[2622] | 1 | #!/usr/bin/env python |
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| 2 | """Polygon manipulations |
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| 3 | |
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| 4 | """ |
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| 5 | |
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| 6 | |
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| 7 | try: |
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| 8 | from scipy import Float, Int, zeros, ones, array, concatenate, reshape, dot |
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| 9 | except: |
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[2633] | 10 | #print 'Could not find scipy - using Numeric' |
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[2622] | 11 | from Numeric import Float, Int, zeros, ones, array, concatenate, reshape, dot |
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| 12 | |
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| 13 | |
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| 14 | from math import sqrt |
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| 15 | from utilities.numerical_tools import ensure_numeric |
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[3051] | 16 | from geospatial_data.geospatial_data import ensure_absolute |
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[2622] | 17 | |
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| 18 | def point_on_line(x, y, x0, y0, x1, y1): |
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| 19 | """Determine whether a point is on a line segment |
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| 20 | |
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| 21 | Input: x, y, x0, x0, x1, y1: where |
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| 22 | point is given by x, y |
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| 23 | line is given by (x0, y0) and (x1, y1) |
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| 24 | |
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| 25 | """ |
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| 26 | |
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| 27 | a = array([x - x0, y - y0]) |
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| 28 | a_normal = array([a[1], -a[0]]) |
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| 29 | |
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| 30 | b = array([x1 - x0, y1 - y0]) |
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| 31 | |
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| 32 | if dot(a_normal, b) == 0: |
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| 33 | #Point is somewhere on the infinite extension of the line |
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| 34 | |
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| 35 | len_a = sqrt(sum(a**2)) |
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| 36 | len_b = sqrt(sum(b**2)) |
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| 37 | if dot(a, b) >= 0 and len_a <= len_b: |
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| 38 | return True |
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| 39 | else: |
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| 40 | return False |
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| 41 | else: |
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| 42 | return False |
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| 43 | |
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| 44 | |
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[3054] | 45 | def is_inside_polygon(point, polygon, closed=True, verbose=False): |
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[3052] | 46 | """Determine if one point is inside a polygon |
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| 47 | |
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| 48 | See inside_polygon for more details |
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| 49 | """ |
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| 50 | |
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[3054] | 51 | indices = inside_polygon(point, polygon, closed, verbose) |
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[3052] | 52 | |
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| 53 | if indices.shape[0] == 1: |
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| 54 | return True |
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| 55 | elif indices.shape[0] == 0: |
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| 56 | return False |
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| 57 | else: |
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| 58 | msg = 'is_inside_polygon must be invoked with one point only' |
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| 59 | raise msg |
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| 60 | |
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| 61 | |
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[3054] | 62 | def inside_polygon(points, polygon, closed=True, verbose=False): |
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[2622] | 63 | """Determine points inside a polygon |
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| 64 | |
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| 65 | Functions inside_polygon and outside_polygon have been defined in |
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| 66 | terms af separate_by_polygon which will put all inside indices in |
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| 67 | the first part of the indices array and outside indices in the last |
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| 68 | |
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| 69 | See separate_points_by_polygon for documentation |
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[3054] | 70 | |
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| 71 | points and polygon can be a geospatial instance, |
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| 72 | a list or a numeric array |
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[2622] | 73 | """ |
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| 74 | |
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| 75 | if verbose: print 'Checking input to inside_polygon' |
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| 76 | |
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| 77 | try: |
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[3054] | 78 | points = ensure_absolute(points) |
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[2622] | 79 | except NameError, e: |
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| 80 | raise NameError, e |
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| 81 | except: |
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| 82 | msg = 'Points could not be converted to Numeric array' |
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| 83 | raise msg |
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| 84 | |
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| 85 | try: |
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[3054] | 86 | polygon = ensure_absolute(polygon) |
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[2622] | 87 | except NameError, e: |
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| 88 | raise NameError, e |
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| 89 | except: |
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| 90 | msg = 'Polygon %s could not be converted to Numeric array' %(str(polygon)) |
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| 91 | raise msg |
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| 92 | |
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| 93 | if len(points.shape) == 1: |
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[3052] | 94 | # Only one point was passed in. Convert to array of points |
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| 95 | points = reshape(points, (1,2)) |
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[2622] | 96 | |
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| 97 | indices, count = separate_points_by_polygon(points, polygon, |
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| 98 | closed=closed, |
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| 99 | verbose=verbose) |
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| 100 | |
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[3052] | 101 | # Return indices of points inside polygon |
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| 102 | return indices[:count] |
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| 103 | |
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| 104 | |
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| 105 | |
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| 106 | def is_outside_polygon(point, polygon, closed=True, verbose=False, |
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| 107 | points_geo_ref=None, polygon_geo_ref=None): |
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| 108 | """Determine if one point is outside a polygon |
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| 109 | |
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| 110 | See outside_polygon for more details |
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| 111 | """ |
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| 112 | |
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| 113 | indices = outside_polygon(point, polygon, closed, verbose) |
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| 114 | #points_geo_ref, polygon_geo_ref) |
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| 115 | |
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| 116 | if indices.shape[0] == 1: |
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| 117 | return True |
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| 118 | elif indices.shape[0] == 0: |
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| 119 | return False |
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[2622] | 120 | else: |
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[3052] | 121 | msg = 'is_outside_polygon must be invoked with one point only' |
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| 122 | raise msg |
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| 123 | |
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[2622] | 124 | |
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| 125 | def outside_polygon(points, polygon, closed = True, verbose = False): |
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| 126 | """Determine points outside a polygon |
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| 127 | |
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| 128 | Functions inside_polygon and outside_polygon have been defined in |
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| 129 | terms af separate_by_polygon which will put all inside indices in |
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| 130 | the first part of the indices array and outside indices in the last |
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| 131 | |
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| 132 | See separate_points_by_polygon for documentation |
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| 133 | """ |
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| 134 | |
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| 135 | if verbose: print 'Checking input to outside_polygon' |
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| 136 | try: |
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| 137 | points = ensure_numeric(points, Float) |
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| 138 | except NameError, e: |
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| 139 | raise NameError, e |
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| 140 | except: |
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| 141 | msg = 'Points could not be converted to Numeric array' |
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| 142 | raise msg |
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| 143 | |
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| 144 | try: |
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| 145 | polygon = ensure_numeric(polygon, Float) |
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| 146 | except NameError, e: |
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| 147 | raise NameError, e |
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| 148 | except: |
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| 149 | msg = 'Polygon could not be converted to Numeric array' |
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| 150 | raise msg |
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| 151 | |
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| 152 | |
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| 153 | if len(points.shape) == 1: |
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[3052] | 154 | # Only one point was passed in. Convert to array of points |
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| 155 | points = reshape(points, (1,2)) |
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[2622] | 156 | |
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| 157 | indices, count = separate_points_by_polygon(points, polygon, |
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| 158 | closed=closed, |
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| 159 | verbose=verbose) |
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| 160 | |
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[3052] | 161 | # Return indices of points outside polygon |
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| 162 | if count == len(indices): |
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| 163 | # No points are outside |
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| 164 | return array([]) |
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[2622] | 165 | else: |
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[3052] | 166 | return indices[count:][::-1] #return reversed |
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[2655] | 167 | |
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[2622] | 168 | |
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[2655] | 169 | def in_and_outside_polygon(points, polygon, closed = True, verbose = False): |
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| 170 | """Determine points inside and outside a polygon |
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[2622] | 171 | |
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[2655] | 172 | See separate_points_by_polygon for documentation |
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| 173 | |
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| 174 | Returns an array of points inside and an array of points outside the polygon |
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| 175 | """ |
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| 176 | |
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| 177 | if verbose: print 'Checking input to outside_polygon' |
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| 178 | try: |
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| 179 | points = ensure_numeric(points, Float) |
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| 180 | except NameError, e: |
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| 181 | raise NameError, e |
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| 182 | except: |
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| 183 | msg = 'Points could not be converted to Numeric array' |
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| 184 | raise msg |
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| 185 | |
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| 186 | try: |
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| 187 | polygon = ensure_numeric(polygon, Float) |
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| 188 | except NameError, e: |
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| 189 | raise NameError, e |
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| 190 | except: |
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| 191 | msg = 'Polygon could not be converted to Numeric array' |
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| 192 | raise msg |
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| 193 | |
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[3052] | 194 | if len(points.shape) == 1: |
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| 195 | # Only one point was passed in. Convert to array of points |
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| 196 | points = reshape(points, (1,2)) |
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[2655] | 197 | |
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| 198 | |
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| 199 | indices, count = separate_points_by_polygon(points, polygon, |
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| 200 | closed=closed, |
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| 201 | verbose=verbose) |
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[3052] | 202 | |
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| 203 | # Returns indices of points inside and indices of points outside |
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[2655] | 204 | # the polygon |
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[3052] | 205 | |
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[2655] | 206 | if count == len(indices): |
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| 207 | # No points are outside |
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| 208 | return indices[:count],[] |
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| 209 | else: |
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| 210 | return indices[:count], indices[count:][::-1] #return reversed |
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| 211 | |
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| 212 | |
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[2622] | 213 | def separate_points_by_polygon(points, polygon, |
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| 214 | closed = True, verbose = False): |
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| 215 | """Determine whether points are inside or outside a polygon |
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| 216 | |
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| 217 | Input: |
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| 218 | points - Tuple of (x, y) coordinates, or list of tuples |
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| 219 | polygon - list of vertices of polygon |
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| 220 | closed - (optional) determine whether points on boundary should be |
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| 221 | regarded as belonging to the polygon (closed = True) |
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| 222 | or not (closed = False) |
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| 223 | |
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| 224 | Outputs: |
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| 225 | indices: array of same length as points with indices of points falling |
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| 226 | inside the polygon listed from the beginning and indices of points |
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| 227 | falling outside listed from the end. |
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| 228 | |
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| 229 | count: count of points falling inside the polygon |
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| 230 | |
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| 231 | The indices of points inside are obtained as indices[:count] |
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| 232 | The indices of points outside are obtained as indices[count:] |
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| 233 | |
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| 234 | |
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| 235 | Examples: |
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| 236 | U = [[0,0], [1,0], [1,1], [0,1]] #Unit square |
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| 237 | |
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| 238 | separate_points_by_polygon( [[0.5, 0.5], [1, -0.5], [0.3, 0.2]], U) |
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| 239 | will return the indices [0, 2, 1] and count == 2 as only the first |
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| 240 | and the last point are inside the unit square |
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| 241 | |
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| 242 | Remarks: |
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| 243 | The vertices may be listed clockwise or counterclockwise and |
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| 244 | the first point may optionally be repeated. |
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| 245 | Polygons do not need to be convex. |
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| 246 | Polygons can have holes in them and points inside a hole is |
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| 247 | regarded as being outside the polygon. |
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| 248 | |
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| 249 | Algorithm is based on work by Darel Finley, |
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| 250 | http://www.alienryderflex.com/polygon/ |
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| 251 | |
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| 252 | """ |
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| 253 | |
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| 254 | #Input checks |
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| 255 | |
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| 256 | |
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| 257 | try: |
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| 258 | points = ensure_numeric(points, Float) |
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| 259 | except NameError, e: |
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| 260 | raise NameError, e |
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| 261 | except: |
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| 262 | msg = 'Points could not be converted to Numeric array' |
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| 263 | raise msg |
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| 264 | |
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| 265 | try: |
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| 266 | polygon = ensure_numeric(polygon, Float) |
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| 267 | except NameError, e: |
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| 268 | raise NameError, e |
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| 269 | except: |
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| 270 | msg = 'Polygon could not be converted to Numeric array' |
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| 271 | raise msg |
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| 272 | |
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| 273 | assert len(polygon.shape) == 2,\ |
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| 274 | 'Polygon array must be a 2d array of vertices' |
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| 275 | |
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| 276 | assert polygon.shape[1] == 2,\ |
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| 277 | 'Polygon array must have two columns' |
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| 278 | |
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| 279 | assert len(points.shape) == 2,\ |
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| 280 | 'Points array must be a 2d array' |
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| 281 | |
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| 282 | assert points.shape[1] == 2,\ |
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| 283 | 'Points array must have two columns' |
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| 284 | |
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| 285 | N = polygon.shape[0] #Number of vertices in polygon |
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| 286 | M = points.shape[0] #Number of points |
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| 287 | |
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| 288 | px = polygon[:,0] |
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| 289 | py = polygon[:,1] |
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| 290 | |
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| 291 | #Used for an optimisation when points are far away from polygon |
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| 292 | minpx = min(px); maxpx = max(px) |
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| 293 | minpy = min(py); maxpy = max(py) |
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| 294 | |
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| 295 | |
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| 296 | #Begin main loop |
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| 297 | indices = zeros(M, Int) |
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| 298 | |
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| 299 | inside_index = 0 #Keep track of points inside |
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| 300 | outside_index = M-1 #Keep track of points outside (starting from end) |
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| 301 | |
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| 302 | for k in range(M): |
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| 303 | |
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| 304 | if verbose: |
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| 305 | if k %((M+10)/10)==0: print 'Doing %d of %d' %(k, M) |
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| 306 | |
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| 307 | #for each point |
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| 308 | x = points[k, 0] |
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| 309 | y = points[k, 1] |
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| 310 | |
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| 311 | inside = False |
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| 312 | |
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| 313 | if not x > maxpx or x < minpx or y > maxpy or y < minpy: |
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| 314 | #Check polygon |
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| 315 | for i in range(N): |
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| 316 | j = (i+1)%N |
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| 317 | |
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| 318 | #Check for case where point is contained in line segment |
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| 319 | if point_on_line(x, y, px[i], py[i], px[j], py[j]): |
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| 320 | if closed: |
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| 321 | inside = True |
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| 322 | else: |
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| 323 | inside = False |
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| 324 | break |
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| 325 | else: |
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| 326 | #Check if truly inside polygon |
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| 327 | if py[i] < y and py[j] >= y or\ |
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| 328 | py[j] < y and py[i] >= y: |
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| 329 | if px[i] + (y-py[i])/(py[j]-py[i])*(px[j]-px[i]) < x: |
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| 330 | inside = not inside |
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| 331 | |
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| 332 | if inside: |
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| 333 | indices[inside_index] = k |
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| 334 | inside_index += 1 |
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| 335 | else: |
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| 336 | indices[outside_index] = k |
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| 337 | outside_index -= 1 |
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| 338 | |
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| 339 | return indices, inside_index |
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| 340 | |
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| 341 | |
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| 342 | def separate_points_by_polygon_c(points, polygon, |
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| 343 | closed = True, verbose = False): |
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| 344 | """Determine whether points are inside or outside a polygon |
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| 345 | |
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| 346 | C-wrapper |
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| 347 | """ |
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| 348 | |
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| 349 | |
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| 350 | if verbose: print 'Checking input to separate_points_by_polygon' |
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| 351 | |
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| 352 | |
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| 353 | #Input checks |
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| 354 | |
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| 355 | assert isinstance(closed, bool), 'Keyword argument "closed" must be boolean' |
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| 356 | assert isinstance(verbose, bool), 'Keyword argument "verbose" must be boolean' |
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| 357 | |
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| 358 | |
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| 359 | try: |
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| 360 | points = ensure_numeric(points, Float) |
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| 361 | except NameError, e: |
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| 362 | raise NameError, e |
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| 363 | except: |
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| 364 | msg = 'Points could not be converted to Numeric array' |
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| 365 | raise msg |
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| 366 | |
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| 367 | #if verbose: print 'Checking input to separate_points_by_polygon 2' |
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| 368 | try: |
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| 369 | polygon = ensure_numeric(polygon, Float) |
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| 370 | except NameError, e: |
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| 371 | raise NameError, e |
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| 372 | except: |
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| 373 | msg = 'Polygon could not be converted to Numeric array' |
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| 374 | raise msg |
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| 375 | |
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| 376 | if verbose: print 'check' |
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| 377 | |
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| 378 | assert len(polygon.shape) == 2,\ |
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| 379 | 'Polygon array must be a 2d array of vertices' |
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| 380 | |
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| 381 | assert polygon.shape[1] == 2,\ |
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| 382 | 'Polygon array must have two columns' |
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| 383 | |
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| 384 | assert len(points.shape) == 2,\ |
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| 385 | 'Points array must be a 2d array' |
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| 386 | |
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| 387 | assert points.shape[1] == 2,\ |
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| 388 | 'Points array must have two columns' |
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| 389 | |
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| 390 | N = polygon.shape[0] #Number of vertices in polygon |
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| 391 | M = points.shape[0] #Number of points |
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| 392 | |
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| 393 | from polygon_ext import separate_points_by_polygon |
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| 394 | |
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| 395 | if verbose: print 'Allocating array for indices' |
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| 396 | |
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| 397 | indices = zeros( M, Int ) |
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| 398 | |
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| 399 | if verbose: print 'Calling C-version of inside poly' |
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| 400 | |
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| 401 | count = separate_points_by_polygon(points, polygon, indices, |
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| 402 | int(closed), int(verbose)) |
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| 403 | |
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| 404 | return indices, count |
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| 405 | |
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| 406 | |
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[2912] | 407 | def polygon_area(polygon): |
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| 408 | """ Determin area of arbitrary polygon |
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| 409 | Reference |
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| 410 | http://mathworld.wolfram.com/PolygonArea.html |
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| 411 | """ |
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| 412 | |
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| 413 | n = len(polygon) |
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| 414 | poly_area = 0.0 |
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[2622] | 415 | |
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[2912] | 416 | for i in range(n): |
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| 417 | pti = polygon[i] |
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| 418 | if i == n-1: |
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| 419 | pt1 = polygon[0] |
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| 420 | else: |
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| 421 | pt1 = polygon[i+1] |
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| 422 | xi = pti[0] |
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| 423 | yi1 = pt1[1] |
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| 424 | xi1 = pt1[0] |
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| 425 | yi = pti[1] |
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| 426 | poly_area += xi*yi1 - xi1*yi |
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| 427 | |
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| 428 | return abs(poly_area/2) |
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| 429 | |
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[2955] | 430 | def plot_polygons(polygons, figname, verbose=False): |
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[2912] | 431 | |
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| 432 | """ Take list of polygons and plot. |
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| 433 | |
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| 434 | Inputs: |
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| 435 | |
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| 436 | polygons - list of polygons |
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| 437 | |
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| 438 | figname - name to save figure to |
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| 439 | |
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| 440 | Outputs: |
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| 441 | |
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| 442 | - list of min and max of x and y coordinates |
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| 443 | - plot of polygons |
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| 444 | """ |
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| 445 | |
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| 446 | from pylab import ion, hold, plot, axis, figure, legend, savefig, xlabel, ylabel, title, close |
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| 447 | |
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| 448 | assert type(polygons) == list,\ |
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[2955] | 449 | 'input must be a list of polygons' |
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| 450 | |
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[2912] | 451 | ion() |
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| 452 | hold(True) |
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| 453 | |
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| 454 | minx = 1e10 |
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| 455 | maxx = 0.0 |
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| 456 | miny = 1e10 |
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| 457 | maxy = 0.0 |
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[2955] | 458 | |
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| 459 | for polygon in polygons: |
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| 460 | x, y = poly_xy(polygon) |
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[2912] | 461 | if min(x) < minx: minx = min(x) |
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| 462 | if max(x) > maxx: maxx = max(x) |
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| 463 | if min(y) < miny: miny = min(y) |
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| 464 | if max(y) > maxy: maxy = max(y) |
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| 465 | plot(x,y,'r-') |
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| 466 | xlabel('x') |
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| 467 | ylabel('y') |
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| 468 | |
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| 469 | savefig(figname) |
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| 470 | |
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| 471 | close('all') |
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| 472 | |
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| 473 | vec = [minx,maxx,miny,maxy] |
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| 474 | |
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| 475 | return vec |
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| 476 | |
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[2955] | 477 | def poly_xy(polygon, verbose=False): |
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[2912] | 478 | """ this is used within plot_polygons so need to duplicate |
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| 479 | the first point so can have closed polygon in plot |
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| 480 | """ |
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| 481 | |
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[2955] | 482 | if verbose: print 'Checking input to poly_xy' |
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[2912] | 483 | |
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[2955] | 484 | try: |
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| 485 | polygon = ensure_numeric(polygon, Float) |
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| 486 | except NameError, e: |
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| 487 | raise NameError, e |
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| 488 | except: |
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| 489 | msg = 'Polygon %s could not be converted to Numeric array' %(str(polygon)) |
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| 490 | raise msg |
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| 491 | |
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| 492 | x = polygon[:,0] |
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| 493 | y = polygon[:,1] |
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| 494 | x = concatenate((x, [polygon[0,0]]), axis = 0) |
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| 495 | y = concatenate((y, [polygon[0,1]]), axis = 0) |
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[2912] | 496 | |
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| 497 | return x, y |
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[2955] | 498 | |
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| 499 | # x = [] |
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| 500 | # y = [] |
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| 501 | # n = len(poly) |
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| 502 | # firstpt = poly[0] |
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| 503 | # for i in range(n): |
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| 504 | # thispt = poly[i] |
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| 505 | # x.append(thispt[0]) |
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| 506 | # y.append(thispt[1]) |
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[2912] | 507 | |
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[2955] | 508 | # x.append(firstpt[0]) |
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| 509 | # y.append(firstpt[1]) |
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| 510 | |
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| 511 | # return x, y |
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| 512 | |
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[2622] | 513 | class Polygon_function: |
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| 514 | """Create callable object f: x,y -> z, where a,y,z are vectors and |
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| 515 | where f will return different values depending on whether x,y belongs |
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| 516 | to specified polygons. |
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| 517 | |
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| 518 | To instantiate: |
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| 519 | |
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| 520 | Polygon_function(polygons) |
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| 521 | |
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| 522 | where polygons is a list of tuples of the form |
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| 523 | |
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| 524 | [ (P0, v0), (P1, v1), ...] |
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| 525 | |
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| 526 | with Pi being lists of vertices defining polygons and vi either |
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| 527 | constants or functions of x,y to be applied to points with the polygon. |
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| 528 | |
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| 529 | The function takes an optional argument, default which is the value |
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| 530 | (or function) to used for points not belonging to any polygon. |
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| 531 | For example: |
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| 532 | |
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| 533 | Polygon_function(polygons, default = 0.03) |
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| 534 | |
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| 535 | If omitted the default value will be 0.0 |
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| 536 | |
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| 537 | Note: If two polygons overlap, the one last in the list takes precedence |
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| 538 | |
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| 539 | Coordinates specified in the call are assumed to be relative to the origin (georeference) |
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| 540 | e.g. used by domain. By specifying the optional argument georeference, all points are made relative. |
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| 541 | |
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| 542 | FIXME: This should really work with geo_spatial point sets. |
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| 543 | """ |
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| 544 | |
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| 545 | def __init__(self, regions, default = 0.0, geo_reference = None): |
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| 546 | |
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| 547 | try: |
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| 548 | len(regions) |
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| 549 | except: |
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| 550 | msg = 'Polygon_function takes a list of pairs (polygon, value). Got %s' %polygons |
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| 551 | raise msg |
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| 552 | |
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| 553 | |
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| 554 | T = regions[0] |
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| 555 | try: |
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| 556 | a = len(T) |
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| 557 | except: |
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| 558 | msg = 'Polygon_function takes a list of pairs (polygon, value). Got %s' %polygons |
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| 559 | raise msg |
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| 560 | |
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| 561 | assert a == 2, 'Must have two component each: %s' %T |
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| 562 | |
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| 563 | |
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| 564 | if geo_reference is None: |
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| 565 | from coordinate_transforms.geo_reference import Geo_reference |
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| 566 | geo_reference = Geo_reference() |
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| 567 | |
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| 568 | |
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| 569 | self.default = default |
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| 570 | |
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| 571 | #Make points in polygons relative to geo_reference |
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| 572 | self.regions = [] |
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| 573 | for polygon, value in regions: |
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| 574 | P = geo_reference.change_points_geo_ref(polygon) |
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| 575 | self.regions.append( (P, value) ) |
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| 576 | |
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| 577 | |
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| 578 | |
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| 579 | |
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| 580 | def __call__(self, x, y): |
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| 581 | x = array(x).astype(Float) |
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| 582 | y = array(y).astype(Float) |
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| 583 | |
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| 584 | N = len(x) |
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| 585 | assert len(y) == N |
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| 586 | |
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| 587 | points = concatenate( (reshape(x, (N, 1)), |
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| 588 | reshape(y, (N, 1))), axis=1 ) |
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| 589 | |
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| 590 | if callable(self.default): |
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| 591 | z = self.default(x,y) |
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| 592 | else: |
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| 593 | z = ones(N, Float) * self.default |
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| 594 | |
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| 595 | for polygon, value in self.regions: |
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| 596 | indices = inside_polygon(points, polygon) |
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| 597 | |
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| 598 | #FIXME: This needs to be vectorised |
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| 599 | if callable(value): |
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| 600 | for i in indices: |
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| 601 | xx = array([x[i]]) |
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| 602 | yy = array([y[i]]) |
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| 603 | z[i] = value(xx, yy)[0] |
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| 604 | else: |
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| 605 | for i in indices: |
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| 606 | z[i] = value |
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| 607 | |
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| 608 | return z |
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| 609 | |
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| 610 | def read_polygon(filename,split=','): |
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| 611 | """Read points assumed to form a polygon. |
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| 612 | There must be exactly two numbers in each line separated by a comma. |
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| 613 | No header. |
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| 614 | """ |
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| 615 | |
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| 616 | #Get polygon |
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| 617 | fid = open(filename) |
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| 618 | lines = fid.readlines() |
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| 619 | fid.close() |
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| 620 | polygon = [] |
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| 621 | for line in lines: |
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| 622 | fields = line.split(split) |
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| 623 | polygon.append( [float(fields[0]), float(fields[1])] ) |
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| 624 | |
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| 625 | return polygon |
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| 626 | |
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| 627 | def populate_polygon(polygon, number_of_points, seed = None, exclude = None): |
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| 628 | """Populate given polygon with uniformly distributed points. |
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| 629 | |
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| 630 | Input: |
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| 631 | polygon - list of vertices of polygon |
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| 632 | number_of_points - (optional) number of points |
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| 633 | seed - seed for random number generator (default=None) |
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| 634 | exclude - list of polygons (inside main polygon) from where points should be excluded |
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| 635 | |
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| 636 | Output: |
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| 637 | points - list of points inside polygon |
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| 638 | |
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| 639 | Examples: |
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| 640 | populate_polygon( [[0,0], [1,0], [1,1], [0,1]], 5 ) |
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| 641 | will return five randomly selected points inside the unit square |
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| 642 | """ |
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| 643 | |
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| 644 | from random import uniform, seed as seed_function |
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| 645 | |
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| 646 | seed_function(seed) |
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| 647 | |
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| 648 | points = [] |
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| 649 | |
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| 650 | #Find outer extent of polygon |
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| 651 | max_x = min_x = polygon[0][0] |
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| 652 | max_y = min_y = polygon[0][1] |
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| 653 | for point in polygon[1:]: |
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| 654 | x = point[0] |
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| 655 | if x > max_x: max_x = x |
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| 656 | if x < min_x: min_x = x |
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| 657 | y = point[1] |
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| 658 | if y > max_y: max_y = y |
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| 659 | if y < min_y: min_y = y |
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| 660 | |
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| 661 | |
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| 662 | while len(points) < number_of_points: |
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| 663 | x = uniform(min_x, max_x) |
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| 664 | y = uniform(min_y, max_y) |
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| 665 | |
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| 666 | append = False |
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[3052] | 667 | if is_inside_polygon([x,y], polygon): |
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[2622] | 668 | |
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| 669 | append = True |
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| 670 | |
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| 671 | #Check exclusions |
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| 672 | if exclude is not None: |
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| 673 | for ex_poly in exclude: |
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[3052] | 674 | if is_inside_polygon([x,y], ex_poly): |
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[2622] | 675 | append = False |
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| 676 | |
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| 677 | |
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| 678 | if append is True: |
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| 679 | points.append([x,y]) |
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| 680 | |
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| 681 | return points |
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| 682 | |
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| 683 | def point_in_polygon(polygon, delta=1e-8): |
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| 684 | """Return a point inside a given polygon which will be close to the |
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| 685 | polygon edge. |
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| 686 | |
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| 687 | Input: |
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| 688 | polygon - list of vertices of polygon |
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| 689 | delta - the square root of 2 * delta is the maximum distance from the |
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| 690 | polygon points and the returned point. |
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| 691 | Output: |
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| 692 | points - a point inside polygon |
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| 693 | |
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| 694 | searches in all diagonals and up and down (not left and right) |
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| 695 | """ |
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| 696 | import exceptions |
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| 697 | class Found(exceptions.Exception): pass |
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| 698 | |
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| 699 | point_in = False |
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| 700 | while not point_in: |
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| 701 | try: |
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| 702 | for poly_point in polygon: #[1:]: |
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| 703 | for x_mult in range (-1,2): |
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| 704 | for y_mult in range (-1,2): |
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| 705 | x = poly_point[0] |
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| 706 | y = poly_point[1] |
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| 707 | if x == 0: |
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| 708 | x_delta = x_mult*delta |
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| 709 | else: |
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| 710 | x_delta = x+x_mult*x*delta |
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| 711 | |
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| 712 | if y == 0: |
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| 713 | y_delta = y_mult*delta |
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| 714 | else: |
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| 715 | y_delta = y+y_mult*y*delta |
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| 716 | |
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| 717 | point = [x_delta, y_delta] |
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| 718 | #print "point",point |
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[3052] | 719 | if is_inside_polygon(point, polygon, closed=False): |
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[2622] | 720 | raise Found |
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| 721 | except Found: |
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| 722 | point_in = True |
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| 723 | else: |
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| 724 | delta = delta*0.1 |
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| 725 | return point |
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| 726 | |
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| 727 | |
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| 728 | |
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| 729 | ############################################## |
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| 730 | #Initialise module |
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| 731 | |
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| 732 | import compile |
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| 733 | if compile.can_use_C_extension('polygon_ext.c'): |
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| 734 | from polygon_ext import point_on_line |
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| 735 | separate_points_by_polygon = separate_points_by_polygon_c |
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| 736 | |
---|
| 737 | |
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| 738 | if __name__ == "__main__": |
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| 739 | pass |
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