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faster_solver_maybe.py
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import numpy as np
import numpy.ma as ma
import numpy.linalg as LA
import time
from scipy.optimize import LinearConstraint, OptimizeResult, minimize
import coxeter
import rowan
import awkward as ak
#----- messing around -----
big_arr = np.array([
[[[1,2,3],[4,5,6],[1,1,1],[0,0,0]],[[7,8,9],[2,4,6],[1,1,1],[0,0,0]],[[1,3,5],[4,6,8],[1,1,1],[0,0,0]],[[3,5,7],[2,6,9],[1,1,1],[0,0,0]]],
[[[1,2,3],[4,5,6],[1,1,1],[0,0,0]],[[7,8,9],[2,4,6],[1,1,1],[0,0,0]],[[1,3,5],[4,6,8],[1,1,1],[0,0,0]],[[3,5,7],[2,6,9],[1,1,1],[0,0,0]]]
])
img_arr = np.array([
[1,1,1],
[2,2,2]
]).reshape(2,1,1,3)
neg_one_list = [[2,3],[0,2],[1,4,6]]
neg_one_list[0].insert(5, neg_one_list[0][0])
# neg_one_list[:][-1:] = -1
# print('Hello:',neg_one_list)
# print(big_arr * img_arr)
arr = np.array([
[1,200,3.37521],
[3,5,7]
])
tile = np.tile(arr, (3,1))
# print(tile)
repeat = np.repeat(arr, 3, axis=0)
# print(repeat)
# print(ak.sum(ak.Array(arr * ak.Array([1,2,2])), axis=1, highlevel=False))
variable = ak.to_list(ak.sum(arr * np.array([1,2,2]), axis=1))
# print(variable)
variable_ak = ak.Array([variable])
# print(variable_ak)
# print(ak.to_numpy(variable_ak))
# print(ak.Array([2, 3.521987, 94.19348]))
test = ak.Array([
[[1,2,3], [4,5,6],[7,8,9]],
[[9,4,5]],
[[3,7,5], [8,5,2]]
])
test_broadcast = ak.broadcast_fields(np.array([2,2.5672,9.2538]), test)
# print(test_broadcast)
test0 = test*ak.Array([2,2.5672,9.2538])
# print(test0[0])
test_bool = test == ak.Array([1,2,3])
# test_np = ak.pad_none(test, 3, axis=1)
# test_np.show()
# test_np = ak.to_numpy(test_np)
# print(test_np)
# print(test_np + np.array([1,3,4.5]))
test_num = ak.num(test, axis=1)
# print(test_num)
# test_num_tot = ak.sum(test_num)
# test_vect_diff = np.tile(np.array([[1,1,0],[0,2,-1]]).reshape(2,1,3), (1, test_num_tot, 1))
# print(test_vect_diff)
# test_unflatten = ak.unflatten(test_vect_diff, ak.flatten(ak.Array([test_num, test_num])), axis=1)
# big_test = ak.Array([test, test])
# print(ak.sum(big_test * test_unflatten, axis=3))
# print(test[test_bool])
up_test = ak.Array([
[15, 30, 42],
[37],
[30, 28]
])
# print(test0 <= up_test)
con_col1 = ak.Array([
[[1,2,3]],
[[9,4,5]],
[[2,7,5]]
])
con_col2 = ak.Array([
[[4,5,6], [7,8,9], [3,5,7]],
[[2,4,1], [], []],
[[], [8,5,2], [6,9,2]]
])
con_col3 = ak.Array([
[[], []],
[[2,5,0], []],
[[1,0,6], [8,6,9]]
])
con_mat = ak.concatenate((con_col1, con_col2, con_col3), axis=1)
con_counts = ak.num(con_mat, axis=2)
con_counts = ak.flatten(con_counts[con_counts != 0])
con_mat = ak.flatten(con_mat, axis=2)
con_mat = ak.unflatten(con_mat, con_counts, axis=1)
# print(con_mat[0])
# print(con_mat[1])
# print(con_mat[2])
none_ak = ak.Array([
[[], [], []]
])
none_counts = ak.num(none_ak, axis=2)
none_counts = ak.flatten(none_counts[none_counts != 0])
none_ak = ak.flatten(none_ak, axis=2)
none_ak = ak.unflatten(none_ak, none_counts, axis=1)
# print(none_ak)
#
start = time.time()
first_list = []
for i in (-1, 0, 1):
for j in (-1, 0, 1):
for k in (-1, 0, 1):
first_list.append((i, j, k))
# print( i, j, k)
middle = time.time()
ijk_list = np.array([
(-1, -1, -1), (-1, -1, 0), (-1, -1, 1),
(-1, 0, -1), (-1, 0, 0), (-1, 0, 1),
(-1, 1, -1), (-1, 1, 0), (-1, 1, 1),
(0, -1, -1), (0, -1, 0), (0, -1, 1),
(0, 0, -1), (0, 0, 0), (0, 0, 1),
(0, 1, -1), (0, 1, 0), (0, 1, 1),
(1, -1, -1), (1, -1, 0), (1, -1, 1),
(1, 0, -1), (1, 0, 0), (1, 0, 1),
(1, 1, -1), (1, 1, 0), (1, 1, 1)
])
second_list = []
for ijk in ijk_list:
second_list.append(ijk)
# print(ijk[0], ijk[1], ijk[2])
end = time.time()
# print('First time:', middle-start)
# print('Second time:', end-middle)
# print('Difference in time:', (middle-start)/(end-middle))
def distance_point_point (pt1, pt2):
v = pt2 - pt1
return np.sqrt(v[0]**2 + v[1]**2 + v[2]**2)
def distance_point_point_multiple (pts1, pts2):
v = pts2 - pts1
# print(v)
output = np.sqrt(v[:,0]**2 + v[:,1]**2 + v[:,2]**2)
# print(output)
return output
def distance_point_point_new_maybe (pt1, pt2):
if len(pt1) > 3 and len(pt1)%3 == 0:
pts1 = pt1.reshape((int(len(pt1)/3), 3))
pts2 = pt2.reshape((len(pts1),3))
v = pts2 - pts1
output = np.min(np.sqrt(v[:,0]**2 + v[:,1]**2 + v[:,2]**2))
else:
v = pt2 - pt1
output = np.sqrt(v[0]**2 + v[1]**2 + v[2]**2)
return output
points1 = np.array([
[0,0,0],
[1,0,0],
[0,1,0],
[0,0,1],
[1,1,0],
[1,0,1],
[0,1,1],
[1,1,1],
[2,0,0],
[0,2,0],
[0,0,2],
[2,2,0],
[2,0,2],
[0,2,2],
[2,1,1],
[1,2,1],
[1,1,2],
[2,2,1],
[2,1,2],
[1,2,2],
[2,2,2],
[2,2,3],
[3,1,1],
[1,3,1],
[1,1,3],
[3,3,1],
[3,1,3],
[1,3,3],
[3,2,2],
[3,3,2],
[3,3,3],
[4,3,3],
[4,4,3],
[4,4,4],
[5,4,4],
[5,5,4],
[5,5,5],
[6,5,5],
[6,6,5],
[6,6,6],
])
points1 = np.asarray(list(points1) * 5)
shape_pos = np.array([
[2,2,2],[4,4,3],
# [2,2,2],[4,4,3],
# [2,2,2],[4,4,3],
# [2,2,2],[4,4,3],
# [2,2,2],[4,4,3],
# [2,2,2],[4,4,3],
])
vertices = [
#Jen Shape 1
# [-0.67167939, -0.13433588, 0.26867175],
# [-0.67167939, 0.13433588, -0.26867175],
# [-0.50375954, -0.50375954, 0.50375954],
# [-0.50375954, 0.50375954, -0.50375954],
# [-0.33583969, -0.33583969, -0.33583969],
# [-0.33583969, 0.33583969, 0.33583969],
# [-0.26867175, -0.67167939, 0.13433588],
# [-0.26867175, 0.67167939, -0.13433588],
# [-0.13433588, -0.26867175, 0.67167939],
# [-0.13433588, 0.26867175, -0.67167939],
# [ 0.13433588, -0.26867175, -0.67167939],
# [ 0.13433588, 0.26867175, 0.67167939],
# [ 0.26867175, -0.67167939, -0.13433588],
# [ 0.26867175, 0.67167939, 0.13433588],
# [ 0.33583969, -0.33583969, 0.33583969],
# [ 0.33583969, 0.33583969, -0.33583969],
# [ 0.50375954, -0.50375954, -0.50375954],
# [ 0.50375954, 0.50375954, 0.50375954],
# [ 0.67167939, -0.13433588, -0.26867175],
# [ 0.67167939, 0.13433588, 0.26867175]
#Jen Shape 2
# [-0.71962257, -0.28497054, 0.28784903],
# [-0.71962257, 0.28497054, -0.28784903],
# [-0.71258997, -0.71258997, 0.71258997],
# [-0.71258997, 0.71258997, -0.71258997],
# [-0.28784903, -0.71962257, 0.28497054],
# [-0.28784903, 0.71962257, -0.28497054],
# [-0.28497054, -0.28784903, 0.71962257],
# [-0.28497054, 0.28784903, -0.71962257],
# [-0.24279215, -0.24279215, -0.24279215],
# [-0.24279215, 0.24279215, 0.24279215],
# [ 0.24279215, -0.24279215, 0.24279215],
# [ 0.24279215, 0.24279215, -0.24279215],
# [ 0.28497054, -0.28784903, -0.71962257],
# [ 0.28497054, 0.28784903, 0.71962257],
# [ 0.28784903, -0.71962257, -0.28497054],
# [ 0.28784903, 0.71962257, 0.28497054],
# [ 0.71258997, -0.71258997, -0.71258997],
# [ 0.71258997, 0.71258997, 0.71258997],
# [ 0.71962257, -0.28497054, -0.28784903],
# [ 0.71962257, 0.28497054, 0.28784903]
#Jen Shape 3
# [-0.68808966, 0. , -0.34404483],
# [-0.68808966, 0. , 0.34404483],
# [-0.34404483, -0.59590312, -0.34404483],
# [-0.34404483, -0.59590312, 0.34404483],
# [-0.34404483, 0.59590312, -0.34404483],
# [-0.34404483, 0.59590312, 0.34404483],
# [ 0.34404483, -0.59590312, -0.34404483],
# [ 0.34404483, -0.59590312, 0.34404483],
# [ 0.34404483, 0.59590312, -0.34404483],
# [ 0.34404483, 0.59590312, 0.34404483],
# [ 0.68808966, 0. , -0.34404483],
# [ 0.68808966, 0. , 0.34404483],
# [-0.93743438, 0.54122799, 0. ],
# [ 0.93743438, 0.54122799, 0. ]
#Jen Shape 4
[-0.15009435, -0.15009435, -0.63580989],
[-0.15009435, -0.15009435, 0.63580989],
[-0.15009435, 0.15009435, -0.63580989],
[-0.15009435, 0.15009435, 0.63580989],
[-0.15009435, -0.63580989, -0.15009435],
[-0.15009435, 0.63580989, -0.15009435],
[ 0. , -0.39295212, -0.54304647],
[ 0. , 0.39295212, -0.54304647],
[ 0.15009435, -0.15009435, -0.63580989],
[ 0.15009435, -0.15009435, 0.63580989],
[ 0.15009435, 0.15009435, -0.63580989],
[ 0.15009435, 0.15009435, 0.63580989],
[ 0.15009435, -0.63580989, -0.15009435],
[ 0.15009435, 0.63580989, -0.15009435],
[-0.54304647, 0. , -0.39295212],
[-0.54304647, 0. , 0.39295212],
[-0.24285777, -0.48571553, -0.39295212],
[-0.24285777, 0.48571553, -0.39295212],
[-0.48571553, -0.39295212, -0.24285777],
[-0.48571553, -0.39295212, 0.24285777],
[-0.48571553, 0.39295212, -0.24285777],
[-0.48571553, 0.39295212, 0.24285777],
[-0.63580989, -0.15009435, -0.15009435],
[-0.63580989, -0.15009435, 0.15009435],
[-0.63580989, 0.15009435, -0.15009435],
[-0.63580989, 0.15009435, 0.15009435],
[-0.39295212, -0.54304647, 0. ],
[-0.39295212, -0.24285777, -0.48571553],
[-0.39295212, -0.24285777, 0.48571553],
[-0.39295212, 0.24285777, -0.48571553],
[-0.39295212, 0.24285777, 0.48571553],
[-0.39295212, 0.54304647, 0. ],
[ 0.24285777, -0.48571553, -0.39295212],
[ 0.24285777, 0.48571553, -0.39295212],
[ 0.48571553, -0.39295212, -0.24285777],
[ 0.48571553, -0.39295212, 0.24285777],
[ 0.48571553, 0.39295212, -0.24285777],
[ 0.48571553, 0.39295212, 0.24285777],
[ 0.63580989, -0.15009435, -0.15009435],
[ 0.63580989, -0.15009435, 0.15009435],
[ 0.63580989, 0.15009435, -0.15009435],
[ 0.63580989, 0.15009435, 0.15009435],
[ 0.39295212, -0.54304647, 0. ],
[ 0.39295212, -0.24285777, -0.48571553],
[ 0.39295212, -0.24285777, 0.48571553],
[ 0.39295212, 0.24285777, -0.48571553],
[ 0.39295212, 0.24285777, 0.48571553],
[ 0.39295212, 0.54304647, 0. ],
[ 0.54304647, 0. , -0.39295212],
[ 0.54304647, 0. , 0.39295212]
#Dodecahedron
# (0.5, 0.5, 0.5),
# (-0.5, 0.5, 0.5),
# (-0.5, -0.5, 0.5),
# (-0.5, 0.5, -0.5),
# (0.5, -0.5, 0.5),
# (0.5, -0.5, -0.5),
# (0.5, 0.5, -0.5),
# (-0.5, -0.5, -0.5),
# (0, 0.5/((1+np.sqrt(5))*0.5), 0.5*((1+np.sqrt(5))*0.5)),
# (0, -0.5/((1+np.sqrt(5))*0.5), 0.5*((1+np.sqrt(5))*0.5)),
# (0, 0.5/((1+np.sqrt(5))*0.5), -0.5*((1+np.sqrt(5))*0.5)),
# (0, -0.5/((1+np.sqrt(5))*0.5), -0.5*((1+np.sqrt(5))*0.5)),
# (0.5/((1+np.sqrt(5))*0.5), 0.5*((1+np.sqrt(5))*0.5), 0),
# (-0.5/((1+np.sqrt(5))*0.5), 0.5*((1+np.sqrt(5))*0.5), 0),
# (0.5/((1+np.sqrt(5))*0.5), -0.5*((1+np.sqrt(5))*0.5), 0),
# (-0.5/((1+np.sqrt(5))*0.5), -0.5*((1+np.sqrt(5))*0.5), 0),
# (0.5*((1+np.sqrt(5))*0.5), 0, 0.5/((1+np.sqrt(5))*0.5)),
# (-0.5*((1+np.sqrt(5))*0.5), 0, 0.5/((1+np.sqrt(5))*0.5)),
# (0.5*((1+np.sqrt(5))*0.5), 0, -0.5/((1+np.sqrt(5))*0.5)),
# (-0.5*((1+np.sqrt(5))*0.5), 0, -0.5/((1+np.sqrt(5))*0.5)),
#Tetrahedron
# (0, 0, 0.5),
# (0, 0.7071, -0.5),
# (0.5*np.sqrt(3/2), -0.3535, -0.5),
# (-0.5*np.sqrt(3/2), -0.3535, -0.5),
#Octahedron
# (-0.5, 0, 0),
# (0.5, 0, 0),
# (0, -0.5, 0),
# (0, 0.5, 0),
# (0, 0, -0.5),
# (0, 0, 0.5),
#Cube
# (0.5, 0.5, 0.5),
# (-0.5, 0.5, 0.5),
# (-0.5, -0.5, 0.5),
# (-0.5, 0.5, -0.5),
# (0.5, -0.5, 0.5),
# (0.5, -0.5, -0.5),
# (0.5, 0.5, -0.5),
# (-0.5, -0.5, -0.5),
]
orientations = [
(1,0,0,0), (0.3647046, 0.1159188, -0.2798528, 0.8804747),
# (1,0,0,0), (0.3647046, 0.1159188, -0.2798528, 0.8804747),
# (1,0,0,0), (0.3647046, 0.1159188, -0.2798528, 0.8804747),
# (1,0,0,0), (0.3647046, 0.1159188, -0.2798528, 0.8804747),
# (1,0,0,0), (0.3647046, 0.1159188, -0.2798528, 0.8804747),
# (1,0,0,0), (0.3647046, 0.1159188, -0.2798528, 0.8804747),
]
shapes = []
new_halfspaces = []
for i, pos in enumerate(shape_pos):
rot_vert = rowan.rotate(orientations[i], vertices)
tmpshape = coxeter.shapes.ConvexPolyhedron(vertices=rot_vert)
normals = tmpshape.normals
num_faces = tmpshape.num_faces
face_dist = np.sum(tmpshape.face_centroids*normals, axis=1)
dx = 0.001
norms = np.asarray(tmpshape.normals)
tmpcentroid = np.asarray(tmpshape.centroid)
norm_dists = []
for norm in norms:
x = tmpcentroid
dx_n = 0
while tmpshape.is_inside(x):
dx_n = dx_n + 1
x = tmpcentroid + dx_n * dx * norm
norm_dists.append((dx_n - 1) * dx)
halfspace = []
image_diff = [[6,0,0], [0,0,0], [-6,0,0]]
for image in image_diff:
position = pos + image
upper_bounds = normals.dot(position) + face_dist
smile = np.block([normals, upper_bounds.reshape((num_faces,1))])
halfspace.append(smile)
new_halfspaces.append(halfspace)
shapes.append(tmpshape)
new_halfspaces = np.asarray(new_halfspaces)
# new_halfspaces = np.array([
# [[[0,0,1, 2.5],[0,0,-1, -1.5],[1,0,0, 8.5],
# [-1,0,0, -7.5],[0,1,0, 2.5],[0,-1,0, -1.5]],
# [[0,0,1, 2.5],[0,0,-1, -1.5],[1,0,0, 2.5],
# [-1,0,0, -1.5],[0,1,0, 2.5],[0,-1,0, -1.5]],
# [[0,0,1, 2.5],[0,0,-1, -1.5],[1,0,0, -3.5],
# [-1,0,0, 4.5],[0,1,0, 2.5],[0,-1,0, -1.5]]],
# [[[ 1/np.sqrt(3), 1/np.sqrt(3), 1/np.sqrt(3), 10.315],
# [-1/np.sqrt(3),-1/np.sqrt(3),-1/np.sqrt(3), -9.315],
# [ 1/np.sqrt(3), 1/np.sqrt(3),-1/np.sqrt(3), 6.851],
# [-1/np.sqrt(3),-1/np.sqrt(3), 1/np.sqrt(3), -5.851],
# [ 1/np.sqrt(2),-1/np.sqrt(2), 0, 4.743],
# [-1/np.sqrt(2), 1/np.sqrt(2), 0, -3.743]],
# [ [ 1/np.sqrt(3), 1/np.sqrt(3), 1/np.sqrt(3), 6.851],
# [-1/np.sqrt(3),-1/np.sqrt(3),-1/np.sqrt(3), -5.851],
# [ 1/np.sqrt(3), 1/np.sqrt(3),-1/np.sqrt(3), 3.387],
# [-1/np.sqrt(3),-1/np.sqrt(3), 1/np.sqrt(3), -2.387],
# [ 1/np.sqrt(2),-1/np.sqrt(2), 0, 0.5],
# [-1/np.sqrt(2), 1/np.sqrt(2), 0, 0.5]],
# [ [ 1/np.sqrt(3), 1/np.sqrt(3), 1/np.sqrt(3), 3.387],
# [-1/np.sqrt(3),-1/np.sqrt(3),-1/np.sqrt(3), -2.387],
# [ 1/np.sqrt(3), 1/np.sqrt(3),-1/np.sqrt(3), -0.207],
# [-1/np.sqrt(3),-1/np.sqrt(3), 1/np.sqrt(3), 1.207],
# [ 1/np.sqrt(2),-1/np.sqrt(2), 0, -3.743],
# [-1/np.sqrt(2), 1/np.sqrt(2), 0, 4.743]]],
# ])
# print(new_halfspaces.shape)
# halfspaces_ub = new_halfspaces[0][:,-1]
# halfspaces_values = []
# for i in new_halfspaces:
# halfspaces_values.append(i[:,:-1].flatten())
# halfspaces_values = np.array(halfspaces_values)
# print(halfspaces_values)
# constraint = LinearConstraint(new_halfspaces[0], -np.inf, 6)
# # print(constraint.residual(3))
# other_constraint = (-np.inf<=new_halfspaces.dot(3))*(new_halfspaces.dot(3)<=6)
# print((-np.inf<=new_halfspaces.dot(3))*(new_halfspaces.dot(3)<=6))
#----- Current Min Dist Calculations -----
current_start = time.time()
r_list = []
for s, x in enumerate(shape_pos):
r = []
for i in range(len(points1)):
min_list = []
x_list = []
for n in new_halfspaces[s]:
current_min = minimize(
fun=distance_point_point,
x0=np.zeros(3),
args=(points1[i],),
constraints=[LinearConstraint(n[:,:-1], -np.inf, n[:,-1])],
tol = 0.0000000001
)
if current_min.success == False:
print(current_min.message)
# print(n[:,:-1].dot(current_min.x) <= n[:,-1])
min_list.append(current_min.fun)
# x_list.append(current_min.x)
# print('min',np.asarray(min_list))
# print('x',np.asarray(x_list))
r.append(np.min(min_list))
r_list.append(np.asarray(r))
r_list = np.asarray(r_list)
# print(r_list.shape)
current_end = time.time()
def hell_if_i_know (pts1, pts2):
diff = pts2 - pts1
mag = np.sqrt(np.sum(diff**2))
return mag
def uhhh (pts1, pt2):
width = int(len(pts1)/3)
pts1 = pts1.reshape((width, 3))
pts2 = np.tile(pt2, width).reshape((width, 3))
diff = pts2 - pts1
mag = np.sqrt(np.sum(diff**2, axis=1))
return mag
def why_not (q, A, a):
result = A.dot(q)
diff = a - result
mag = np.sqrt(np.sum(diff**2))
return mag
n_faces = len(new_halfspaces[0][0])
n_shapes = len(shape_pos)
n_constraints = 3
new_mega_ub = []
for zeros_l in range(n_shapes*n_constraints):
shape_ind = zeros_l//n_constraints
constraint_ind = zeros_l%n_constraints
zeros_w = n_shapes*n_constraints-zeros_l-1
if zeros_l == 0:
block = np.block([
[new_halfspaces[shape_ind][constraint_ind,:,:-1], np.zeros((n_faces, zeros_w*3))]
])
elif zeros_l == (n_shapes*3)-1:
block = np.block([
[new_mega_matrix],
[np.zeros((n_faces, zeros_l*3)), new_halfspaces[shape_ind][constraint_ind,:,:-1]]
])
else:
block = np.block([
[new_mega_matrix],
[np.zeros((n_faces, zeros_l*3)), new_halfspaces[shape_ind][constraint_ind,:,:-1],np.zeros((n_faces, zeros_w*3))]
])
new_mega_matrix = block
new_mega_ub.append(new_halfspaces[shape_ind][constraint_ind,:,-1])
new_mega_ub = np.asarray(new_mega_ub).flatten()
# print(new_mega_matrix.shape)
# print(new_mega_ub.shape)
#----- New Min Dist Calculations -----
new_start = time.time()
# r_list_new = []
# for i in range(len(points1)):
# xp_min = minimize(
# fun=hell_if_i_know,
# x0=np.zeros(n_shapes*n_constraints*3),
# args=(np.tile(points1[i],(n_shapes*n_constraints))),
# constraints=[LinearConstraint(new_mega_matrix, -np.inf, new_mega_ub)]
# )
# xp_min_list = uhhh(xp_min.x, points1[i])
# find_min = np.min(xp_min_list.reshape((n_shapes, n_constraints)), axis=1)
# r_list_new.append(find_min)
# r_list_new = np.asarray(r_list_new)
# r_list_new = np.transpose(r_list_new)
new_end = time.time()
#----- Other New Dist Calculations -----
other_start = time.time()
other_r_list = []
for s, x in enumerate(shape_pos):
other_r = []
for i in range(len(points1)):
# other_mega_matrix = np.block([
# [new_halfspaces[s][0,:,:-1], np.zeros((n_faces, 6))],
# [np.zeros((n_faces,3)),new_halfspaces[s][1,:,:-1],np.zeros((n_faces,3))],
# [np.zeros((n_faces,6)),new_halfspaces[s][2,:,:-1]]
# ])
# other_mega_ub = np.array([new_halfspaces[s][0,:,-1], new_halfspaces[s][1,:,-1], new_halfspaces[s][2,:,-1]]).flatten()
images_pos = (x+np.array([6,0,0]), x, x+np.array([-6,0,0]))
dist_images_list = np.sqrt(np.sum((images_pos - points1[i])**2, axis=1))
con_ind = np.argmin(dist_images_list)
other_min = minimize(
fun=distance_point_point,
x0=np.zeros(3),
args=(points1[i],),
constraints=[LinearConstraint(new_halfspaces[s][con_ind,:,:-1],-np.inf,new_halfspaces[s][con_ind,:,-1])]
)
other_min_list = uhhh(other_min.x, points1[i])
# # print(n[:,:-1].dot(current_min.x) <= n[:,-1])
# min_list.append(current_min.fun)
# # x_list.append(current_min.x)
# # print('min',np.asarray(min_list))
# # print('x',np.asarray(x_list))
other_r.append(np.min(other_min_list))
other_r_list.append(np.asarray(other_r))
other_r_list = np.asarray(other_r_list)
# print(r_list.shape)
other_end = time.time()
def get_edge_face_neighbors (shape):
# face_ragged_list = shape.faces
# new_ragged_list = np.array([])
# for rag_i in range(len(face_ragged_list)):
# new_arr = np.append(face_ragged_list[rag_i],np.array([face_ragged_list[rag_i][0], -1]))
# new_ragged_list = np.append(new_ragged_list, new_arr)
# list_len = len(new_ragged_list)
# print(new_ragged_list)
# face_edge_mat = np.block([new_ragged_list[:-1].reshape(list_len-1,1), new_ragged_list[1:].reshape(list_len-1,1)])
# print(face_edge_mat.shape)
faces = ak.Array(shape.faces)
faces_len = shape.num_faces
num_edges = shape.num_edges
faces_plus = ak.concatenate((faces, ak.to_numpy(faces[:,0]).reshape(faces_len,1), np.array([-1]*faces_len).reshape(faces_len,1)), axis=1)
faces_flat = ak.to_numpy(ak.flatten(faces_plus))
list_len = len(faces_flat)
face_edge_mat = np.block([faces_flat[:-1].reshape(list_len-1,1), faces_flat[1:].reshape(list_len-1,1)])
fe_mat_inds = np.arange(0,list_len-1,1)
find_num_edges = fe_mat_inds[(fe_mat_inds==0) + (np.any(face_edge_mat==-1, axis=1))]
find_num_edges[:][0] = -1
find_num_edges = find_num_edges.reshape(faces_len,2)
face_num_edges = find_num_edges[:,1] - find_num_edges[:,0] -1
face_correspond_inds = np.repeat(np.arange(0,faces_len,1), face_num_edges)
# print(face_correspond_inds)
true_face_edge_mat = np.tile(face_edge_mat[np.all(face_edge_mat!=-1, axis=1)].reshape(num_edges*2,1,2), (1, num_edges,1))
# edge_ind_bool0 = np.any(np.all(true_face_edge_mat == shape.edges.reshape(1, num_edges, 2), axis=2), axis=1)
# ef_sort_bool0 = np.all(true_face_edge_mat == shape.edges.reshape(1, num_edges, 2), axis=2)
# edges1_reshape = np.hstack(((shape.edges[:,1]).reshape(num_edges,1), (shape.edges[:,0]).reshape(num_edges,1)))
# edge_ind_bool1 = np.any(np.all(true_face_edge_mat == edges1_reshape.reshape(1,num_edges,2), axis=2), axis=1)
# ef_sort_bool1 = np.all(true_face_edge_mat == edges1_reshape.reshape(1,num_edges,2), axis=2)
# ef_sort = np.tile(np.arange(0, num_edges, 1), (num_edges*2, 1))
# print(ef_sort[ef_sort_bool1])
# print(ef_sort[ef_sort_bool0])
# print(face_correspond_inds[edge_ind_bool0])
# print(edge_ind_bool)
# print(true_face_edge_mat.shape)
edges1_reshape = np.hstack(((shape.edges[:,1]).reshape(num_edges,1), (shape.edges[:,0]).reshape(num_edges,1)))
new_edge_ind_bool0 = np.all(true_face_edge_mat == shape.edges.reshape(1, num_edges, 2), axis=2)
new_edge_ind_bool1 = np.all(true_face_edge_mat == edges1_reshape.reshape(1,num_edges,2), axis=2)
new_face_corr_inds = np.tile(face_correspond_inds.reshape(2*num_edges,1), (1,num_edges))
ef_neighbor0 = np.sum(new_face_corr_inds*new_edge_ind_bool0, axis=0).reshape(num_edges, 1)
ef_neighbor1 = np.sum(new_face_corr_inds*new_edge_ind_bool1, axis=0).reshape(num_edges, 1)
ef_neighbor = np.hstack((ef_neighbor0, ef_neighbor1))
# face_inds = np.arange(0, shape.num_faces, 1)
# edge_face_neighbors = []
# for edge in shape.edges:
# edge1_bool = faces == edge[0]
# edge2_bool = faces == edge[1]
# check_edge = ak.sum(edge1_bool + edge2_bool, axis=1) == 2
# neighbors = face_inds[check_edge]
# sum_edges = edge1_bool + edge2_bool
# face_verts = faces[sum_edges * check_edge]
# flat_face_verts = ak.ravel(face_verts)
# reshape_face_verts = np.array(flat_face_verts).reshape((2,2))
# # print(reshape_face_verts)
# face_verts_bool = (reshape_face_verts != edge)[:,0] +1 -1
# face_all_verts0 = np.array(faces[check_edge][:,0]).reshape((2,1))
# face_all_verts_last = np.array(faces[check_edge][:,-1]).reshape((2,1))
# first_last_verts = np.block([face_all_verts0, face_all_verts_last])
# # print(first_last_verts)
# ind_edge_bool = (np.sum(first_last_verts == edge, axis=1) == 2) +1 -1
# switch_neighbor_bool = face_verts_bool + ind_edge_bool
# # print('edge', edge)
# # print('switch bool', switch_neighbor_bool)
# # print('previous neighbor', neighbors)
# neighbors = neighbors[switch_neighbor_bool]
# # print('new neighbor', neighbors)
# edge_face_neighbors.append(neighbors)
# edge_face_neighbors = np.asarray(edge_face_neighbors)
# print(np.all(edge_face_neighbors == ef_neighbor))
# print('old', edge_face_neighbors)
return ef_neighbor
def bounds_for_images (bounds, constraint):
#for the EBT code, will need lx, ly, lz, a, b, & c variables
# con_num = ak.num(constraint, axis=1)
# con_num_sum = ak.sum(con_num)
# image_diff = np.tile(np.array([[6,0,0], [0,0,0], [-6,0,0]]).reshape(3,1,3), (1,con_num_sum, 1))
# big_con_num = ak.flatten(ak.Array([con_num, con_num, con_num]))
# image_diff_unflatten = ak.unflatten(image_diff, big_con_num, axis=1)
big_bounds = np.array([bounds, bounds, bounds])
big_constraint = np.array([constraint, constraint, constraint])
image_diff = np.array([[6,0,0],[0,0,0],[-6,0,0]]).reshape(3,1,1,3)
new_bounds = big_bounds + (np.sum(big_constraint * image_diff, axis=3))
return new_bounds
def point_to_edge_distance (point, vert, edge_vector, multiple=False):
if multiple:
edge_units = edge_vector / LA.norm(edge_vector, axis=1).reshape(len(edge_vector), 1)
dist = LA.norm(((vert - point) - (np.sum((vert-point)*edge_units, axis=1).reshape(len(edge_vector),1) *edge_units)), axis=1)
return dist
edge_vect_mag = LA.norm(edge_vector)
if edge_vect_mag == 0:
return
edge_unit = edge_vector / edge_vect_mag
dist = LA.norm((vert - point) - ((vert - point).dot(edge_unit)*edge_unit))
return dist
def point_to_face_distance(point, vert, face_normal, multiple=False):
if multiple:
vert_point_vect = -1*vert + point
face_unit = face_normal / LA.norm(face_normal, axis=1).reshape(len(face_normal), 1)
dist = np.sum(vert_point_vect*face_unit, axis=1)
return dist
vert_point_vect = point - vert
face_unit = face_normal / LA.norm(face_normal)
dist = vert_point_vect.dot(face_unit)
return dist
def get_vert_boundaries (shp_vert, shp_edges, shp_edge_vert, n_verts, n_edges, x):
#Tiling for set up
nverts_edge_vert0 = np.tile(shp_edge_vert[:,0], (n_verts, 1))
nverts_edge_vert1 = np.tile(shp_edge_vert[:,1], (n_verts, 1))
vert_inds = np.arange(0, n_verts, 1).reshape((n_verts, 1))
nverts_tile_edges = np.tile(shp_edges, (n_verts, 1)).reshape((n_verts, n_edges, 3))
#Creating the bools need to get the edges that correspond to each vertice
evbool0 = np.expand_dims(nverts_edge_vert0 == vert_inds, axis=2)
evbool1 = np.expand_dims(nverts_edge_vert1 == vert_inds, axis=2)
#Removing the None values from the ak arrays
ak_vert_neg = nverts_tile_edges * evbool0
ak_vert_pos = nverts_tile_edges * evbool1 * (-1)
#Concatenating the ak arrays together to make the vertice constraint array | shape:(n_vert, #, 3)
vert_constraint = ak.to_numpy(ak_vert_neg + ak_vert_pos)
#Building the boundary conditions
vert_bounds = np.sum(vert_constraint * (shp_vert+x).reshape(n_verts,1,3), axis=2)
return vert_constraint, vert_bounds
def get_edge_boundaries (shp_vert, shp_edges, shp_faces, shp_edge_vert, shp_edge_face, n_edges, x):
new_edge_constraint = np.zeros((n_edges, 4, 3))
new_edge_bounds = np.zeros((n_edges, 4))
edge_constraint_col_1 = shp_edges
edge_constraint_col_2 = -1*shp_edges
edge_constraint_col_3 = np.cross(shp_edges, shp_faces[shp_edge_face[:,1]])
edge_constraint_col_4 = -1*np.cross(shp_edges, shp_faces[shp_edge_face[:,0]])
new_edge_constraint[:,0] = edge_constraint_col_1
new_edge_constraint[:,1] = edge_constraint_col_2
new_edge_constraint[:,2] = edge_constraint_col_3
new_edge_constraint[:,3] = edge_constraint_col_4
new_edge_verts = np.zeros((n_edges, 2, 3))
new_edge_verts[:,0] = shp_vert[shp_edge_vert[:,0]] + x
new_edge_verts[:,1] = shp_vert[shp_edge_vert[:,1]] + x
edge_bounds_1 = np.sum(new_edge_constraint[:,0] *(new_edge_verts[:,1]), axis=1)
edge_bounds_2 = np.sum(new_edge_constraint[:,1] *(new_edge_verts[:,0]), axis=1)
edge_bounds_3 = np.sum(new_edge_constraint[:,2] *(new_edge_verts[:,0]), axis=1)
edge_bounds_4 = np.sum(new_edge_constraint[:,3] *(new_edge_verts[:,0]), axis=1)
new_edge_bounds[:,0] = edge_bounds_1
new_edge_bounds[:,1] = edge_bounds_2
new_edge_bounds[:,2] = edge_bounds_3
new_edge_bounds[:,3] = edge_bounds_4
return new_edge_constraint, new_edge_bounds
def get_face_boundaries (shp_vert, shp_edges, shp_faces, shp_edge_vert, shp_edge_face, n_edges, n_faces, x, face_centroids):
#Setting up
nfaces_tile_edges = np.tile(shp_edges, (n_faces, 1)).reshape((n_faces, n_edges, 3)) #Edge vectors tiled
nfaces_tile_efneighbors = np.tile(shp_edge_face, (n_faces, 1)) #Tiling shp_edge_face so that it is now shape (n_faces, n_edges, 2)
efneighbors0 = nfaces_tile_efneighbors[:,0].reshape((n_faces, n_edges)) #breaking nfaces_tile_efneighbors into the first column [0]
efneighbors1 = nfaces_tile_efneighbors[:,1].reshape((n_faces, n_edges)) #second column [1] of nfaces_tile_efneighbors
faces_inds = np.arange(0, n_faces, 1).reshape((n_faces, 1)) #Making an array containing the indices of the faces
#Creating bools to find the edges that correspond to each face
efbool0 = (efneighbors0 == faces_inds)
efbool1 = (efneighbors1 == faces_inds)
ak_edges_mask0 = nfaces_tile_edges * efbool0.reshape((n_faces, n_edges, 1))
ak_edges_mask1 = nfaces_tile_edges * efbool1.reshape((n_faces, n_edges, 1))
faces_repeat = np.repeat(shp_faces, n_edges, axis=0).reshape((n_faces, n_edges, 3))
neg_constraints = np.cross(ak_edges_mask0, faces_repeat)
pos_constraints = -1* np.cross(ak_edges_mask1, faces_repeat)
face_normals = -1* shp_faces
new_face_constraints = np.zeros((n_faces, n_edges+1, 3))
new_face_constraints[:,0] = face_normals
new_face_constraints[:,1:] = neg_constraints + pos_constraints
#bounds
nfaces_tile_evneighbors = np.tile(shp_edge_vert, (n_faces, 1)).reshape((n_faces, n_edges, 2))
neg_face_verts = (shp_vert[(nfaces_tile_evneighbors[:,:,0]*efbool0)] + x)
pos_face_verts = (shp_vert[(nfaces_tile_evneighbors[:,:,1]*efbool1)] + x)
neg_bounds = np.sum(neg_constraints * neg_face_verts, axis=2)
pos_bounds = np.sum(pos_constraints * pos_face_verts, axis=2)
norm_distances = (face_centroids + x)
normal_bounds = np.sum(face_normals*norm_distances, axis=1)
new_face_bounds = np.zeros((n_faces, n_edges+1))
new_face_bounds[:,0] = normal_bounds
new_face_bounds[:,1:] = neg_bounds + pos_bounds
return new_face_constraints, new_face_bounds
bc_start = time.time()
bc_mid = 0
bc_edge = 0
bc_face = 0
bc_vert = 0
bc_for = 0
bc_r_list = []
for s,x in enumerate(shape_pos):
#TODO: normalize all constraints so that they are unit vectors!!!?
shp = shapes[s]
shp_faces = shp.normals
shp_vert = shp.vertices
shp_edges = shp.edge_vectors
shp_edge_vert = shp.edges #column [0]: o--> | column [1]: o<--
bc_mid_s = time.time()
shp_edge_face = get_edge_face_neighbors(shp)
bc_mid_e = time.time()
bc_mid += (bc_mid_e - bc_mid_s)
n_faces = shp.num_faces #number of faces
n_edges = shp.num_edges #number of edges
n_verts = shp.num_vertices #number of vertices
face_centroids = shp.face_centroids
bc_vert_s = time.time()
vert_constraint, vert_bounds = get_vert_boundaries (shp_vert, shp_edges, shp_edge_vert, n_verts, n_edges, x)
img_vert_bounds = bounds_for_images(vert_bounds, vert_constraint)
bc_vert_e = time.time()
bc_vert += (bc_vert_e - bc_vert_s)
bc_edge_s = time.time()
new_edge_constraint, new_edge_bounds = get_edge_boundaries (shp_vert, shp_edges, shp_faces, shp_edge_vert, shp_edge_face, n_edges, x)
img_edge_bounds = bounds_for_images(new_edge_bounds, new_edge_constraint)
bc_edge_e = time.time()
bc_edge += (bc_edge_e - bc_edge_s)
bc_face_s = time.time()
new_face_constraints, new_face_bounds = get_face_boundaries (shp_vert, shp_edges, shp_faces, shp_edge_vert, shp_edge_face, n_edges, n_faces, x, face_centroids)
img_face_bounds = bounds_for_images(new_face_bounds, new_face_constraints)
bc_face_e = time.time()
bc_face += (bc_face_e - bc_face_s)
# faces = np.asarray(shp.faces)
# print(shp_edge_vert)
# print(shp_edge_face)
# print(faces)
# bc_edge_s = time.time()
#----- Building the Edge Sections (Constraints & Boundary Conditions) -----
# new_edge_constraint = np.zeros((len(shp_edges), 4, 3))
# new_edge_bounds = np.zeros((len(shp_edges), 4))
# edge_constraint_col_1 = -1*shp_edges
# edge_constraint_col_2 = shp_edges
# edge_constraint_col_3 = -1*np.cross(shp_edges, shp_faces[shp_edge_face[:,1]])
# edge_constraint_col_4 = np.cross(shp_edges, shp_faces[shp_edge_face[:,0]])
# new_edge_constraint[:,0] = edge_constraint_col_1
# new_edge_constraint[:,1] = edge_constraint_col_2
# new_edge_constraint[:,2] = edge_constraint_col_3
# new_edge_constraint[:,3] = edge_constraint_col_4
# # new_edge_constraint = np.block([edge_constraint_col_1, edge_constraint_col_2, edge_constraint_col_3, edge_constraint_col_4]).reshape(n_edges, 4, 3)
# new_edge_verts = np.zeros((len(shp_edges), 2, 3))
# new_edge_verts[:,0] = shp_vert[shp_edge_vert[:,0]] + x
# new_edge_verts[:,1] = shp_vert[shp_edge_vert[:,1]] + x
# edge_bounds_1 = np.sum(new_edge_constraint[:,0] *(new_edge_verts[:,1]), axis=1)
# edge_bounds_2 = np.sum(new_edge_constraint[:,1] *(new_edge_verts[:,0]), axis=1)
# edge_bounds_3 = np.sum(new_edge_constraint[:,2] *(new_edge_verts[:,0]), axis=1)
# edge_bounds_4 = np.sum(new_edge_constraint[:,3] *(new_edge_verts[:,0]), axis=1)
# new_edge_bounds[:,0] = edge_bounds_1
# new_edge_bounds[:,1] = edge_bounds_2
# new_edge_bounds[:,2] = edge_bounds_3
# new_edge_bounds[:,3] = edge_bounds_4
# new_edge_bounds = np.block([edge_bounds_1, edge_bounds_2, edge_bounds_3, edge_bounds_4]).reshape(n_edges, 4)
# print(new_edge_constraint.dot(np.array([2,3,3])) >= new_edge_bounds)
#constraint matrix normals are pointing inwards, so use lower bounds
# img_edge_bounds = bounds_for_images(new_edge_bounds, new_edge_constraint)
# bc_edge_e = time.time()
# bc_edge += (bc_edge_e - bc_edge_s)
# bc_face_s = time.time()
#----- Building the Face Sections (Constraints & Boundary Conditions) -----
#Setting up
# nfaces_tile_edges = np.tile(shp_edges, (n_faces, 1)).reshape((n_faces, n_edges, 3)) #Edge vectors tiled
# nfaces_tile_efneighbors = np.tile(shp_edge_face, (n_faces, 1)) #Tiling shp_edge_face so that it is now shape (n_faces, n_edges, 2)
# efneighbors0 = nfaces_tile_efneighbors[:,0].reshape((n_faces, n_edges)) #breaking nfaces_tile_efneighbors into the first column [0]
# efneighbors1 = nfaces_tile_efneighbors[:,1].reshape((n_faces, n_edges)) #second column [1] of nfaces_tile_efneighbors
# faces_inds = np.arange(0, n_faces, 1).reshape((n_faces, 1)) #Making an array containing the indices of the faces
# #Creating bools to find the edges that correspond to each face
# efbool0 = (efneighbors0 == faces_inds)
# efbool1 = (efneighbors1 == faces_inds)
# #Applying the bools to get the edge vectors corresponding to each face
# # ak_edges_mask0 = ak.to_numpy(ak.mask(nfaces_tile_edges, efbool0)) #Applying the bool: efbool0 to ak_tile_edges, but returning Nones for False instead of removing them
# # ak_edges_mask1 = ak.to_numpy(ak.mask(nfaces_tile_edges, efbool1))#^---
# ak_edges_mask0 = nfaces_tile_edges * efbool0.reshape((n_faces, n_edges, 1))
# ak_edges_mask1 = nfaces_tile_edges * efbool1.reshape((n_faces, n_edges, 1))
# faces_repeat = np.repeat(shp_faces, n_edges, axis=0).reshape((n_faces, n_edges, 3))
# # print('numpy',ak_edges_mask0[0])
# # print('numpy',ak_edges_mask1[0])
# #Creating the constraints that are a -1 cross product (edges X faces) (points inwards)
# # neg_constraints = ak.from_numpy(-1*np.cross(ak_edges_mask0, faces_repeat)) #Doing the cross product of the edges to the faces
# # neg_constraints = ak.drop_none(ak.nan_to_none(neg_constraints)) #changing the NaN back to None, and then dropping the None
# # neg_counts = ak.num(neg_constraints, axis=2)
# # neg_counts = ak.flatten(neg_counts[neg_counts != 0])
# # neg_constraints = ak.flatten(neg_constraints, axis=2)
# # neg_constraints = ak.unflatten(neg_constraints, neg_counts, axis=1)
# # neg_con_count = ak.num(neg_constraints, axis=1)
# neg_constraints = -1* np.cross(ak_edges_mask0, faces_repeat)
# # print(neg_con_count)
# #Creating the constraints that are a +1 cross product (edges X faces) (points inwards)
# # pos_constraints = ak.from_numpy(np.cross(ak_edges_mask1, faces_repeat))
# # pos_constraints = ak.drop_none(ak.nan_to_none(pos_constraints))
# # pos_counts = ak.num(pos_constraints, axis=2)
# # pos_counts = ak.flatten(pos_counts[pos_counts != 0])
# # pos_constraints = ak.flatten(pos_constraints, axis=2)
# # pos_constraints = ak.unflatten(pos_constraints, pos_counts, axis=1)
# # pos_con_count = ak.num(pos_constraints, axis=1)
# pos_constraints = np.cross(ak_edges_mask1, faces_repeat)
# # print(pos_con_count)
# #Creating the constraints that come from the normals of each face
# face_normals = shp_faces
# #Concatenating the separate constraints together into one
# # new_face_constraints = ak.concatenate((face_normals, neg_constraints, pos_constraints), axis=1)
# # face_con_counts = ak.num(new_face_constraints, axis=2)
# # face_con_counts = ak.flatten(face_con_counts[face_con_counts != 0])
# # new_face_constraints = ak.flatten(new_face_constraints, axis=2)
# # new_face_constraints = ak.to_numpy(ak.unflatten(new_face_constraints, face_con_counts, axis=1))
# new_face_constraints = np.zeros((n_faces, n_edges+1, 3))
# new_face_constraints[:,0] = face_normals