import numpy as np
import pyvista as pv
from scipy.spatial import Delaunay
from scipy.spatial.distance import squareform, pdist
from itertools import product
from ntrfc.utils.pyvista_utils.line import polyline_from_points, refine_spline
def calcConcaveHull(x, y, alpha):
"""
origin: https://stackoverflow.com/questions/50549128/boundary-enclosing-a-given-set-of-points/50714300#50714300
"""
points = []
for i in range(len(x)):
points.append([x[i], y[i]])
points = np.asarray(points)
def alpha_shape(points, alpha, only_outer=True):
"""
Compute the alpha shape (concave hull) of a set of points.
:param points: np.array of shape (n,2) points.
:param alpha: alpha value.
:param only_outer: boolean value to specify if we keep only the outer border
or also inner edges.
:return: set of (i,j) pairs representing edges of the alpha-shape. (i,j) are
the indices in the points array.
"""
assert points.shape[0] > 3, "Need at least four points"
def add_edge(edges, i, j):
"""
Add an edge between the i-th and j-th points,
if not in the list already
"""
if (i, j) in edges or (j, i) in edges:
# already added
assert (j, i) in edges, "Can't go twice over same directed edge right?"
if only_outer:
# if both neighboring triangles are in shape, it's not a boundary edge
edges.remove((j, i))
return
edges.add((i, j))
tri = Delaunay(points)
edges = set()
# Loop over triangles:
# ia, ib, ic = indices of corner points of the triangle
for ia, ib, ic in tri.vertices:
pa = points[ia]
pb = points[ib]
pc = points[ic]
# Computing radius of triangle circumcircle
# www.mathalino.com/reviewer/derivation-of-formulas/derivation-of-formula-for-radius-of-circumcircle
a = np.sqrt((pa[0] - pb[0]) ** 2 + (pa[1] - pb[1]) ** 2)
b = np.sqrt((pb[0] - pc[0]) ** 2 + (pb[1] - pc[1]) ** 2)
c = np.sqrt((pc[0] - pa[0]) ** 2 + (pc[1] - pa[1]) ** 2)
s = (a + b + c) / 2.0
A = (s * (s - a) * (s - b) * (s - c))
if A > 0:
area = np.sqrt(A)
circum_r = a * b * c / (4.0 * area)
if circum_r < alpha:
add_edge(edges, ia, ib)
add_edge(edges, ib, ic)
add_edge(edges, ic, ia)
return edges
def find_edges_with(i, edge_set):
i_first = [j for (x, j) in edge_set if x == i]
i_second = [j for (j, x) in edge_set if x == i]
return i_first, i_second
def stitch_boundaries(edges):
edge_set = edges.copy()
boundary_lst = []
while len(edge_set) > 0:
boundary = []
edge0 = edge_set.pop()
boundary.append(edge0)
last_edge = edge0
while len(edge_set) > 0:
i, j = last_edge
j_first, j_second = find_edges_with(j, edge_set)
if j_first:
edge_set.remove((j, j_first[0]))
edge_with_j = (j, j_first[0])
boundary.append(edge_with_j)
last_edge = edge_with_j
elif j_second:
edge_set.remove((j_second[0], j))
edge_with_j = (j, j_second[0]) # flip edge rep
boundary.append(edge_with_j)
last_edge = edge_with_j
if edge0[0] == last_edge[1]:
break
boundary_lst.append(boundary)
return boundary_lst
edges = alpha_shape(points, alpha)
boundary_lst = stitch_boundaries(edges)
x_new = []
y_new = []
for i in range(len(boundary_lst[0])):
x_new.append(points[boundary_lst[0][i][0]][0])
y_new.append(points[boundary_lst[0][i][0]][1])
return x_new, y_new
def midLength(ind_1, ind_2, sortedPoly):
"""
calc length of a midline
:param ind_1: index LE
:param ind_2: index TE
:param sortedPoly: pv.PolyData sorted
:return: length
"""
psPoly, ssPoly = extractSidePolys(ind_1, ind_2, sortedPoly)
midsPoly = midline_from_sides(ind_1, ind_2, sortedPoly.points, psPoly, ssPoly)
arclength = midsPoly.compute_arc_length()["arc_length"]
midslength = sum(arclength)
return midslength
def midline_from_sides(ind_hk, ind_vk, points, psPoly, ssPoly):
x_ps, y_ps = psPoly.points[::, 0], psPoly.points[::, 1]
x_ss, y_ss = ssPoly.points[::, 0], ssPoly.points[::, 1]
midsres = 100
if x_ps[0] < x_ps[-1]:
ax, ay = refine_spline(x_ps[::-1], y_ps[::-1], midsres)
else:
ax, ay = refine_spline(x_ps, y_ps, midsres)
if x_ss[0] < x_ss[-1]:
bx, by = refine_spline(x_ss[::-1], y_ss[::-1], midsres)
else:
bx, by = refine_spline(x_ss, y_ss, midsres)
xmids, ymids = ((ax + bx) / 2, (ay + by) / 2)
xmids = np.array(xmids)[::-1][1:-1]
ymids = np.array(ymids)[::-1][1:-1]
xmids[0] = points[ind_vk][0]
ymids[0] = points[ind_vk][1]
xmids[-1] = points[ind_hk][0]
ymids[-1] = points[ind_hk][1]
midsPoly = polyline_from_points(np.stack((xmids, ymids, np.zeros(len(ymids)))).T)
return midsPoly
def calc_largedistant_idx(x_koords, y_koords):
A = np.dstack((x_koords, y_koords))[0]
D = squareform(pdist(A))
# N = np.max(D)
I = np.argmax(D)
I_row, I_col = np.unravel_index(I, D.shape)
index_1 = I_row
index_2 = I_col
return index_1, index_2
def extract_vk_hk(sortedPoly, verbose=False):
"""
This function is calculating the leading-edge and trailing edge of a long 2d-body
The function is not 100% reliable yet. The computation is iterative and it can take a while
Points in origPoly and sortedPoly have to have defined points on the LE and TE, otherwise a LE or TE is not defined
and it will be random which point will be found near the LE / TE
:param origPoly: all original points, unsorted
:param sortedPoly: sorted via calcConcaveHull
:param verbose: bool (True -> plots, False -> silent)
:return: returns indexes of LE(vk) and TE(hk) from sortedPoints
"""
xs, ys = sortedPoly.points[::, 0], sortedPoly.points[::, 1]
ind_1, ind_2 = calc_largedistant_idx(xs, ys)
allowed_shift = 1
midLength0 = midLength(ind_1, ind_2, sortedPoly)
nopt = sortedPoly.number_of_points
checked_combs = {}
found = True
while (found):
shifts = np.arange(-allowed_shift, allowed_shift + 1)
ind_1_ts = (shifts + ind_1) % nopt
ind_2_ts = (shifts + ind_2) % nopt
combs = list(product(ind_1_ts, ind_2_ts))
for key in combs:
if key not in checked_combs.keys():
checked_combs[key] = False
midLengths = []
for ind_1_t, ind2_t in combs:
if checked_combs[(ind_1_t, ind2_t)] == False:
checked_combs[(ind_1_t, ind2_t)] = True
midLengths.append(midLength(ind_1_t, ind2_t, sortedPoly))
else:
midLengths.append(0)
cids = midLengths.index(max(midLengths))
ind_1_n, ind_2_n = combs[cids]
midLength_new = midLength(ind_1_n, ind_2_n, sortedPoly)
if midLength_new > midLength0:
ind_1, ind_2 = ind_1_n, ind_2_n
midLength0 = midLength_new
allowed_shift += 1
found = True
else:
found = False
if sortedPoly.points[ind_1][0] > sortedPoly.points[ind_2][0]:
ind_vk = ind_2
ind_hk = ind_1
else:
ind_vk = ind_1
ind_hk = ind_2
return ind_hk, ind_vk
def extractSidePolys(ind_hk, ind_vk, sortedPoly):
xs, ys = list(sortedPoly.points[::, 0]), list(sortedPoly.points[::, 1])
if ind_vk < ind_hk:
x_ss = xs[ind_vk:ind_hk + 1]
y_ss = ys[ind_vk:ind_hk + 1]
y_ps = ys[ind_hk:] + ys[:ind_vk + 1]
x_ps = xs[ind_hk:] + xs[:ind_vk + 1]
else:
x_ss = xs[ind_hk:ind_vk + 1]
y_ss = ys[ind_hk:ind_vk + 1]
y_ps = ys[ind_vk:] + ys[:ind_hk + 1]
x_ps = xs[ind_vk:] + xs[:ind_hk + 1]
psl_helper = polyline_from_points(np.stack((x_ps, y_ps, np.zeros(len(x_ps)))).T)
ssl_helper = polyline_from_points(np.stack((x_ss, y_ss, np.zeros(len(x_ss)))).T)
if psl_helper.length > ssl_helper.length:
psPoly = pv.PolyData(ssl_helper.points)
ssPoly = pv.PolyData(psl_helper.points)
else:
psPoly = pv.PolyData(psl_helper.points)
ssPoly = pv.PolyData(ssl_helper.points)
return ssPoly, psPoly