DEM/max_rect.py at main · EduardHeijkoop/DEM · GitHub

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import numpy as np
import cvxpy
# from shapely.geometry import Polygon
import shapely
from dem_utils import get_lonlat_geometry

# def rect2poly(ll, ur):
#     """
#     Convert rectangle defined by lower left/upper right
#     to a closed polygon representation.
#     """
#     x0, y0 = ll
#     x1, y1 = ur

#     return [
#         [x0, y0],
#         [x0, y1],
#         [x1, y1],
#         [x1, y0],
#         [x0, y0]
#     ]


# def get_intersection(coords):
#     """Given an input list of coordinates, find the intersection
#     section of corner coordinates. Returns geojson of the
#     interesection polygon.
#     """
#     ipoly = None
#     for coord in coords:
#         if ipoly is None:
#             ipoly = shapely.geometry.Polygon(coord)
#         else:
#             tmp = shapely.geometry.Polygon(coord)
#             ipoly = ipoly.intersection(tmp)

#     # close the polygon loop by adding the first coordinate again
#     first_x = ipoly.exterior.coords.xy[0][0]
#     first_y = ipoly.exterior.coords.xy[1][0]
#     ipoly.exterior.coords.xy[0].append(first_x)
#     ipoly.exterior.coords.xy[1].append(first_y)

#     inter_coords = zip(
#         ipoly.exterior.coords.xy[0], ipoly.exterior.coords.xy[1])

#     inter_gj = {"geometry":
#                 {"coordinates": [inter_coords],
#                  "type": "Polygon"},
#                 "properties": {}, "type": "Feature"}

#     return inter_gj, inter_coords


def two_pts_to_line(pt1, pt2):
    """
    Create a line from two points in form of
    a1(x) + a2(y) = b
    """
    pt1 = [float(p) for p in pt1]
    pt2 = [float(p) for p in pt2]
    try:
        slp = (pt2[1] - pt1[1]) / (pt2[0] - pt1[0])
    except ZeroDivisionError:
        slp = 1e5 * (pt2[1] - pt1[1])
    a1 = -slp
    a2 = 1.
    b = -slp * pt1[0] + pt1[1]
    return a1, a2, b


def pts_to_leq(coords):
    """
    Converts a set of points to form Ax = b, but since
    x is of length 2 this is like A1(x1) + A2(x2) = B.
    returns A1, A2, B
    """
    A1 = []
    A2 = []
    B = []
    for i in range(len(coords) - 1):
        pt1 = coords[i]
        pt2 = coords[i + 1]
        a1, a2, b = two_pts_to_line(pt1, pt2)
        A1.append(a1)
        A2.append(a2)
        B.append(b)
    return A1, A2, B


def get_maximal_rectangle(polygon:shapely.geometry.Polygon,buffer_val=0.001):
    """
    Find the largest, inscribed, axis-aligned rectangle.
    :param coordinates:
        A list of of [x, y] pairs describing a closed, convex polygon.
    Obtained from https://github.com/planetlabs/maxrect
    and edited with https://stackoverflow.com/questions/70586297/cvxpy-solvers-produce-solutions-of-different-shapes
    """
    #Get lon/lat from shapely polygon
    lon,lat = get_lonlat_geometry(polygon,append_nan=False)
    coordinates = [[ln,lt] for ln,lt in zip(lon,lat)]
    coordinates = np.array(coordinates)
    x_range = np.max(coordinates, axis=0)[0]-np.min(coordinates, axis=0)[0]
    y_range = np.max(coordinates, axis=0)[1]-np.min(coordinates, axis=0)[1]
    scale = np.array([x_range, y_range])
    sc_coordinates = coordinates/scale
    poly = shapely.geometry.Polygon(sc_coordinates)
    inside_pt = (poly.representative_point().x,
                 poly.representative_point().y)
    A1, A2, B = pts_to_leq(sc_coordinates)
    bl = cvxpy.Variable(2)
    tr = cvxpy.Variable(2)
    br = cvxpy.Variable(2)
    tl = cvxpy.Variable(2)
    obj = cvxpy.Maximize(cvxpy.log(tr[0] - bl[0]) + cvxpy.log(tr[1] - bl[1]))
    constraints = [bl[0] == tl[0],
                   br[0] == tr[0],
                   tl[1] == tr[1],
                   bl[1] == br[1],
                   ]
    for i in range(len(B)):
        if inside_pt[0] * A1[i] + inside_pt[1] * A2[i] <= B[i]:
            constraints.append(bl[0] * A1[i] + bl[1] * A2[i] <= B[i])
            constraints.append(tr[0] * A1[i] + tr[1] * A2[i] <= B[i])
            constraints.append(br[0] * A1[i] + br[1] * A2[i] <= B[i])
            constraints.append(tl[0] * A1[i] + tl[1] * A2[i] <= B[i])
        else:
            constraints.append(bl[0] * A1[i] + bl[1] * A2[i] >= B[i])
            constraints.append(tr[0] * A1[i] + tr[1] * A2[i] >= B[i])
            constraints.append(br[0] * A1[i] + br[1] * A2[i] >= B[i])
            constraints.append(tl[0] * A1[i] + tl[1] * A2[i] >= B[i])
    prob = cvxpy.Problem(obj, constraints)
    # prob.solve(solver=cvxpy.CVXOPT, verbose=False, max_iters=1000, reltol=1e-9)
    prob.solve()
    bottom_left = np.array(bl.value).T * scale
    top_right = np.array(tr.value).T * scale
    return bottom_left[0]+buffer_val,bottom_left[1]+buffer_val,top_right[0]-buffer_val,top_right[1]-buffer_val