def calculate_gradient(points, dps, cells_dic, polygon_bd):
npoints = points.shape[0]
D = np.zeros((npoints,1), np.float32)
for npt in range(npoints):
if npt not in cells_dic:
continue
cell = cells_dic[npt]
poly = polygon(dps[cell])
region = poly & polygon_bd
D[npt] = region.area()
return D
def intersect_ray_polygon(ray, poly, scale, thresh=0.001):
a = ray[0:2]
b = ray[0:2] + scale * ray[2:4]
c = [b[0] + thresh, b[1] + thresh]
tri = polygon(np.array([a, b, c]))
region = poly & tri
npoints = region.nPoints()
if npoints == 0:
return []
equal_thresh = 0.00001
for ii in range(npoints):
if np.sum(np.abs(region[0][ii] - a) > equal_thresh):
return region[0][ii]
return []
def Geojsonify(data, Type='Point'):
# Determine which function to use
if Type == 'Point':
return point(data)
elif Type == 'LineString':
return line_string(data)
elif Type == 'Polygon':
return polygon(data)
else:
print("Error: Type has to be either Point, LineString, or Polygon")
if _iter % 20 == 0:
plot_diagram(points, faces_pd, cells_dic, dps, dps_bd, points_bd, scale = 1.0)
return new_h
def calculate_gradient(points, dps, cells_dic, polygon_bd):
npoints = points.shape[0]
D = np.zeros((npoints,1), np.float32)
for npt in range(npoints):
if npt not in cells_dic:
continue
cell = cells_dic[npt]
poly = polygon(dps[cell])
region = poly & polygon_bd
D[npt] = region.area()
return D
if __name__ == '__main__':
npoints = 50
points = np.random.random((npoints, 2))
minxy = np.min(points, axis = 0) - 0.1
maxxy = np.max(points, axis = 0) + 0.1
scale = np.sqrt(np.sum((maxxy - minxy)**2))
points_bd = np.array([[minxy[0], minxy[1]], [minxy[0], maxxy[1]], [maxxy[0], maxxy[1]], [maxxy[0], minxy[1]], [minxy[0], minxy[1]]])
polygon_bd = polygon(points_bd)
delta = (maxxy[0] - minxy[0]) * (maxxy[1] - minxy[1]) / npoints * np.ones((npoints, 1), np.float32)
new_h = None
new_h = discrete_optimal_transform(points, delta, polygon_bd, scale, new_h, learnrate = 0.05, max_iter = 2000, epsilon = 1e-5)
def power_diagram_2d(points, h=None):
npoints = points.shape[0]
if h is None:
h = np.zeros((points.shape[0], 1), np.float32)
pl = np.concatenate(
(points, np.sum(points * points, axis=1, keepdims=True) - h), axis=1)
hull = convexhull(pl)
ind = hull.equations[:, 2] < 0
nfaces = np.sum(ind)
faces = hull.simplices[ind]
dps = np.zeros((nfaces, 2), np.float32)
dic = dict()
for _face, cnt in zip(faces, xrange(nfaces)):
dps[cnt] = face_dual_uv(pl[_face])
left, right = _cmp(_face[0], _face[1])
_dict_update(dic, '%d_%d' % (left, right), cnt)
left, right = _cmp(_face[0], _face[2])
_dict_update(dic, '%d_%d' % (left, right), cnt)
left, right = _cmp(_face[2], _face[1])
_dict_update(dic, '%d_%d' % (left, right), cnt)
cells_dic = dict()
flag_bd = np.zeros((npoints), np.int32)
for _face, cnt in zip(faces, xrange(nfaces)):
for pos in range(3):
if _face[pos] in cells_dic:
continue
cell = [cnt]
flag_bd[_face[pos]] = compute_cell(_face, pos, faces, dic, cell)
cells_dic.update({_face[pos]: cell})
dps_bd = np.zeros((np.sum(flag_bd), 2), np.float32)
minxy = np.min(dps, axis=0) - 1.0
maxxy = np.max(dps, axis=0) + 1.0
scale = np.sqrt(np.sum((maxxy - minxy)**2))
points_bd = np.array([[minxy[0], minxy[0]], [minxy[0], maxxy[1]],
[maxxy[0], maxxy[1]], [maxxy[0], minxy[1]],
[minxy[0], minxy[0]]])
polygon_bd = polygon(points_bd)
cnt = 0
for ii in xrange(npoints):
if flag_bd[ii]:
flag_bd[ii] = nfaces + cnt
cnt += 1
cnt = 0
for ii in xrange(npoints):
if flag_bd[ii] == 0:
continue
cell = cells_dic[ii]
for pp in faces[cell[0]]:
if pp != ii and flag_bd[pp]:
B_inx = pp
for pp in faces[cell[-1]]:
if pp != ii and flag_bd[pp]:
C_inx = pp
if ccw(points[ii], points[B_inx], points[C_inx]):
face_num = cell[0]
other_inx = B_inx
cell.insert(0, flag_bd[ii])
cell.append(flag_bd[C_inx])
else:
face_num = cell[-1]
other_inx = C_inx
cell.append(flag_bd[ii])
cell.insert(0, flag_bd[B_inx])
vec = points[ii] - points[other_inx]
ray = np.array([dps[face_num, 0], dps[face_num, 1], -vec[1], vec[0]])
point_inter = intersect_ray_polygon(ray, polygon_bd, scale)
if point_inter == []:
print 'intersect_ray_polygon error!'
dps_bd[cnt] = np.array(point_inter)
cnt += 1
return dps, dps_bd, cells_dic, faces