Newer
Older
from scipy.spatial import Delaunay
from ntrfc.utils.math.vectorcalc import calc_largedistant_idx, vecAngle
from ntrfc.utils.pyvista_utils.line import polyline_from_points, refine_spline
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
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. currently only used in the iterative computation of LE and TE index of a profile. probably
this method is not necessary, as it is only two lines
:param ind_1: index LE
:param ind_2: index TE
:param sortedPoly: pv.PolyData sorted
:return: length
"""
Malte Nyhuis
committed
psPoly, ssPoly = extractSidePolys(ind_1, ind_2, sortedPoly)
midsPoly = midline_from_sides(ind_1, ind_2, sortedPoly.points, psPoly, ssPoly)
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
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 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
"""
Malte Nyhuis
committed
def checkLength(ind_1, ind_2, sortedPoly):
"""
calc length of a midline. currently only used in the iterative computation of LE and TE index of a profile. probably
this method is not necessary, as it is only two lines
: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)
arclengths = midsPoly.compute_arc_length()["arc_length"]
midslength = sum(arclengths)
return midslength
xs, ys = sortedPoly.points[::, 0], sortedPoly.points[::, 1]
ind_1, ind_2 = calc_largedistant_idx(xs, ys)
allowed_shift = 1
Malte Nyhuis
committed
midLength0 = checkLength(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
Malte Nyhuis
committed
midLengths.append(checkLength(ind_1_t, ind2_t, sortedPoly))
else:
midLengths.append(0)
cids = midLengths.index(max(midLengths))
ind_1_n, ind_2_n = combs[cids]
Malte Nyhuis
committed
midLength_new = checkLength(ind_1_n, ind_2_n, sortedPoly)
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
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
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
def extract_geo_paras(points, alpha, verbose=False):
"""
This function is extracting profile-data as stagger-angle, midline, psPoly, ssPoly and more from a set of points
Be careful, you need a suitable alpha-parameter in order to get the right geometry
The calculation of the leading-edge and trailing-edge index needs time and its not 100% reliable (yet)
Keep in mind, to check the results!
:param points: array of points in 3d with the shape (n,3)
:param alpha: nondimensional alpha-coefficient (calcConcaveHull)
:param verbose: bool for plots
:return: points, psPoly, ssPoly, ind_vk, ind_hk, midsPoly, beta_leading, beta_trailing
"""
xs, ys = calcConcaveHull(points[:, 0], points[:, 1], alpha)
points = np.stack((xs, ys, np.zeros(len(xs)))).T
sortedPoly = pv.PolyData(points)
ind_hk, ind_vk = extract_vk_hk( sortedPoly)
psPoly, ssPoly = extractSidePolys(ind_hk, ind_vk, sortedPoly)
midsPoly = midline_from_sides(ind_hk, ind_vk, points, psPoly, ssPoly)
#compute angles from 2d-midline
xmids, ymids = midsPoly.points[::, 0], midsPoly.points[::, 1]
vk_tangent = np.stack((xmids[0] - xmids[1], ymids[0] - ymids[1], 0)).T
hk_tangent = np.stack((xmids[-2] - xmids[-1], ymids[-2] - ymids[-1], 0)).T
camber = np.stack((xmids[0] - xmids[-1], ymids[0] - ymids[-1], 0)).T[::-1]
beta_leading = vecAngle(vk_tangent, np.array([0, 1, 0])) / np.pi * 180
beta_trailing = vecAngle(hk_tangent, np.array([0, 1, 0])) / np.pi * 180
camber_angle = vecAngle(camber, np.array([0, 1, 0])) / np.pi * 180
if verbose:
p = pv.Plotter()
p.add_mesh(points, color="orange", label="points")
p.add_mesh(psPoly, color="green", label="psPoly")
p.add_mesh(ssPoly, color="black", label="ssPoly")
p.add_mesh(midsPoly, color="black", label="midsPoly")
p.add_mesh(pv.Line((0,0,0),(midsPoly.length,0,0)))
p.add_legend()
p.show()
return points, psPoly, ssPoly, ind_vk, ind_hk, midsPoly, beta_leading, beta_trailing, camber_angle