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Class to compute if a point(s) lies inside/outside/on-side of a polygon.

UPDATE: The class now works with sequences of points.

This is a Python 3 implementation of the Sloan's improved version (FORTRAN 77 code) of the Nordbeck and Rystedt algorithm, published in the paper:

SLOAN, S.W. (1985): A point-in-polygon program. Adv. Eng. Software, Vol 7, No. 1, pp 45-47.

This class has 1 public method (is_inside) that returns the minimum distance to the nearest point of the polygon:

If is_inside < 0 then point is outside the polygon. If is_inside = 0 then point in on a side of the polygon. If is_inside > 0 then point is inside the polygon.

Python, 209 lines
 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 #!/usr/bin/env python3 '''Class to compute if a point lies inside/outside/on-side of a polygon. This is a Python 3 implementation of the Sloan's improved version of the Nordbeck and Rystedt algorithm, published in the paper: SLOAN, S.W. (1985): A point-in-polygon program. Adv. Eng. Software, Vol 7, No. 1, pp 45-47. This class has 1 method (is_inside) that returns the minimum distance to the nearest point of the polygon: If is_inside < 0 then point is outside the polygon. If is_inside = 0 then point in on a side of the polygon. If is_inside > 0 then point is inside the polygon. ''' import numpy as np def _det(xvert, yvert): '''Compute twice the area of the triangle defined by points with using determinant formula. Input parameters: xvert -- A vector of nodal x-coords (array-like). yvert -- A vector of nodal y-coords (array-like). Output parameters: Twice the area of the triangle defined by the points. Notes: _det is positive if points define polygon in anticlockwise order. _det is negative if points define polygon in clockwise order. _det is zero if at least two of the points are concident or if all points are collinear. ''' xvert = np.asfarray(xvert) yvert = np.asfarray(yvert) x_prev = np.concatenate(([xvert[-1]], xvert[:-1])) y_prev = np.concatenate(([yvert[-1]], yvert[:-1])) return np.sum(yvert * x_prev - xvert * y_prev, axis=0) class Polygon: '''Polygon object. Input parameters: x -- A sequence of nodal x-coords. y -- A sequence of nodal y-coords. ''' def __init__(self, x, y): if len(x) != len(y): raise IndexError('x and y must be equally sized.') self.x = np.asfarray(x) self.y = np.asfarray(y) # Closes the polygon if were open x1, y1 = x, y xn, yn = x[-1], y[-1] if x1 != xn or y1 != yn: self.x = np.concatenate((self.x, [x1])) self.y = np.concatenate((self.y, [y1])) # Anti-clockwise coordinates if _det(self.x, self.y) < 0: self.x = self.x[::-1] self.y = self.y[::-1] def is_inside(self, xpoint, ypoint, smalld=1e-12): '''Check if point is inside a general polygon. Input parameters: xpoint -- The x-coord of the point to be tested. ypoint -- The y-coords of the point to be tested. smalld -- A small float number. xpoint and ypoint could be scalars or array-like sequences. Output parameters: mindst -- The distance from the point to the nearest point of the polygon. If mindst < 0 then point is outside the polygon. If mindst = 0 then point in on a side of the polygon. If mindst > 0 then point is inside the polygon. Notes: An improved version of the algorithm of Nordbeck and Rydstedt. REF: SLOAN, S.W. (1985): A point-in-polygon program. Adv. Eng. Software, Vol 7, No. 1, pp 45-47. ''' xpoint = np.asfarray(xpoint) ypoint = np.asfarray(ypoint) # Scalar to array if xpoint.shape is tuple(): xpoint = np.array([xpoint], dtype=float) ypoint = np.array([ypoint], dtype=float) scalar = True else: scalar = False # Check consistency if xpoint.shape != ypoint.shape: raise IndexError('x and y has different shapes') # If snear = True: Dist to nearest side < nearest vertex # If snear = False: Dist to nearest vertex < nearest side snear = np.ma.masked_all(xpoint.shape, dtype=bool) # Initialize arrays mindst = np.ones_like(xpoint, dtype=float) * np.inf j = np.ma.masked_all(xpoint.shape, dtype=int) x = self.x y = self.y n = len(x) - 1 # Number of sides/vertices defining the polygon # Loop over each side defining polygon for i in range(n): d = np.ones_like(xpoint, dtype=float) * np.inf # Start of side has coords (x1, y1) # End of side has coords (x2, y2) # Point has coords (xpoint, ypoint) x1 = x[i] y1 = y[i] x21 = x[i + 1] - x1 y21 = y[i + 1] - y1 x1p = x1 - xpoint y1p = y1 - ypoint # Points on infinite line defined by # x = x1 + t * (x1 - x2) # y = y1 + t * (y1 - y2) # where # t = 0 at (x1, y1) # t = 1 at (x2, y2) # Find where normal passing through (xpoint, ypoint) intersects # infinite line t = -(x1p * x21 + y1p * y21) / (x21 ** 2 + y21 ** 2) tlt0 = t < 0 tle1 = (0 <= t) & (t <= 1) # Normal intersects side d[tle1] = ((x1p[tle1] + t[tle1] * x21) ** 2 + (y1p[tle1] + t[tle1] * y21) ** 2) # Normal does not intersects side # Point is closest to vertex (x1, y1) # Compute square of distance to this vertex d[tlt0] = x1p[tlt0] ** 2 + y1p[tlt0] ** 2 # Store distances mask = d < mindst mindst[mask] = d[mask] j[mask] = i # Point is closer to (x1, y1) than any other vertex or side snear[mask & tlt0] = False # Point is closer to this side than to any other side or vertex snear[mask & tle1] = True if np.ma.count(snear) != snear.size: raise IndexError('Error computing distances') mindst **= 0.5 # Point is closer to its nearest vertex than its nearest side, check if # nearest vertex is concave. # If the nearest vertex is concave then point is inside the polygon, # else the point is outside the polygon. jo = j.copy() jo[j == 0] -= 1 area = _det([x[j + 1], x[j], x[jo - 1]], [y[j + 1], y[j], y[jo - 1]]) mindst[~snear] = np.copysign(mindst, area)[~snear] # Point is closer to its nearest side than to its nearest vertex, check # if point is to left or right of this side. # If point is to left of side it is inside polygon, else point is # outside polygon. area = _det([x[j], x[j + 1], xpoint], [y[j], y[j + 1], ypoint]) mindst[snear] = np.copysign(mindst, area)[snear] # Point is on side of polygon mindst[np.fabs(mindst) < smalld] = 0 # If input values were scalar then the output should be too if scalar: mindst = float(mindst) return mindst # TEST if __name__ == '__main__': # Define a triangle xvert = [10, 90, 90] yvert = [10, 90, 10] poly = Polygon(xvert, yvert) # Test x = np.arange(101) xx, yy = np.meshgrid(x, x) grid = poly.is_inside(xx, yy) # Plot try: import matplotlib.pyplot as plt except ImportError: print(grid) else: plt.contour(xx, yy, grid, levels=np.linspace(-100, 100, 51), colors='k') plt.pcolor(xx, yy, grid, vmin=-80, vmax=80, cmap=plt.get_cmap('RdBu')) plt.colorbar() plt.title('Distance to polygon border') plt.show(block=True)

Sloan's is the best algorithm I've found to solve the point-in-polygon problem. Created by PG on Sun, 16 Dec 2012 (MIT)