def test_circumcenter():
r"""Test circumcenter function."""
pt0 = [0, 0]
pt1 = [10, 10]
pt2 = [10, 0]
cc = circumcenter(pt0, pt1, pt2)
truth = [5., 5.]
assert_array_almost_equal(truth, cc)
def test_circumcenter():
r"""Test circumcenter function."""
pt0 = [0, 0]
pt1 = [10, 10]
pt2 = [10, 0]
cc = circumcenter(pt0, pt1, pt2)
truth = [5., 5.]
assert_array_almost_equal(truth, cc)
def nn_point(xp, yp, variable, grid_loc, tri, neighbors, triangle_info):
r"""Generate a natural neighbor interpolation of the given
observations to the given point using the Liang and Hale (2010)
approach. The interpolation will fail if the grid point has no
natural neighbors.
Liang, Luming, and Dave Hale. A stable and fast implementation
of natural neighbor interpolation. (2010).
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: (N, 2) ndarray
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)
warnings.warn(message)
return np.nan
polygon = list()
polygon.append(c2)
p2 = p3
return sum([x / total_area for x in area_list])
ax.set_aspect('equal', 'datalim')
def draw_polygon_with_info(ax, polygon, off_x=0, off_y=0):
"""Draw one of the natural neighbor polygons with some information."""
pts = np.array(polygon)[ConvexHull(polygon).vertices]
for i, pt in enumerate(pts):
ax.plot([pt[0], pts[(i + 1) % len(pts)][0]],
[pt[1], pts[(i + 1) % len(pts)][1]], 'k-')
avex, avey = np.mean(pts, axis=0)
ax.annotate('area: {:.3f}'.format(polygons.area(pts)), xy=(avex + off_x, avey + off_y),
fontsize=12)
cc1 = triangles.circumcenter((53, 66), (15, 60), (30, 30))
cc2 = triangles.circumcenter((34, 24), (53, 66), (30, 30))
draw_polygon_with_info(ax, [cc[0], cc1, cc2])
cc1 = triangles.circumcenter((53, 66), (15, 60), (30, 30))
cc2 = triangles.circumcenter((15, 60), (8, 24), (30, 30))
draw_polygon_with_info(ax, [cc[0], cc[1], cc1, cc2], off_x=-9, off_y=3)
cc1 = triangles.circumcenter((8, 24), (34, 24), (30, 30))
cc2 = triangles.circumcenter((15, 60), (8, 24), (30, 30))
draw_polygon_with_info(ax, [cc[1], cc1, cc2], off_x=-15)
cc1 = triangles.circumcenter((8, 24), (34, 24), (30, 30))
cc2 = triangles.circumcenter((34, 24), (53, 66), (30, 30))
draw_polygon_with_info(ax, [cc[0], cc[1], cc1, cc2])
plt.axes().set_aspect('equal', 'datalim')
def draw_polygon_with_info(polygon, off_x=0, off_y=0):
"""Draw one of the natural neighbor polygons with some information."""
pts = np.array(polygon)[ConvexHull(polygon).vertices]
for i, pt in enumerate(pts):
plt.plot([pt[0], pts[(i + 1) % len(pts)][0]],
[pt[1], pts[(i + 1) % len(pts)][1]], 'k-')
avex, avey = np.mean(pts, axis=0)
plt.annotate('area: {:.3f}'.format(polygons.area(pts)), xy=(avex + off_x, avey + off_y),
fontsize=12)
cc1 = triangles.circumcenter((53, 66), (15, 60), (30, 30))
cc2 = triangles.circumcenter((34, 24), (53, 66), (30, 30))
draw_polygon_with_info([cc[0], cc1, cc2])
cc1 = triangles.circumcenter((53, 66), (15, 60), (30, 30))
cc2 = triangles.circumcenter((15, 60), (8, 24), (30, 30))
draw_polygon_with_info([cc[0], cc[1], cc1, cc2], off_x=-9, off_y=3)
cc1 = triangles.circumcenter((8, 24), (34, 24), (30, 30))
cc2 = triangles.circumcenter((15, 60), (8, 24), (30, 30))
draw_polygon_with_info([cc[1], cc1, cc2], off_x=-15)
cc1 = triangles.circumcenter((8, 24), (34, 24), (30, 30))
cc2 = triangles.circumcenter((34, 24), (53, 66), (30, 30))
draw_polygon_with_info([cc[0], cc[1], cc1, cc2])