'z_max', 'l_mean', 'l_std', 'l_min', 'l_max', 'ang_mean',
'ang_std', 'ang_min', 'ang_max', 'area_mean', 'area_std',
'area_min', 'area_max', 'conv_hull_vol', 'conv_hull_cx',
'conv_hull_cy', 'conv_hull_cz'
]]
return X
def minimum_bounding_rectangle(points):
"""
Find the smallest bounding rectangle for a set of points.
Returns a set of points representing the corners of the bounding box.
:param points: a list of coordinates
:rval: an nx2 matrix of coordinates
"""
points = np.array(points)
points = points.reshape(len(points), 2)
pi2 = np.pi / 2.
# get the convex hull for the points
hull_points = points[ConvexHull(points).vertices]
# calculate edge angles
edges = np.zeros((len(hull_points) - 1, 2))
edges = hull_points[1:] - hull_points[:-1]
angles = np.zeros((len(edges)))
angles = np.arctan2(edges[:, 1], edges[:, 0])
angles = np.abs(np.mod(angles, pi2))
angles = np.unique(angles)
# find rotation matrices
# XXX both work
rotations = np.vstack([
np.cos(angles),
np.cos(angles - pi2),
np.cos(angles + pi2),
np.cos(angles)
]).T
# rotations = np.vstack([
# np.cos(angles),
# -np.sin(angles),
# np.sin(angles),
# np.cos(angles)]).T
rotations = rotations.reshape((-1, 2, 2))
# apply rotations to the hull
rot_points = np.dot(rotations, hull_points.T)
# find the bounding points
min_x = np.nanmin(rot_points[:, 0], axis=1)
max_x = np.nanmax(rot_points[:, 0], axis=1)
min_y = np.nanmin(rot_points[:, 1], axis=1)
max_y = np.nanmax(rot_points[:, 1], axis=1)
# find the box with the best area
areas = (max_x - min_x) * (max_y - min_y)
best_idx = np.argmin(areas)
# return the best box
x1 = max_x[best_idx]
x2 = min_x[best_idx]
y1 = max_y[best_idx]
y2 = min_y[best_idx]
r = rotations[best_idx]
rval = np.zeros((4, 2))
rval[0] = np.dot([x1, y2], r)
rval[1] = np.dot([x2, y2], r)
rval[2] = np.dot([x2, y1], r)
rval[3] = np.dot([x1, y1], r)
return rval
def get_explored_surface(self):
"""Compute convex hull on the array of coordinates"""
tmp_hull = ConvexHull(self.coordinates)
return tmp_hull.volume
def __init__(self, references, filter='', verbose=True):
"""Phase-diagram.
references: list of (name, energy) tuples
List of references. The energy must be the total energy and not
energy per atom. The names can also be dicts like
``{'Zn': 1, 'O': 2}`` which would be equivalent to ``'ZnO2'``.
filter: str or list of str
Use only those references that match the given filter.
Example: ``filter='ZnO'`` will select those that
contain zinc or oxygen.
verbose: bool
Write information.
"""
if not references:
raise ValueError("You must provide a non-empty list of references"
" for the phase diagram! "
"You have provided '{}'".format(references))
filter = parse_formula(filter)[0]
self.verbose = verbose
self.species = OrderedDict()
self.references = []
for name, energy in references:
if isinstance(name, basestring):
count = parse_formula(name)[0]
else:
count = name
name = formula_hill(count)
if filter and any(symbol not in filter for symbol in count):
continue
natoms = 0
for symbol, n in count.items():
natoms += n
if symbol not in self.species:
self.species[symbol] = len(self.species)
self.references.append((count, energy, name, natoms))
ns = len(self.species)
self.symbols = [None] * ns
for symbol, id in self.species.items():
self.symbols[id] = symbol
if verbose:
print('Species:', ', '.join(self.symbols))
print('References:', len(self.references))
for i, (count, energy, name, natoms) in enumerate(self.references):
print('{:<5}{:10}{:10.3f}'.format(i, name, energy))
self.points = np.zeros((len(self.references), ns + 1))
for s, (count, energy, name, natoms) in enumerate(self.references):
for symbol, n in count.items():
self.points[s, self.species[symbol]] = n / natoms
self.points[s, -1] = energy / natoms
if len(self.points) == ns:
# Simple case that qhull would choke on:
self.simplices = np.arange(ns).reshape((1, ns))
self.hull = np.ones(ns, bool)
else:
hull = ConvexHull(self.points[:, 1:])
# Find relevant simplices:
ok = hull.equations[:, -2] < 0
self.simplices = hull.simplices[ok]
# Create a mask for those points that are on the convex hull:
self.hull = np.zeros(len(self.points), bool)
for simplex in self.simplices:
self.hull[simplex] = True
if verbose:
print('Simplices:', len(self.simplices))
def baseline(x_input,y_input,bir,method, **kwargs):
"""Allows subtracting a baseline under a x y spectrum.
Parameters
----------
x_input : ndarray
x values.
y_input : ndarray
y values.
bir : ndarray
Contain the regions of interest, organised per line.
For instance, roi = np.array([[100., 200.],[500.,600.]]) will
define roi between 100 and 200 as well as between 500 and 600.
Note: This is NOT used by the "als" and "arPLS" algorithms, but still is a requirement when calling the function.
bir and method probably will become args in a futur iteration of rampy to solve this.
methods : str
"poly": polynomial fitting, with splinesmooth the degree of the polynomial.
"unispline": spline with the UnivariateSpline function of Scipy, splinesmooth is
the spline smoothing factor (assume equal weight in the present case);
"gcvspline": spline with the gcvspl.f algorythm, really robust.
Spectra must have x, y, ese in it, and splinesmooth is the smoothing factor;
For gcvspline, if ese are not provided we assume ese = sqrt(y).
Requires the installation of gcvspline with a "pip install gcvspline" call prior to use;
"exp": exponential background;
"log": logarythmic background;
"rubberband": rubberband baseline fitting;
"als": automatic least square fitting following Eilers and Boelens 2005;
"arPLS": automatic baseline fit using the algorithm from Baek et al. 2015
Baseline correction using asymmetrically reweighted penalized least squares smoothing, Analyst 140: 250-257.
kwargs
------
polynomial_order : Int
The degree of the polynomial (0 for a constant), default = 1.
s : Float
spline smoothing coefficient for the unispline and gcvspline algorithms.
lam : Float
float, the lambda smoothness parameter for the ALS and ArPLS algorithms. Typical values are between 10**2 to 10**9, default = 10**5.
p : Float
float, for the ALS algorithm, advised value between 0.001 to 0.1, default = 0.01.
ratio : float
ratio parameter of the arPLS algorithm. default = 0.01.
niter : Int
number of iteration of the ALS algorithm, default = 10.
p0_exp : List
containg the starting parameter for the exp baseline fit with curve_fit. Default = [1.,1.,1.].
p0_log : List
containg the starting parameter for the log baseline fit with curve_fit. Default = [1.,1.,1.,1.].
Returns
-------
out1 : ndarray
Contain the corrected signal.
out2 : ndarray
Contain the baseline.
"""
# we get the signals in the bir
yafit_unscaled = get_portion_interest(x_input,y_input,bir)
# signal standard standardization with sklearn
# this helps for polynomial fitting
X_scaler = preprocessing.StandardScaler().fit(x_input.reshape(-1, 1))
Y_scaler = preprocessing.StandardScaler().fit(y_input.reshape(-1, 1))
# transformation
x = X_scaler.transform(x_input.reshape(-1, 1))
y = Y_scaler.transform(y_input.reshape(-1, 1))
yafit = np.copy(yafit_unscaled)
yafit[:,0] = X_scaler.transform(yafit_unscaled[:,0].reshape(-1, 1))[:,0]
yafit[:,1] = Y_scaler.transform(yafit_unscaled[:,1].reshape(-1, 1))[:,0]
y = y.reshape(len(y_input))
if method == 'poly':
# optional parameters
poly_order = kwargs.get('polynomial_order',1)
coeffs = np.polyfit(yafit[:,0],yafit[:,1],poly_order)
baseline_fitted = np.polyval(coeffs,x)
elif method == 'unispline':
# optional parameters
splinesmooth = kwargs.get('s',2.0)
# fit of the baseline
coeffs = UnivariateSpline(yafit[:,0],yafit[:,1], s=splinesmooth)
baseline_fitted = coeffs(x)
elif method == 'gcvspline':
try:
from gcvspline import gcvspline, splderivative
except ImportError:
print('ERROR: Install gcvspline to use this mode (needs a working FORTRAN compiler).')
# optional parameters
splinesmooth = kwargs.get('s',2.0)
# Spline baseline with mode 1 of gcvspl.f, see gcvspline documentation
c, wk, ier = gcvspline(yafit[:,0],yafit[:,1],np.sqrt(np.abs(yafit[:,1])),splinesmooth,splmode = 1) # gcvspl with mode 1 and smooth factor
baseline_fitted = splderivative(x,yafit[:,0],c)
elif method == 'gaussian':
### Baseline is of the type y = a*exp(-log(2)*((x-b)/c)**2)
# optional parameters
p0_gauss = kwargs.get('p0_gaussian',[1.,1.,1.])
## fit of the baseline
coeffs, pcov = curve_fit(rampy.gaussian,yafit[:,0],yafit[:,1],p0 = p0_gauss)
baseline_fitted = rampy.gaussian(x,coeffs[0],coeffs[1],coeffs[2])
elif method == 'exp':
### Baseline is of the type y = a*exp(b*(x-xo))
# optional parameters
p0_exp = kwargs.get('p0_exp',[1.,1.,1.])
## fit of the baseline
coeffs, pcov = curve_fit(rampy.funexp,yafit[:,0],yafit[:,1],p0 = p0_exp)
baseline_fitted = rampy.funexp(x,coeffs[0],coeffs[1],coeffs[2])
elif method == 'log':
### Baseline is of the type y = a*exp(b*(x-xo))
# optional parameters
p0_log = kwargs.get('p0_log',[1.,1.,1.,1.])
## fit of the baseline
coeffs, pcov = curve_fit(rampy.funlog,yafit[:,0],yafit[:,1],p0 = p0_log)
baseline_fitted = rampy.funlog(x,coeffs[0],coeffs[1],coeffs[2],coeffs[3])
elif method == 'rubberband':
# code from this stack-exchange forum
#https://dsp.stackexchange.com/questions/2725/how-to-perform-a-rubberband-correction-on-spectroscopic-data
# Find the convex hull
v = ConvexHull(np.array([x, y])).vertices
# Rotate convex hull vertices until they start from the lowest one
v = np.roll(v, -v.argmin())
# Leave only the ascending part
v = v[:v.argmax()]
# Create baseline using linear interpolation between vertices
baseline_fitted = np.interp(x, x[v], y[v])
elif method == 'als':
# Matlab code in Eilers et Boelens 2005
# Python addaptation found on stackoverflow: https://stackoverflow.com/questions/29156532/python-baseline-correction-library
# optional parameters
lam = kwargs.get('lam',1.0*10**5)
p = kwargs.get('p',0.01)
niter = kwargs.get('niter',10)
# starting the algorithm
L = len(y)
D = sparse.csc_matrix(np.diff(np.eye(L), 2))
w = np.ones(L)
for i in range(niter):
W = sparse.spdiags(w, 0, L, L)
Z = W + lam * D.dot(D.transpose())
z = sparse.linalg.spsolve(Z, w*y)
w = p * (y > z) + (1-p) * (y < z)
baseline_fitted = z
elif method == 'arPLS':
# Adaptation of the Matlab code in Baek et al 2015
# optional parameters
lam = kwargs.get('lam',1.0*10**5)
ratio = kwargs.get('ratio',0.01)
N = len(y)
D = sparse.csc_matrix(np.diff(np.eye(N), 2))
w = np.ones(N)
while True:
W = sparse.spdiags(w, 0, N, N)
Z = W + lam * D.dot(D.transpose())
z = sparse.linalg.spsolve(Z, w*y)
d = y - z
# make d- and get w^t with m and s
dn = d[d<0]
m = np.mean(dn)
s = np.std(dn)
wt = 1.0/(1 + np.exp( 2* (d-(2*s-m))/s ) )
# check exit condition and backup
if norm(w-wt)/norm(w) < ratio:
break
w = wt
baseline_fitted = z
return y_input.reshape(-1,1)-Y_scaler.inverse_transform(baseline_fitted.reshape(-1, 1)), Y_scaler.inverse_transform(baseline_fitted.reshape(-1, 1))
def get_pourbaix_domains(pourbaix_entries, limits=None):
"""
Returns a set of pourbaix stable domains (i. e. polygons) in
pH-V space from a list of pourbaix_entries
This function works by using scipy's HalfspaceIntersection
function to construct all of the 2-D polygons that form the
boundaries of the planes corresponding to individual entry
gibbs free energies as a function of pH and V. Hyperplanes
of the form a*pH + b*V + 1 - g(0, 0) are constructed and
supplied to HalfspaceIntersection, which then finds the
boundaries of each pourbaix region using the intersection
points.
Args:
pourbaix_entries ([PourbaixEntry]): Pourbaix entries
with which to construct stable pourbaix domains
limits ([[float]]): limits in which to do the pourbaix
analysis
Returns:
Returns a dict of the form {entry: [boundary_points]}.
The list of boundary points are the sides of the N-1
dim polytope bounding the allowable ph-V range of each entry.
"""
if limits is None:
limits = [[-2, 16], [-4, 4]]
# Get hyperplanes
hyperplanes = [
np.array([-PREFAC * entry.npH, -entry.nPhi, 0, -entry.energy]) *
entry.normalization_factor for entry in pourbaix_entries
]
hyperplanes = np.array(hyperplanes)
hyperplanes[:, 2] = 1
max_contribs = np.max(np.abs(hyperplanes), axis=0)
g_max = np.dot(-max_contribs, [limits[0][1], limits[1][1], 0, 1])
# Add border hyperplanes and generate HalfspaceIntersection
border_hyperplanes = [[-1, 0, 0,
limits[0][0]], [1, 0, 0, -limits[0][1]],
[0, -1, 0, limits[1][0]],
[0, 1, 0, -limits[1][1]], [0, 0, -1, 2 * g_max]]
hs_hyperplanes = np.vstack([hyperplanes, border_hyperplanes])
interior_point = np.average(limits, axis=1).tolist() + [g_max]
hs_int = HalfspaceIntersection(hs_hyperplanes,
np.array(interior_point))
# organize the boundary points by entry
pourbaix_domains = {entry: [] for entry in pourbaix_entries}
for intersection, facet in zip(hs_int.intersections,
hs_int.dual_facets):
for v in facet:
if v < len(pourbaix_entries):
this_entry = pourbaix_entries[v]
pourbaix_domains[this_entry].append(intersection)
# Remove entries with no pourbaix region
pourbaix_domains = {k: v for k, v in pourbaix_domains.items() if v}
pourbaix_domain_vertices = {}
for entry, points in pourbaix_domains.items():
points = np.array(points)[:, :2]
# Initial sort to ensure consistency
points = points[np.lexsort(np.transpose(points))]
center = np.average(points, axis=0)
points_centered = points - center
# Sort points by cross product of centered points,
# isn't strictly necessary but useful for plotting tools
points_centered = sorted(
points_centered,
key=cmp_to_key(lambda x, y: x[0] * y[1] - x[1] * y[0]))
points = points_centered + center
# Create simplices corresponding to pourbaix boundary
simplices = [
Simplex(points[indices])
for indices in ConvexHull(points).simplices
]
pourbaix_domains[entry] = simplices
pourbaix_domain_vertices[entry] = points
return pourbaix_domains, pourbaix_domain_vertices
def density(model, refinement=0):
"""
Create a Voronoi mesh and calculate the local particle density on its vertices.
The local density is calculated as follows:
for each vertex, compute the density of each neighbour region as
one over the area and assign the average of
the neighbouring density to the vertex.
Parameters
----------
model : simulation.builder.Model
the Model object containing
refinement : int (defaults : 0)
number of subdivision for refining the mesh (0 == None)
Returns
-------
tri : matplotlib.tri.Triangulation
the triangulation mesh (refined if set as)
vert_density : numpy.array
the array containing the local denstity associated with the tri mesh
Example
-------
To plot the result using matplotlib use :
.. code-block:: python
import matplotlib.pyplot as plt
tri, density = data_proc.density(model)
plt.tricontour(tri, density) # to draw contours
plt.tricontourf(tri, density) # ot draw filled contours
plt.show()
Note
----
As of now, the numerical results may not be quantitatively accurate
but should qualitatively represent the density.
"""
vor = Voronoi(model.pos)
vert_density = np.zeros(max(vor.vertices.shape)) # density vector
reg_num = np.zeros(max(
vor.vertices.shape)) # nbr of regions per vertex --> averaging
for point_index, reg in enumerate(vor.point_region):
vertices = vor.regions[reg]
if vertices:
if -1 not in vertices:
area = ConvexHull(vor.vertices[vertices]).area # gets the area
vert_density[
vertices] += 1 / area # makes it a density (sort-of)
reg_num[vertices] += 1
vert_density /= reg_num # averaging
# getting rid of really ugly border points
new_vert, vert_density = (
vor.vertices[vor.vertices[:, 0] >= np.min(model.pos[:, 0])],
vert_density[vor.vertices[:, 0] >= np.min(model.pos[:, 0])])
new_vert, vert_density = (
new_vert[new_vert[:, 0] <= np.max(model.pos[:, 0])],
vert_density[new_vert[:, 0] <= np.max(model.pos[:, 0])])
new_vert, vert_density = (
new_vert[new_vert[:, 1] >= np.min(model.pos[:, 1])],
vert_density[new_vert[:, 1] >= np.min(model.pos[:, 1])])
new_vert, vert_density = (
new_vert[new_vert[:, 1] <= np.max(model.pos[:, 1])],
vert_density[new_vert[:, 1] <= np.max(model.pos[:, 1])])
# for triangulation refinement
tri2 = Triangulation(*new_vert.T)
if refinement:
tri2.set_mask(TriAnalyzer(tri2).get_flat_tri_mask(0.1))
refiner = UniformTriRefiner(tri2)
print(len(tri2.neighbors), vert_density.shape)
tri, vert_density = refiner.refine_field(vert_density,
subdiv=refinement)
else:
tri, vert_density = tri2, vert_density
return tri, vert_density
def to_ineq(points):
ineq = ConvexHull(points).equations
return ineq[:, :-1], -ineq[:, -1]
def find_perimeter_nodes(self, pts):
"""
Uses a convex hull to locate the perimeter nodes of the Voronoi grid,
then sets them as fixed value boundary nodes.
It then sets/updates the various relevant node lists held by the grid,
and returns *node_status*, *core_nodes*, *boundary_nodes*.
"""
# Calculate the convex hull for the set of points
from scipy.spatial import ConvexHull
hull = ConvexHull(pts, qhull_options='Qc') # see below why we use 'Qt'
# The ConvexHull object lists the edges that form the hull. We need to
# get from this list of edges the unique set of nodes. To do this, we
# first flatten the list of vertices that make up all the hull edges
# ("simplices"), so it becomes a 1D array. With that, we can use the set()
# function to turn the array into a set, which removes duplicate vertices.
# Then we turn it back into an array, which now contains the set of IDs for
# the nodes that make up the convex hull.
# The next thing to worry about is the fact that the mesh perimeter
# might contain nodes that are co-planar (that is, co-linear in our 2D
# world). For example, if you make a set of staggered points for a
# hexagonal lattice using make_hex_points(), there will be some
# co-linear points along the perimeter. The ones of these that don't
# form convex corners won't be included in convex_hull_nodes, but they
# are nonetheless part of the perimeter and need to be included in
# the list of boundary_nodes. To deal with this, we pass the 'Qt'
# option to ConvexHull, which makes it generate a list of coplanar
# points. We include these in our set of boundary nodes.
convex_hull_nodes = numpy.array(list(set(hull.simplices.flatten())))
coplanar_nodes = hull.coplanar[:,0]
boundary_nodes = numpy.concatenate((convex_hull_nodes, coplanar_nodes))
# Now we'll create the "node_status" array, which contains the code
# indicating whether the node is interior and active (=0) or a
# boundary (=1). This means that all perimeter (convex hull) nodes are
# initially flagged as boundary code 1. An application might wish to change
# this so that, for example, some boundaries are inactive.
node_status = numpy.zeros(len(pts[:,0]), dtype=numpy.int8)
node_status[boundary_nodes] = 1
# It's also useful to have a list of interior nodes
core_nodes = numpy.where(node_status==0)[0]
#save the arrays and update the properties
self.node_status = node_status
self._num_active_nodes = node_status.size
self._num_core_nodes = len(core_nodes)
self._num_core_cells = len(core_nodes)
self.core_cells = numpy.arange(len(core_nodes))
self.node_corecell = numpy.empty(node_status.size)
self.node_corecell.fill(BAD_INDEX_VALUE)
self.node_corecell[core_nodes] = self.core_cells
self.active_cells = numpy.arange(node_status.size)
self.cell_node = core_nodes
self.activecell_node = core_nodes
self.corecell_node = core_nodes
self._boundary_nodes = boundary_nodes
# Return the results
return node_status, core_nodes, boundary_nodes
new_face_vert = [
icosahedron_vertices[face[0]], icosahedron_vertices[face[1]],
icosahedron_vertices[face[2]]
]
face_cache.append(new_face_vert)
faces = np.asarray(face_cache)
#######################################
###### RECURSIVELY MAKING THE ICOSPHERE###
sph_vert, sph_tri = create_unit_sphere_vert(4)
x, y, z = sph_vert[:,
0], sph_vert[:,
1], sph_vert[:,
2] #Arrays corresponting the the cartesian coords
ch = ConvexHull(sph_vert)
"""
hull_indices = np.unique(ch.simplices.flat)
hull_pts = sph_vert[hull_indices, :]
print("len hull points", len(hull_pts))
print(len(ch.simplices))
z_pts = hull_pts[:,2]
zmax = np.max(z_pts)
neighmax = np.max(ch.neighbors)
print("z max", zmax)
print("neigh max", neighmax)
"""
# ch.simplices contains the information of the vertices of each of the faces
#
def GetFloorPolygon(self, i, yamlFilepath):
''' return intersecting surface polygon of floor i, generated from floor cutting '''
result = ""
floor_name = self.floor_name_lst[i]
print(
"current floor, ", floor_name,
"******************************************************************************"
)
#display shapes
#v = self.canvas._display
# set parameters
s = self.s
dbscan = self.dbscan
k = self.k
calcconvexhull = False
use_obb = False
# cutting_height of each building storey
cutting_height = self.storeyElevation_lst[i] + 1.0
# loading customize parameters from the .yml file
yml_file = open(yamlFilepath, 'r')
yml_data = yaml.load(yml_file, Loader=Loader)
str1 = "f" + str(i)
if str1 in yml_data.keys():
dict2 = yml_data[str1]
if 'cutting_height' in dict2.keys():
value = float(dict2['cutting_height'])
cutting_height = self.storeyElevation_lst[i] + value
if 'k' in dict2.keys():
k = float(dict2['k'])
if 'use_obb' in dict2.keys():
if dict2['use_obb'] == True:
use_obb = True
if 's' in dict2.keys():
s = float(dict2['s'])
if 'dbscan' in dict2.keys():
dbscan = float(dict2['dbscan'])
if 'calcconvexhull' in dict2.keys():
if dict2['calcconvexhull'] == True:
calcconvexhull = True
if use_obb:
print(
"use_obb, ", use_obb, "floor name,", floor_name,
" ----------------------------------------------------------------------"
)
pts = GetOrientedBoundingBoxShapeCompound(
self.floor_compound_shapes_lst[i], False)
Z_value = []
for pt in pts:
Z_value.append(pt.Z())
z_max = max(Z_value)
z_min = min(Z_value)
z_mid = 0.5 * (z_max + z_min)
pts_low = []
pts_up = []
for pt in pts:
if pt.Z() < z_mid:
pts_low.append(pt)
else:
pts_up.append(pt)
corners_top = pts_up
pyocc_corners_list = []
for pt in corners_top:
pyocc_corners_list.append([
float("{:.3f}".format(pt.X())),
float("{:.3f}".format(pt.Y()))
])
points = np.array(pyocc_corners_list)
obb_hull = ConvexHull(points)
result = []
for idx in obb_hull.vertices:
result.append(pyocc_corners_list[idx])
poly_footprint = Polygon(result)
return [poly_footprint]
print("cutting height,", cutting_height)
section_shape = GetSectionShape(cutting_height,
self.floor_compound_shapes_lst[i])
#v.DisplayShape(section_shape, color="RED", update=True)
# get the section shape edges
edges = GetShapeEdges(section_shape)
if s != 0:
first_xy = GetEdgeSamplePointsPerDistance(edges, s)
else:
first_xy = GetEdges2DPT(edges)
np_points = np.array(first_xy)
corners = GetNumpyOBB(np_points,
calcconvexhull=calcconvexhull,
show_plot=False)
OBB_poly = Polygon(corners.tolist())
# create result dir
if not os.path.exists('./result/Overlap/' + floor_name):
os.makedirs('./result/Overlap/' + floor_name)
img_filepath = "./result/Overlap/" + floor_name + "/obbAndPoints.png"
# save result as images in the result folder
SavePloyAndPoints(OBB_poly,
np_points,
color='b',
filepath=img_filepath)
cluster_filepath = "./result/Overlap/" + floor_name + "/clusters.png"
cluster_lst = GetDBSCANClusteringlst(np_points,
dbscan,
showplot=False,
saveplot=cluster_filepath)
line = str()
per_floot_poly = []
poly_count = 0
for np_member_array in cluster_lst:
poly_count += 1
print(len(np_member_array))
print("starting concave hull")
hull = concaveHull(np_member_array, k=k, if_optimal=False)
self.WriteConcave2WKT(hull, floor_name, poly_count)
poly = Polygon(hull)
print("polygon validation is: ", poly.is_valid, poly.area)
poly_filepath = "./result/Overlap/" + floor_name + "/polygon" + str(
poly_count) + ".png"
OBB_points = GetNumpyOBB(np_member_array, show_plot=False)
OBB_poly = Polygon(OBB_points.tolist())
print(
"OBB_poly area,", OBB_poly.area, " name,", floor_name,
"---------------------------------------------------------------------"
)
if not poly.is_valid:
print("Try to repair validation:")
new_poly = poly.buffer(0)
line = line + "Repaired_" + str(new_poly.is_valid) + "_" + str(
float("{:.2f}".format(new_poly.area)))
print(new_poly.is_valid, new_poly.area)
un_poly = ops.unary_union(new_poly)
print(type(un_poly), un_poly.is_valid, "Union area,",
un_poly.area)
# if the poly is wrong, replace with OBB_poly
if un_poly.area < (0.3 * OBB_poly.area):
un_poly = OBB_poly
per_floot_poly.append(un_poly)
if un_poly.geom_type == 'MultiPolygon':
for geom in un_poly.geoms:
xs, ys = geom.exterior.xy
plt.plot(xs, ys, color="r")
plt.savefig(poly_filepath)
plt.close()
elif un_poly.geom_type == 'Polygon':
SavePloyAndPoints(un_poly,
np_member_array,
filepath=poly_filepath)
else:
print("Error polygon generation from concave hull failed!")
else:
line = line + "True, Floor Area" + str(
float("{:.2f}".format(poly.area)))
print("Polygon True, no need repair")
SavePloyAndPoints(poly,
np_member_array,
filepath=poly_filepath)
per_floot_poly.append(poly)
return per_floot_poly # [polygon] or [polygons]
def calc_point_offsets(points, scale=0.2, show_plot=False):
"""
Calculate offset point for each point in points which is outside a smooth
rerepresentation of the convex hull of points in 2D. This is useful for
positioning labels or inset axes outside plotted points
"""
Np, _ = points.shape
hull = ConvexHull(points)
vertices = list(hull.vertices)
vertices.insert(0, vertices[-1])
x_h, y_h = points[vertices, 0], points[vertices, 1]
if show_plot:
plt = _import_matplotlib()
plt.plot(x_h, y_h, "r--", lw=2)
def make_t(x, y):
t = np.arange(x.shape[0], dtype=float)
t /= t[-1]
return t
x_h, y_h = _filter_close_points(x_h, y_h)
# again we have to ensure that the path is cyclic
x_h = np.insert(x_h, 0, x_h[-1])
y_h = np.insert(y_h, 0, y_h[-1])
t = make_t(x_h, y_h)
Nt = 100
nt = np.linspace(0, 1, Nt)
cs_x = CubicSpline(t, x_h, bc_type="periodic")
cs_y = CubicSpline(t, y_h, bc_type="periodic")
x_s = cs_x(nt)
y_s = cs_y(nt)
if show_plot:
plt = _import_matplotlib()
plt.plot(x_s, y_s, marker=".")
points_s = np.array([x_s, y_s]).T
lx, ly = np.max(x_s) - np.min(x_s), np.max(y_s) - np.min(y_s)
l = np.sqrt(lx**2.0 + ly**2.0)
offset_points = []
for n in range(Np):
point = points[n]
dist_xy = point - points_s
dist_xy[:, 0] /= lx
dist_xy[:, 1] /= ly
dists = np.linalg.norm(dist_xy, axis=-1)
k = np.argmin(dists)
point_nearest = points_s[k]
if dists[k] < 0.1:
if show_plot:
plt.plot(point_nearest[0],
point_nearest[1],
marker="s",
color="red")
kl, kr = k - 5, k + 5
if kr >= Nt:
kr -= Nt
d = points_s[kr] - points_s[kl]
d[0] /= lx
d[1] /= ly
d = np.array([d[1], -d[0]])
d /= np.linalg.norm(d)
d[0] *= scale * lx
d[1] *= scale * ly
else:
if show_plot:
(line, ) = plt.plot(point_nearest[0],
point_nearest[1],
marker="s")
plt.plot(point[0],
point[1],
marker="o",
color=line.get_color())
d = point_nearest - point
d /= np.linalg.norm(d)
d *= scale * l
point_outside = point_nearest + d
if show_plot:
plt.plot(point_outside[0],
point_outside[1],
marker=".",
color="blue")
offset_points.append(point_outside)
return np.array(offset_points)
def compute(self):
"""ABC API"""
scipy_ConvexHull.__init__(self,
self._points,
self._incremental,
self._qhull_options)