У меня есть код для расширения многоугольника, он работает, умножая xs и ys на коэффициент, а затем повторно центрируя результирующий многоугольник в центре оригинала.
У меня также есть код, чтобы найти значение для коэффициента расширения, учитывая точку, которую должен достичь многоугольник:
import numpy as np
import itertools as IT
import copy
from shapely.geometry import LineString, Point
def getPolyCenter(points):
"""
http://stackoverflow.com/a/14115494/190597 (mgamba)
"""
area = area_of_polygon(*zip(*points))
result_x = 0
result_y = 0
N = len(points)
points = IT.cycle(points)
x1, y1 = next(points)
for i in range(N):
x0, y0 = x1, y1
x1, y1 = next(points)
cross = (x0 * y1) - (x1 * y0)
result_x += (x0 + x1) * cross
result_y += (y0 + y1) * cross
result_x /= (area * 6.0)
result_y /= (area * 6.0)
return (result_x, result_y)
def expandPoly(points, factor):
points = np.array(points, dtype=np.float64)
expandedPoly = points*factor
expandedPoly -= getPolyCenter(expandedPoly)
expandedPoly += getPolyCenter(points)
return np.array(expandedPoly, dtype=np.int64)
def distanceLine2Point(points, point):
points = np.array(points, dtype=np.float64)
point = np.array(point, dtype=np.float64)
points = LineString(points)
point = Point(point)
return points.distance(point)
def distancePolygon2Point(points, point):
distances = []
for i in range(len(points)):
if i==len(points)-1:
j = 0
else:
j = i+1
line = [points[i], points[j]]
distances.append(distanceLine2Point(line, point))
minDistance = np.min(distances)
#index = np.where(distances==minDistance)[0][0]
return minDistance
"""
Returns the distance from a point to the nearest line of the polygon,
AND the distance from where the normal to the line (to reach the point)
intersets the line to the center of the polygon.
"""
def distancePolygon2PointAndCenter(points, point):
distances = []
for i in range(len(points)):
if i==len(points)-1:
j = 0
else:
j = i+1
line = [points[i], points[j]]
distances.append(distanceLine2Point(line, point))
minDistance = np.min(distances)
i = np.where(distances==minDistance)[0][0]
if i==len(points)-1:
j = 0
else:
j = i+1
line = copy.deepcopy([points[i], points[j]])
centerDistance = distanceLine2Point(line, getPolyCenter(points))
return minDistance, centerDistance
minDistance, centerDistance = distancePolygon2PointAndCenter(points, point)
expandedPoly = expandPoly(points, 1+minDistance/centerDistance)
Этот код работает только тогда, когда точка прямо противоположна одной из линий многоугольников.