[5897] | 1 | #!/usr/bin/env python |
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| 2 | |
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[7276] | 3 | """Polygon manipulations""" |
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[5897] | 4 | |
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[7276] | 5 | import numpy as num |
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| 6 | |
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[5897] | 7 | from anuga.utilities.numerical_tools import ensure_numeric |
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[7778] | 8 | from anuga.geospatial_data.geospatial_data import ensure_absolute, \ |
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| 9 | Geospatial_data |
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[7317] | 10 | import anuga.utilities.log as log |
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[5897] | 11 | |
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[7858] | 12 | from aabb import AABB |
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[5897] | 13 | |
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[7276] | 14 | ## |
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| 15 | # @brief Determine whether a point is on a line segment. |
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| 16 | # @param point (x, y) of point in question (tuple, list or array). |
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| 17 | # @param line ((x1,y1), (x2,y2)) for line (tuple, list or array). |
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| 18 | # @param rtol Relative error for 'close'. |
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| 19 | # @param atol Absolute error for 'close'. |
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| 20 | # @return True or False. |
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[5932] | 21 | def point_on_line(point, line, rtol=1.0e-5, atol=1.0e-8): |
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[5897] | 22 | """Determine whether a point is on a line segment |
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| 23 | |
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[7276] | 24 | Input: |
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[5897] | 25 | point is given by [x, y] |
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[7276] | 26 | line is given by [x0, y0], [x1, y1]] or |
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| 27 | the equivalent 2x2 numeric array with each row corresponding to a point. |
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[5897] | 28 | |
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| 29 | Output: |
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| 30 | |
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[7276] | 31 | Note: Line can be degenerate and function still works to discern coinciding |
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| 32 | points from non-coinciding. |
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[5897] | 33 | """ |
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| 34 | |
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| 35 | point = ensure_numeric(point) |
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| 36 | line = ensure_numeric(line) |
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| 37 | |
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| 38 | res = _point_on_line(point[0], point[1], |
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[7858] | 39 | line[0, 0], line[0, 1], |
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| 40 | line[1, 0], line[1, 1], |
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[5897] | 41 | rtol, atol) |
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[7276] | 42 | |
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[5897] | 43 | return bool(res) |
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| 44 | |
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| 45 | |
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[5942] | 46 | ###### |
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| 47 | # Result functions used in intersection() below for collinear lines. |
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| 48 | # (p0,p1) defines line 0, (p2,p3) defines line 1. |
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| 49 | ###### |
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[5897] | 50 | |
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[5942] | 51 | # result functions for possible states |
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[7858] | 52 | def lines_dont_coincide(p0, p1, p2, p3): |
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| 53 | return (3, None) |
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| 54 | |
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| 55 | def lines_0_fully_included_in_1(p0, p1, p2, p3): |
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| 56 | return (2, num.array([p0, p1])) |
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| 57 | |
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| 58 | def lines_1_fully_included_in_0(p0, p1, p2, p3): |
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| 59 | return (2, num.array([p2, p3])) |
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| 60 | |
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| 61 | def lines_overlap_same_direction(p0, p1, p2, p3): |
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| 62 | return (2, num.array([p0, p3])) |
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| 63 | |
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| 64 | def lines_overlap_same_direction2(p0, p1, p2, p3): |
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| 65 | return (2, num.array([p2, p1])) |
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| 66 | |
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| 67 | def lines_overlap_opposite_direction(p0, p1, p2, p3): |
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| 68 | return (2, num.array([p0, p2])) |
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| 69 | |
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| 70 | def lines_overlap_opposite_direction2(p0, p1, p2, p3): |
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| 71 | return (2, num.array([p3, p1])) |
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[5897] | 72 | |
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[5942] | 73 | # this function called when an impossible state is found |
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[7276] | 74 | def lines_error(p1, p2, p3, p4): |
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| 75 | raise RuntimeError, ('INTERNAL ERROR: p1=%s, p2=%s, p3=%s, p4=%s' |
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| 76 | % (str(p1), str(p2), str(p3), str(p4))) |
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[5897] | 77 | |
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[7778] | 78 | collinear_result = { |
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| 79 | # line 0 starts on 1, 0 ends 1, 1 starts 0, 1 ends 0 |
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| 80 | # 0s1 0e1 1s0 1e0 |
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| 81 | (False, False, False, False): lines_dont_coincide, |
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| 82 | (False, False, False, True ): lines_error, |
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| 83 | (False, False, True, False): lines_error, |
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| 84 | (False, False, True, True ): lines_1_fully_included_in_0, |
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| 85 | (False, True, False, False): lines_error, |
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| 86 | (False, True, False, True ): lines_overlap_opposite_direction2, |
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| 87 | (False, True, True, False): lines_overlap_same_direction2, |
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| 88 | (False, True, True, True ): lines_1_fully_included_in_0, |
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| 89 | (True, False, False, False): lines_error, |
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| 90 | (True, False, False, True ): lines_overlap_same_direction, |
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| 91 | (True, False, True, False): lines_overlap_opposite_direction, |
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| 92 | (True, False, True, True ): lines_1_fully_included_in_0, |
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| 93 | (True, True, False, False): lines_0_fully_included_in_1, |
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| 94 | (True, True, False, True ): lines_0_fully_included_in_1, |
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| 95 | (True, True, True, False): lines_0_fully_included_in_1, |
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| 96 | (True, True, True, True ): lines_0_fully_included_in_1 |
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| 97 | } |
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[5942] | 98 | |
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[7276] | 99 | ## |
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| 100 | # @brief Finds intersection point of two line segments. |
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| 101 | # @param line0 First line ((x1,y1), (x2,y2)). |
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| 102 | # @param line1 Second line ((x1,y1), (x2,y2)). |
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| 103 | # @param rtol Relative error for 'close'. |
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| 104 | # @param atol Absolute error for 'close'. |
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| 105 | # @return (status, value) where: |
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| 106 | # status = 0 - no intersection, value set to None |
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| 107 | # 1 - intersection found, value=(x,y) |
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| 108 | # 2 - lines collienar, overlap, value=overlap segment |
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| 109 | # 3 - lines collinear, no overlap, value is None |
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| 110 | # 4 - lines parallel, value is None |
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[5932] | 111 | def intersection(line0, line1, rtol=1.0e-5, atol=1.0e-8): |
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[7276] | 112 | """Returns intersecting point between two line segments. |
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[5897] | 113 | |
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[7276] | 114 | However, if parallel lines coincide partly (i.e. share a common segment), |
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[5897] | 115 | the line segment where lines coincide is returned |
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| 116 | |
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| 117 | Inputs: |
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| 118 | line0, line1: Each defined by two end points as in: [[x0, y0], [x1, y1]] |
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[5942] | 119 | A line can also be a 2x2 numpy array with each row |
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[5897] | 120 | corresponding to a point. |
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| 121 | |
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| 122 | Output: |
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[7276] | 123 | status, value - where status and value is interpreted as follows: |
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[5942] | 124 | status == 0: no intersection, value set to None. |
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| 125 | status == 1: intersection point found and returned in value as [x,y]. |
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[7276] | 126 | status == 2: Collinear overlapping lines found. |
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| 127 | Value takes the form [[x0,y0], [x1,y1]]. |
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[5942] | 128 | status == 3: Collinear non-overlapping lines. Value set to None. |
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[7276] | 129 | status == 4: Lines are parallel. Value set to None. |
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[5897] | 130 | """ |
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| 131 | |
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| 132 | # FIXME (Ole): Write this in C |
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| 133 | |
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[7276] | 134 | line0 = ensure_numeric(line0, num.float) |
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| 135 | line1 = ensure_numeric(line1, num.float) |
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[5897] | 136 | |
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[7841] | 137 | x0 = line0[0, 0]; y0 = line0[0, 1] |
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| 138 | x1 = line0[1, 0]; y1 = line0[1, 1] |
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[5897] | 139 | |
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[7841] | 140 | x2 = line1[0, 0]; y2 = line1[0, 1] |
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| 141 | x3 = line1[1, 0]; y3 = line1[1, 1] |
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[5897] | 142 | |
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| 143 | denom = (y3-y2)*(x1-x0) - (x3-x2)*(y1-y0) |
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| 144 | u0 = (x3-x2)*(y0-y2) - (y3-y2)*(x0-x2) |
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| 145 | u1 = (x2-x0)*(y1-y0) - (y2-y0)*(x1-x0) |
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[7276] | 146 | |
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[6158] | 147 | if num.allclose(denom, 0.0, rtol=rtol, atol=atol): |
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[5942] | 148 | # Lines are parallel - check if they are collinear |
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[6158] | 149 | if num.allclose([u0, u1], 0.0, rtol=rtol, atol=atol): |
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[5942] | 150 | # We now know that the lines are collinear |
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| 151 | state_tuple = (point_on_line([x0, y0], line1, rtol=rtol, atol=atol), |
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| 152 | point_on_line([x1, y1], line1, rtol=rtol, atol=atol), |
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| 153 | point_on_line([x2, y2], line0, rtol=rtol, atol=atol), |
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| 154 | point_on_line([x3, y3], line0, rtol=rtol, atol=atol)) |
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[5897] | 155 | |
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[7858] | 156 | return collinear_result[state_tuple]([x0, y0], [x1, y1], |
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| 157 | [x2, y2], [x3, y3]) |
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[5897] | 158 | else: |
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[5942] | 159 | # Lines are parallel but aren't collinear |
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[7276] | 160 | return 4, None #FIXME (Ole): Add distance here instead of None |
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[5897] | 161 | else: |
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[5942] | 162 | # Lines are not parallel, check if they intersect |
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[5897] | 163 | u0 = u0/denom |
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[7276] | 164 | u1 = u1/denom |
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[5897] | 165 | |
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| 166 | x = x0 + u0*(x1-x0) |
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| 167 | y = y0 + u0*(y1-y0) |
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| 168 | |
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| 169 | # Sanity check - can be removed to speed up if needed |
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[6158] | 170 | assert num.allclose(x, x2 + u1*(x3-x2), rtol=rtol, atol=atol) |
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[7276] | 171 | assert num.allclose(y, y2 + u1*(y3-y2), rtol=rtol, atol=atol) |
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[5897] | 172 | |
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| 173 | # Check if point found lies within given line segments |
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[7276] | 174 | if 0.0 <= u0 <= 1.0 and 0.0 <= u1 <= 1.0: |
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[5897] | 175 | # We have intersection |
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[6158] | 176 | return 1, num.array([x, y]) |
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[5897] | 177 | else: |
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| 178 | # No intersection |
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| 179 | return 0, None |
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| 180 | |
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[7276] | 181 | ## |
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| 182 | # @brief Finds intersection point of two line segments. |
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| 183 | # @param line0 First line ((x1,y1), (x2,y2)). |
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| 184 | # @param line1 Second line ((x1,y1), (x2,y2)). |
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| 185 | # @return (status, value) where: |
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| 186 | # status = 0 - no intersection, value set to None |
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| 187 | # 1 - intersection found, value=(x,y) |
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| 188 | # 2 - lines collienar, overlap, value=overlap segment |
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| 189 | # 3 - lines collinear, no overlap, value is None |
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| 190 | # 4 - lines parallel, value is None |
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| 191 | # @note Wrapper for C function. |
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[5897] | 192 | def NEW_C_intersection(line0, line1): |
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[7276] | 193 | """Returns intersecting point between two line segments. |
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[5897] | 194 | |
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[7276] | 195 | However, if parallel lines coincide partly (i.e. share a common segment), |
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[5897] | 196 | the line segment where lines coincide is returned |
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| 197 | |
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| 198 | Inputs: |
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| 199 | line0, line1: Each defined by two end points as in: [[x0, y0], [x1, y1]] |
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[7276] | 200 | A line can also be a 2x2 numpy array with each row |
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[5897] | 201 | corresponding to a point. |
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| 202 | |
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| 203 | Output: |
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[7276] | 204 | status, value - where status and value is interpreted as follows: |
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| 205 | status == 0: no intersection, value set to None. |
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| 206 | status == 1: intersection point found and returned in value as [x,y]. |
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| 207 | status == 2: Collinear overlapping lines found. |
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| 208 | Value takes the form [[x0,y0], [x1,y1]]. |
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| 209 | status == 3: Collinear non-overlapping lines. Value set to None. |
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| 210 | status == 4: Lines are parallel. Value set to None. |
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[5897] | 211 | """ |
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| 212 | |
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[7276] | 213 | line0 = ensure_numeric(line0, num.float) |
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| 214 | line1 = ensure_numeric(line1, num.float) |
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[5897] | 215 | |
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[7841] | 216 | status, value = _intersection(line0[0, 0], line0[0, 1], |
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| 217 | line0[1, 0], line0[1, 1], |
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| 218 | line1[0, 0], line1[0, 1], |
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| 219 | line1[1, 0], line1[1, 1]) |
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[5897] | 220 | |
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| 221 | return status, value |
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| 222 | |
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[6534] | 223 | def is_inside_triangle(point, triangle, |
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| 224 | closed=True, |
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[6535] | 225 | rtol=1.0e-12, |
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| 226 | atol=1.0e-12, |
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[7841] | 227 | check_inputs=True): |
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[6534] | 228 | """Determine if one point is inside a triangle |
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| 229 | |
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| 230 | This uses the barycentric method: |
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| 231 | |
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| 232 | Triangle is A, B, C |
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| 233 | Point P can then be written as |
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| 234 | |
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| 235 | P = A + alpha * (C-A) + beta * (B-A) |
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| 236 | or if we let |
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| 237 | v=P-A, v0=C-A, v1=B-A |
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| 238 | |
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| 239 | v = alpha*v0 + beta*v1 |
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[5897] | 240 | |
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[6534] | 241 | Dot this equation by v0 and v1 to get two: |
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| 242 | |
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| 243 | dot(v0, v) = alpha*dot(v0, v0) + beta*dot(v0, v1) |
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| 244 | dot(v1, v) = alpha*dot(v1, v0) + beta*dot(v1, v1) |
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| 245 | |
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| 246 | or if a_ij = dot(v_i, v_j) and b_i = dot(v_i, v) |
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| 247 | the matrix equation: |
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| 248 | |
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| 249 | a_00 a_01 alpha b_0 |
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| 250 | = |
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| 251 | a_10 a_11 beta b_1 |
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| 252 | |
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| 253 | Solving for alpha and beta yields: |
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| 254 | |
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| 255 | alpha = (b_0*a_11 - b_1*a_01)/denom |
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| 256 | beta = (b_1*a_00 - b_0*a_10)/denom |
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| 257 | |
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| 258 | with denom = a_11*a_00 - a_10*a_01 |
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| 259 | |
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| 260 | The point is in the triangle whenever |
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| 261 | alpha and beta and their sums are in the unit interval. |
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| 262 | |
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| 263 | rtol and atol will determine how close the point has to be to the edge |
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[6535] | 264 | before it is deemed to be on the edge. |
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[6534] | 265 | |
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| 266 | """ |
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[5897] | 267 | |
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[6544] | 268 | triangle = ensure_numeric(triangle) |
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[7276] | 269 | point = ensure_numeric(point, num.float) |
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[6544] | 270 | |
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[6534] | 271 | if check_inputs is True: |
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| 272 | msg = 'is_inside_triangle must be invoked with one point only' |
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| 273 | assert num.allclose(point.shape, [2]), msg |
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| 274 | |
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[6544] | 275 | |
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[6541] | 276 | # Use C-implementation |
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[6535] | 277 | return bool(_is_inside_triangle(point, triangle, int(closed), rtol, atol)) |
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[6534] | 278 | |
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[7687] | 279 | def is_complex(polygon, verbose=False): |
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[7690] | 280 | """Check if a polygon is complex (self-intersecting). |
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| 281 | Uses a sweep algorithm that is O(n^2) in the worst case, but |
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| 282 | for most normal looking polygons it'll be O(n log n). |
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| 283 | |
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| 284 | polygon is a list of points that define a closed polygon. |
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| 285 | verbose will print a list of the intersection points if true |
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| 286 | |
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| 287 | Return True if polygon is complex. |
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| 288 | """ |
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| 289 | |
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| 290 | def key_xpos(item): |
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[7858] | 291 | """ Return the x coord out of the passed point for sorting key. """ |
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[7690] | 292 | return (item[0][0]) |
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[7686] | 293 | |
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[7690] | 294 | def segments_joined(seg0, seg1): |
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[7841] | 295 | """ See if there are identical segments in the 2 lists. """ |
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[7690] | 296 | for i in seg0: |
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| 297 | for j in seg1: |
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| 298 | if i == j: return True |
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| 299 | return False |
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| 300 | |
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[7686] | 301 | polygon = ensure_numeric(polygon, num.float) |
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| 302 | |
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[7690] | 303 | # build a list of discrete segments from the polygon |
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| 304 | unsorted_segs = [] |
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[7686] | 305 | for i in range(0, len(polygon)-1): |
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[7690] | 306 | unsorted_segs.append([list(polygon[i]), list(polygon[i+1])]) |
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| 307 | unsorted_segs.append([list(polygon[0]), list(polygon[-1])]) |
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| 308 | |
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| 309 | # all segments must point in same direction |
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| 310 | for val in unsorted_segs: |
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| 311 | if val[0][0] > val[1][0]: |
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| 312 | val[0], val[1] = val[1], val[0] |
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| 313 | |
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| 314 | l_x = sorted(unsorted_segs, key=key_xpos) |
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[7686] | 315 | |
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[7690] | 316 | comparisons = 0 |
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| 317 | |
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| 318 | # loop through, only comparing lines that partially overlap in x |
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| 319 | for index, leftmost in enumerate(l_x): |
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| 320 | cmp = index+1 |
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| 321 | while cmp < len(l_x) and leftmost[1][0] > l_x[cmp][0][0]: |
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| 322 | if not segments_joined(leftmost, l_x[cmp]): |
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| 323 | (type, point) = intersection(leftmost, l_x[cmp]) |
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| 324 | comparisons += 1 |
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[7778] | 325 | if type != 0 and type != 4 or (type == 2 and list(point[0]) !=\ |
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| 326 | list(point[1])): |
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[7687] | 327 | if verbose: |
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[7778] | 328 | print 'Self-intersecting polygon found, type ', type |
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| 329 | print 'point', point, |
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[7858] | 330 | print 'vertices: ', leftmost, ' - ', l_x[cmp] |
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[7690] | 331 | return True |
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| 332 | cmp += 1 |
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[7686] | 333 | |
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| 334 | return False |
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| 335 | |
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[6534] | 336 | |
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[5897] | 337 | def is_inside_polygon(point, polygon, closed=True, verbose=False): |
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| 338 | """Determine if one point is inside a polygon |
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| 339 | |
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| 340 | See inside_polygon for more details |
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| 341 | """ |
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| 342 | |
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| 343 | indices = inside_polygon(point, polygon, closed, verbose) |
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| 344 | |
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| 345 | if indices.shape[0] == 1: |
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| 346 | return True |
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| 347 | elif indices.shape[0] == 0: |
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| 348 | return False |
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| 349 | else: |
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| 350 | msg = 'is_inside_polygon must be invoked with one point only' |
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[7841] | 351 | raise Exception(msg) |
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[5897] | 352 | |
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[7276] | 353 | ## |
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| 354 | # @brief Determine which of a set of points are inside a polygon. |
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| 355 | # @param points A set of points (tuple, list or array). |
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| 356 | # @param polygon A set of points defining a polygon (tuple, list or array). |
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| 357 | # @param closed True if points on boundary are considered 'inside' polygon. |
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| 358 | # @param verbose True if this function is to be verbose. |
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| 359 | # @return A list of indices of points inside the polygon. |
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[5897] | 360 | def inside_polygon(points, polygon, closed=True, verbose=False): |
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| 361 | """Determine points inside a polygon |
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| 362 | |
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| 363 | Functions inside_polygon and outside_polygon have been defined in |
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[7276] | 364 | terms of separate_by_polygon which will put all inside indices in |
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[5897] | 365 | the first part of the indices array and outside indices in the last |
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| 366 | |
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| 367 | See separate_points_by_polygon for documentation |
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| 368 | |
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| 369 | points and polygon can be a geospatial instance, |
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| 370 | a list or a numeric array |
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| 371 | """ |
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| 372 | |
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| 373 | try: |
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| 374 | points = ensure_absolute(points) |
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[7858] | 375 | except NameError, err: |
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| 376 | raise NameError, err |
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[5897] | 377 | except: |
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| 378 | # If this fails it is going to be because the points can't be |
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| 379 | # converted to a numeric array. |
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[7276] | 380 | msg = 'Points could not be converted to numeric array' |
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| 381 | raise Exception, msg |
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[5897] | 382 | |
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[6534] | 383 | polygon = ensure_absolute(polygon) |
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[5897] | 384 | try: |
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| 385 | polygon = ensure_absolute(polygon) |
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| 386 | except NameError, e: |
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| 387 | raise NameError, e |
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| 388 | except: |
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| 389 | # If this fails it is going to be because the points can't be |
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| 390 | # converted to a numeric array. |
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[7276] | 391 | msg = ('Polygon %s could not be converted to numeric array' |
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| 392 | % (str(polygon))) |
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| 393 | raise Exception, msg |
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[5897] | 394 | |
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| 395 | if len(points.shape) == 1: |
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| 396 | # Only one point was passed in. Convert to array of points |
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[7276] | 397 | points = num.reshape(points, (1,2)) |
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[5897] | 398 | |
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| 399 | indices, count = separate_points_by_polygon(points, polygon, |
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| 400 | closed=closed, |
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| 401 | verbose=verbose) |
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| 402 | |
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| 403 | # Return indices of points inside polygon |
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| 404 | return indices[:count] |
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| 405 | |
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[7276] | 406 | ## |
---|
| 407 | # @brief Determine if one point is outside a polygon. |
---|
| 408 | # @param point The point of interest. |
---|
| 409 | # @param polygon The polygon to test inclusion in. |
---|
| 410 | # @param closed True if points on boundary are considered 'inside' polygon. |
---|
| 411 | # @param verbose True if this function is to be verbose. |
---|
| 412 | # @return True if point is outside the polygon. |
---|
| 413 | # @note Uses inside_polygon() to do the work. |
---|
[5897] | 414 | def is_outside_polygon(point, polygon, closed=True, verbose=False, |
---|
| 415 | points_geo_ref=None, polygon_geo_ref=None): |
---|
| 416 | """Determine if one point is outside a polygon |
---|
| 417 | |
---|
| 418 | See outside_polygon for more details |
---|
| 419 | """ |
---|
| 420 | |
---|
| 421 | indices = outside_polygon(point, polygon, closed, verbose) |
---|
| 422 | |
---|
| 423 | if indices.shape[0] == 1: |
---|
| 424 | return True |
---|
| 425 | elif indices.shape[0] == 0: |
---|
| 426 | return False |
---|
| 427 | else: |
---|
| 428 | msg = 'is_outside_polygon must be invoked with one point only' |
---|
[7276] | 429 | raise Exception, msg |
---|
[5897] | 430 | |
---|
[7276] | 431 | ## |
---|
| 432 | # @brief Determine which of a set of points are outside a polygon. |
---|
| 433 | # @param points A set of points (tuple, list or array). |
---|
| 434 | # @param polygon A set of points defining a polygon (tuple, list or array). |
---|
| 435 | # @param closed True if points on boundary are considered 'inside' polygon. |
---|
| 436 | # @param verbose True if this function is to be verbose. |
---|
| 437 | # @return A list of indices of points outside the polygon. |
---|
[5897] | 438 | def outside_polygon(points, polygon, closed = True, verbose = False): |
---|
| 439 | """Determine points outside a polygon |
---|
| 440 | |
---|
| 441 | Functions inside_polygon and outside_polygon have been defined in |
---|
[7276] | 442 | terms of separate_by_polygon which will put all inside indices in |
---|
[5897] | 443 | the first part of the indices array and outside indices in the last |
---|
| 444 | |
---|
| 445 | See separate_points_by_polygon for documentation |
---|
| 446 | """ |
---|
| 447 | |
---|
| 448 | try: |
---|
[7276] | 449 | points = ensure_numeric(points, num.float) |
---|
[5897] | 450 | except NameError, e: |
---|
| 451 | raise NameError, e |
---|
| 452 | except: |
---|
[7276] | 453 | msg = 'Points could not be converted to numeric array' |
---|
| 454 | raise Exception, msg |
---|
[5897] | 455 | |
---|
| 456 | try: |
---|
[7276] | 457 | polygon = ensure_numeric(polygon, num.float) |
---|
[5897] | 458 | except NameError, e: |
---|
| 459 | raise NameError, e |
---|
| 460 | except: |
---|
[7276] | 461 | msg = 'Polygon could not be converted to numeric array' |
---|
| 462 | raise Exception, msg |
---|
[5897] | 463 | |
---|
| 464 | if len(points.shape) == 1: |
---|
| 465 | # Only one point was passed in. Convert to array of points |
---|
[7858] | 466 | points = num.reshape(points, (1, 2)) |
---|
[5897] | 467 | |
---|
| 468 | indices, count = separate_points_by_polygon(points, polygon, |
---|
| 469 | closed=closed, |
---|
| 470 | verbose=verbose) |
---|
| 471 | |
---|
| 472 | # Return indices of points outside polygon |
---|
| 473 | if count == len(indices): |
---|
| 474 | # No points are outside |
---|
[6158] | 475 | return num.array([]) |
---|
[5897] | 476 | else: |
---|
| 477 | return indices[count:][::-1] #return reversed |
---|
| 478 | |
---|
[7276] | 479 | ## |
---|
| 480 | # @brief Separate a list of points into two sets inside+outside a polygon. |
---|
| 481 | # @param points A set of points (tuple, list or array). |
---|
| 482 | # @param polygon A set of points defining a polygon (tuple, list or array). |
---|
| 483 | # @param closed True if points on boundary are considered 'inside' polygon. |
---|
| 484 | # @param verbose True if this function is to be verbose. |
---|
| 485 | # @return A tuple (in, out) of point indices for poinst inside amd outside. |
---|
[6534] | 486 | def in_and_outside_polygon(points, polygon, closed=True, verbose=False): |
---|
[5897] | 487 | """Determine points inside and outside a polygon |
---|
| 488 | |
---|
| 489 | See separate_points_by_polygon for documentation |
---|
| 490 | |
---|
[7276] | 491 | Returns an array of points inside and array of points outside the polygon |
---|
[5897] | 492 | """ |
---|
| 493 | |
---|
| 494 | try: |
---|
[7276] | 495 | points = ensure_numeric(points, num.float) |
---|
[5897] | 496 | except NameError, e: |
---|
| 497 | raise NameError, e |
---|
| 498 | except: |
---|
[7276] | 499 | msg = 'Points could not be converted to numeric array' |
---|
| 500 | raise Exception, msg |
---|
[5897] | 501 | |
---|
| 502 | try: |
---|
[7276] | 503 | polygon = ensure_numeric(polygon, num.float) |
---|
[5897] | 504 | except NameError, e: |
---|
| 505 | raise NameError, e |
---|
| 506 | except: |
---|
[7276] | 507 | msg = 'Polygon could not be converted to numeric array' |
---|
| 508 | raise Exception, msg |
---|
[5897] | 509 | |
---|
| 510 | if len(points.shape) == 1: |
---|
| 511 | # Only one point was passed in. Convert to array of points |
---|
[7858] | 512 | points = num.reshape(points, (1, 2)) |
---|
[5897] | 513 | |
---|
| 514 | indices, count = separate_points_by_polygon(points, polygon, |
---|
| 515 | closed=closed, |
---|
| 516 | verbose=verbose) |
---|
[7276] | 517 | |
---|
[5897] | 518 | # Returns indices of points inside and indices of points outside |
---|
| 519 | # the polygon |
---|
| 520 | if count == len(indices): |
---|
| 521 | # No points are outside |
---|
[7778] | 522 | return indices[:count], [] |
---|
[5897] | 523 | else: |
---|
| 524 | return indices[:count], indices[count:][::-1] #return reversed |
---|
| 525 | |
---|
[7778] | 526 | |
---|
| 527 | |
---|
[5897] | 528 | def separate_points_by_polygon(points, polygon, |
---|
[6534] | 529 | closed=True, |
---|
| 530 | check_input=True, |
---|
| 531 | verbose=False): |
---|
[5897] | 532 | """Determine whether points are inside or outside a polygon |
---|
| 533 | |
---|
| 534 | Input: |
---|
| 535 | points - Tuple of (x, y) coordinates, or list of tuples |
---|
| 536 | polygon - list of vertices of polygon |
---|
| 537 | closed - (optional) determine whether points on boundary should be |
---|
| 538 | regarded as belonging to the polygon (closed = True) |
---|
| 539 | or not (closed = False) |
---|
[6534] | 540 | check_input: Allows faster execution if set to False |
---|
[5897] | 541 | |
---|
| 542 | Outputs: |
---|
| 543 | indices: array of same length as points with indices of points falling |
---|
| 544 | inside the polygon listed from the beginning and indices of points |
---|
| 545 | falling outside listed from the end. |
---|
| 546 | |
---|
| 547 | count: count of points falling inside the polygon |
---|
| 548 | |
---|
| 549 | The indices of points inside are obtained as indices[:count] |
---|
| 550 | The indices of points outside are obtained as indices[count:] |
---|
| 551 | |
---|
| 552 | Examples: |
---|
| 553 | U = [[0,0], [1,0], [1,1], [0,1]] #Unit square |
---|
| 554 | |
---|
| 555 | separate_points_by_polygon( [[0.5, 0.5], [1, -0.5], [0.3, 0.2]], U) |
---|
| 556 | will return the indices [0, 2, 1] and count == 2 as only the first |
---|
| 557 | and the last point are inside the unit square |
---|
| 558 | |
---|
| 559 | Remarks: |
---|
| 560 | The vertices may be listed clockwise or counterclockwise and |
---|
| 561 | the first point may optionally be repeated. |
---|
| 562 | Polygons do not need to be convex. |
---|
| 563 | Polygons can have holes in them and points inside a hole is |
---|
| 564 | regarded as being outside the polygon. |
---|
| 565 | |
---|
| 566 | Algorithm is based on work by Darel Finley, |
---|
| 567 | http://www.alienryderflex.com/polygon/ |
---|
| 568 | |
---|
| 569 | Uses underlying C-implementation in polygon_ext.c |
---|
| 570 | """ |
---|
| 571 | |
---|
[6534] | 572 | if check_input: |
---|
| 573 | #Input checks |
---|
[7778] | 574 | assert isinstance(closed, bool), \ |
---|
| 575 | 'Keyword argument "closed" must be boolean' |
---|
| 576 | assert isinstance(verbose, bool), \ |
---|
| 577 | 'Keyword argument "verbose" must be boolean' |
---|
[5897] | 578 | |
---|
[6534] | 579 | try: |
---|
[7276] | 580 | points = ensure_numeric(points, num.float) |
---|
[6534] | 581 | except NameError, e: |
---|
| 582 | raise NameError, e |
---|
| 583 | except: |
---|
[7276] | 584 | msg = 'Points could not be converted to numeric array' |
---|
[7858] | 585 | raise Exception(msg) |
---|
[5897] | 586 | |
---|
[6534] | 587 | try: |
---|
[7276] | 588 | polygon = ensure_numeric(polygon, num.float) |
---|
[6534] | 589 | except NameError, e: |
---|
[7858] | 590 | raise NameError(e) |
---|
[6534] | 591 | except: |
---|
[7276] | 592 | msg = 'Polygon could not be converted to numeric array' |
---|
[7858] | 593 | raise Exception(msg) |
---|
[5897] | 594 | |
---|
[6534] | 595 | msg = 'Polygon array must be a 2d array of vertices' |
---|
| 596 | assert len(polygon.shape) == 2, msg |
---|
[5897] | 597 | |
---|
[6534] | 598 | msg = 'Polygon array must have two columns' |
---|
[7858] | 599 | assert polygon.shape[1] == 2, msg |
---|
[5897] | 600 | |
---|
[7276] | 601 | msg = ('Points array must be 1 or 2 dimensional. ' |
---|
| 602 | 'I got %d dimensions' % len(points.shape)) |
---|
[6534] | 603 | assert 0 < len(points.shape) < 3, msg |
---|
[5897] | 604 | |
---|
[6534] | 605 | if len(points.shape) == 1: |
---|
[7276] | 606 | # Only one point was passed in. Convert to array of points. |
---|
[7858] | 607 | points = num.reshape(points, (1, 2)) |
---|
[5897] | 608 | |
---|
[7276] | 609 | msg = ('Point array must have two columns (x,y), ' |
---|
| 610 | 'I got points.shape[1]=%d' % points.shape[0]) |
---|
| 611 | assert points.shape[1]==2, msg |
---|
[5897] | 612 | |
---|
| 613 | |
---|
[7276] | 614 | msg = ('Points array must be a 2d array. I got %s.' |
---|
| 615 | % str(points[:30])) |
---|
[7858] | 616 | assert len(points.shape) == 2, msg |
---|
[5897] | 617 | |
---|
[6534] | 618 | msg = 'Points array must have two columns' |
---|
[7858] | 619 | assert points.shape[1] == 2, msg |
---|
[5897] | 620 | |
---|
[6534] | 621 | N = polygon.shape[0] # Number of vertices in polygon |
---|
| 622 | M = points.shape[0] # Number of points |
---|
[5897] | 623 | |
---|
[7276] | 624 | indices = num.zeros(M, num.int) |
---|
[5897] | 625 | |
---|
| 626 | count = _separate_points_by_polygon(points, polygon, indices, |
---|
| 627 | int(closed), int(verbose)) |
---|
| 628 | |
---|
[7276] | 629 | if verbose: |
---|
[7317] | 630 | log.critical('Found %d points (out of %d) inside polygon' % (count, M)) |
---|
[7276] | 631 | |
---|
[5897] | 632 | return indices, count |
---|
| 633 | |
---|
[7858] | 634 | |
---|
[7276] | 635 | def polygon_area(input_polygon): |
---|
| 636 | """ Determine area of arbitrary polygon. |
---|
[5897] | 637 | |
---|
[7858] | 638 | input_polygon The polygon to get area of. |
---|
| 639 | |
---|
| 640 | return A scalar value for the polygon area. |
---|
| 641 | |
---|
| 642 | Reference: http://mathworld.wolfram.com/PolygonArea.html |
---|
[5897] | 643 | """ |
---|
[6000] | 644 | # Move polygon to origin (0,0) to avoid rounding errors |
---|
[6001] | 645 | # This makes a copy of the polygon to avoid destroying it |
---|
| 646 | input_polygon = ensure_numeric(input_polygon) |
---|
[7858] | 647 | min_x = min(input_polygon[:, 0]) |
---|
| 648 | min_y = min(input_polygon[:, 1]) |
---|
[6001] | 649 | polygon = input_polygon - [min_x, min_y] |
---|
[6000] | 650 | |
---|
[7276] | 651 | # Compute area |
---|
[5897] | 652 | n = len(polygon) |
---|
| 653 | poly_area = 0.0 |
---|
| 654 | |
---|
| 655 | for i in range(n): |
---|
| 656 | pti = polygon[i] |
---|
| 657 | if i == n-1: |
---|
| 658 | pt1 = polygon[0] |
---|
| 659 | else: |
---|
| 660 | pt1 = polygon[i+1] |
---|
| 661 | xi = pti[0] |
---|
| 662 | yi1 = pt1[1] |
---|
| 663 | xi1 = pt1[0] |
---|
| 664 | yi = pti[1] |
---|
| 665 | poly_area += xi*yi1 - xi1*yi |
---|
[7276] | 666 | |
---|
[5897] | 667 | return abs(poly_area/2) |
---|
| 668 | |
---|
[7778] | 669 | |
---|
[7276] | 670 | def plot_polygons(polygons_points, |
---|
| 671 | style=None, |
---|
| 672 | figname=None, |
---|
| 673 | label=None, |
---|
[7841] | 674 | alpha=None): |
---|
[5897] | 675 | """ Take list of polygons and plot. |
---|
| 676 | |
---|
| 677 | Inputs: |
---|
| 678 | |
---|
| 679 | polygons - list of polygons |
---|
| 680 | |
---|
| 681 | style - style list corresponding to each polygon |
---|
| 682 | - for a polygon, use 'line' |
---|
| 683 | - for points falling outside a polygon, use 'outside' |
---|
[7511] | 684 | - style can also be user defined as in normal pylab plot. |
---|
[7276] | 685 | |
---|
[5897] | 686 | figname - name to save figure to |
---|
| 687 | |
---|
[7516] | 688 | label - title for plotA |
---|
[5897] | 689 | |
---|
[7516] | 690 | alpha - transparency of polygon fill, 0.0=none, 1.0=solid |
---|
| 691 | if not supplied, no fill. |
---|
| 692 | |
---|
[5897] | 693 | Outputs: |
---|
| 694 | |
---|
| 695 | - plot of polygons |
---|
[7276] | 696 | """ |
---|
[5897] | 697 | |
---|
[7841] | 698 | from pylab import ion, hold, plot, savefig, xlabel, \ |
---|
[7516] | 699 | ylabel, title, close, title, fill |
---|
[5897] | 700 | |
---|
[7276] | 701 | assert type(polygons_points) == list, \ |
---|
| 702 | 'input must be a list of polygons and/or points' |
---|
| 703 | |
---|
[5897] | 704 | ion() |
---|
| 705 | hold(True) |
---|
| 706 | |
---|
[7276] | 707 | if label is None: |
---|
| 708 | label = '' |
---|
[5897] | 709 | |
---|
[7516] | 710 | # clamp alpha to sensible range |
---|
| 711 | if alpha: |
---|
| 712 | try: |
---|
| 713 | alpha = float(alpha) |
---|
| 714 | except ValueError: |
---|
| 715 | alpha = None |
---|
| 716 | else: |
---|
[7841] | 717 | alpha = max(0.0, min(1.0, alpha)) |
---|
[7516] | 718 | |
---|
[7858] | 719 | num_points = len(polygons_points) |
---|
[5897] | 720 | colour = [] |
---|
| 721 | if style is None: |
---|
[7276] | 722 | style_type = 'line' |
---|
[5897] | 723 | style = [] |
---|
[7858] | 724 | for i in range(num_points): |
---|
[5897] | 725 | style.append(style_type) |
---|
| 726 | colour.append('b-') |
---|
| 727 | else: |
---|
[7858] | 728 | for style_name in style: |
---|
| 729 | if style_name == 'line': |
---|
| 730 | colour.append('b-') |
---|
| 731 | if style_name == 'outside': |
---|
| 732 | colour.append('r.') |
---|
| 733 | if style_name == 'point': |
---|
| 734 | colour.append('g.') |
---|
| 735 | if style_name not in ['line', 'outside', 'point']: |
---|
| 736 | colour.append(style_name) |
---|
[7276] | 737 | |
---|
[5897] | 738 | for i, item in enumerate(polygons_points): |
---|
[7858] | 739 | pt_x, pt_y = _poly_xy(item) |
---|
| 740 | plot(pt_x, pt_y, colour[i]) |
---|
[7516] | 741 | if alpha: |
---|
[7858] | 742 | fill(pt_x, pt_y, colour[i], alpha=alpha) |
---|
[5897] | 743 | xlabel('x') |
---|
| 744 | ylabel('y') |
---|
| 745 | title(label) |
---|
| 746 | |
---|
| 747 | if figname is not None: |
---|
| 748 | savefig(figname) |
---|
| 749 | else: |
---|
| 750 | savefig('test_image') |
---|
| 751 | |
---|
| 752 | close('all') |
---|
| 753 | |
---|
| 754 | |
---|
[7858] | 755 | def _poly_xy(polygon): |
---|
[5897] | 756 | """ this is used within plot_polygons so need to duplicate |
---|
| 757 | the first point so can have closed polygon in plot |
---|
[7778] | 758 | # @param polygon A set of points defining a polygon. |
---|
| 759 | # @param verbose True if this function is to be verbose. |
---|
| 760 | # @return A tuple (x, y) of X and Y coordinates of the polygon. |
---|
| 761 | # @note We duplicate the first point so can have closed polygon in plot. |
---|
[5897] | 762 | """ |
---|
| 763 | |
---|
| 764 | try: |
---|
[7276] | 765 | polygon = ensure_numeric(polygon, num.float) |
---|
[7858] | 766 | except NameError, err: |
---|
| 767 | raise NameError, err |
---|
[5897] | 768 | except: |
---|
[7276] | 769 | msg = ('Polygon %s could not be converted to numeric array' |
---|
| 770 | % (str(polygon))) |
---|
| 771 | raise Exception, msg |
---|
[5897] | 772 | |
---|
[7858] | 773 | pts_x = num.concatenate((polygon[:, 0], [polygon[0, 0]]), axis = 0) |
---|
| 774 | pts_y = num.concatenate((polygon[:, 1], [polygon[0, 1]]), axis = 0) |
---|
[7276] | 775 | |
---|
[7858] | 776 | return pts_x, pts_y |
---|
[5897] | 777 | |
---|
| 778 | |
---|
[7276] | 779 | ################################################################################ |
---|
| 780 | # Functions to read and write polygon information |
---|
| 781 | ################################################################################ |
---|
[5897] | 782 | |
---|
[7778] | 783 | def read_polygon(filename, delimiter=','): |
---|
[7858] | 784 | """ Read points assumed to form a polygon. |
---|
[7778] | 785 | |
---|
[7858] | 786 | Also checks to make sure polygon is not complex (self-intersecting). |
---|
[7276] | 787 | |
---|
[7858] | 788 | filename Path to file containing polygon data. |
---|
| 789 | delimiter Delimiter to split polygon data with. |
---|
| 790 | A list of point data from the polygon file. |
---|
[7778] | 791 | |
---|
[7858] | 792 | There must be exactly two numbers in each line separated by the delimiter. |
---|
| 793 | No header. |
---|
[5897] | 794 | """ |
---|
| 795 | |
---|
| 796 | fid = open(filename) |
---|
| 797 | lines = fid.readlines() |
---|
| 798 | fid.close() |
---|
| 799 | polygon = [] |
---|
| 800 | for line in lines: |
---|
[7276] | 801 | fields = line.split(delimiter) |
---|
| 802 | polygon.append([float(fields[0]), float(fields[1])]) |
---|
[7686] | 803 | |
---|
[7690] | 804 | # check this is a valid polygon. |
---|
| 805 | if is_complex(polygon, verbose=True): |
---|
[7778] | 806 | msg = 'ERROR: Self-intersecting polygon detected in file ' |
---|
| 807 | msg += filename +'. A complex polygon will not ' |
---|
| 808 | msg += 'necessarily break the algorithms within ANUGA, but it' |
---|
| 809 | msg += 'usually signifies pathological data. Please fix this file.' |
---|
[7690] | 810 | raise Exception, msg |
---|
[7686] | 811 | |
---|
[5897] | 812 | return polygon |
---|
| 813 | |
---|
[7858] | 814 | |
---|
[5897] | 815 | def write_polygon(polygon, filename=None): |
---|
| 816 | """Write polygon to csv file. |
---|
[7276] | 817 | |
---|
| 818 | There will be exactly two numbers, easting and northing, in each line |
---|
| 819 | separated by a comma. |
---|
| 820 | |
---|
| 821 | No header. |
---|
[5897] | 822 | """ |
---|
| 823 | |
---|
| 824 | fid = open(filename, 'w') |
---|
| 825 | for point in polygon: |
---|
[7276] | 826 | fid.write('%f, %f\n' % point) |
---|
[5897] | 827 | fid.close() |
---|
| 828 | |
---|
[7276] | 829 | |
---|
[5897] | 830 | def populate_polygon(polygon, number_of_points, seed=None, exclude=None): |
---|
| 831 | """Populate given polygon with uniformly distributed points. |
---|
| 832 | |
---|
| 833 | Input: |
---|
| 834 | polygon - list of vertices of polygon |
---|
| 835 | number_of_points - (optional) number of points |
---|
| 836 | seed - seed for random number generator (default=None) |
---|
[7276] | 837 | exclude - list of polygons (inside main polygon) from where points |
---|
| 838 | should be excluded |
---|
[5897] | 839 | |
---|
| 840 | Output: |
---|
| 841 | points - list of points inside polygon |
---|
| 842 | |
---|
| 843 | Examples: |
---|
| 844 | populate_polygon( [[0,0], [1,0], [1,1], [0,1]], 5 ) |
---|
| 845 | will return five randomly selected points inside the unit square |
---|
| 846 | """ |
---|
| 847 | |
---|
| 848 | from random import uniform, seed as seed_function |
---|
| 849 | |
---|
| 850 | seed_function(seed) |
---|
| 851 | |
---|
| 852 | points = [] |
---|
| 853 | |
---|
| 854 | # Find outer extent of polygon |
---|
[7858] | 855 | extents = AABB(polygon) |
---|
| 856 | |
---|
[5897] | 857 | while len(points) < number_of_points: |
---|
[7858] | 858 | rand_x = uniform(extents.xmin, extents.xmax) |
---|
| 859 | rand_y = uniform(extents.ymin, extents.ymax) |
---|
[5897] | 860 | |
---|
| 861 | append = False |
---|
[7858] | 862 | if is_inside_polygon([rand_x, rand_y], polygon): |
---|
[5897] | 863 | append = True |
---|
| 864 | |
---|
| 865 | #Check exclusions |
---|
| 866 | if exclude is not None: |
---|
| 867 | for ex_poly in exclude: |
---|
[7858] | 868 | if is_inside_polygon([rand_x, rand_y], ex_poly): |
---|
[5897] | 869 | append = False |
---|
| 870 | |
---|
| 871 | if append is True: |
---|
[7858] | 872 | points.append([rand_x, rand_y]) |
---|
[5897] | 873 | |
---|
| 874 | return points |
---|
| 875 | |
---|
[7778] | 876 | |
---|
[5897] | 877 | def point_in_polygon(polygon, delta=1e-8): |
---|
| 878 | """Return a point inside a given polygon which will be close to the |
---|
| 879 | polygon edge. |
---|
| 880 | |
---|
| 881 | Input: |
---|
| 882 | polygon - list of vertices of polygon |
---|
| 883 | delta - the square root of 2 * delta is the maximum distance from the |
---|
| 884 | polygon points and the returned point. |
---|
| 885 | Output: |
---|
| 886 | points - a point inside polygon |
---|
| 887 | |
---|
[7276] | 888 | searches in all diagonals and up and down (not left and right). |
---|
[5897] | 889 | """ |
---|
[7276] | 890 | |
---|
[6534] | 891 | polygon = ensure_numeric(polygon) |
---|
| 892 | |
---|
[7858] | 893 | while True: |
---|
| 894 | for poly_point in polygon: |
---|
| 895 | for x_mult in range(-1, 2): |
---|
| 896 | for y_mult in range(-1, 2): |
---|
| 897 | pt_x, pt_y = poly_point |
---|
[7276] | 898 | |
---|
[7858] | 899 | if pt_x == 0: |
---|
| 900 | x_delta = x_mult * delta |
---|
| 901 | else: |
---|
| 902 | x_delta = pt_x + x_mult*pt_x*delta |
---|
[5897] | 903 | |
---|
[7858] | 904 | if pt_y == 0: |
---|
| 905 | y_delta = y_mult * delta |
---|
| 906 | else: |
---|
| 907 | y_delta = pt_y + y_mult*pt_y*delta |
---|
[5897] | 908 | |
---|
[7858] | 909 | point = [x_delta, y_delta] |
---|
[7276] | 910 | |
---|
[7858] | 911 | if is_inside_polygon(point, polygon, closed=False): |
---|
| 912 | return point |
---|
| 913 | delta = delta * 0.1 |
---|
[7276] | 914 | |
---|
[5897] | 915 | |
---|
| 916 | def number_mesh_triangles(interior_regions, bounding_poly, remainder_res): |
---|
| 917 | """Calculate the approximate number of triangles inside the |
---|
| 918 | bounding polygon and the other interior regions |
---|
| 919 | |
---|
[7276] | 920 | Polygon areas are converted to square Kms |
---|
[5897] | 921 | |
---|
| 922 | FIXME: Add tests for this function |
---|
| 923 | """ |
---|
[7276] | 924 | |
---|
[5897] | 925 | # TO DO check if any of the regions fall inside one another |
---|
| 926 | |
---|
[7317] | 927 | log.critical('-' * 80) |
---|
| 928 | log.critical('Polygon Max triangle area (m^2) Total area (km^2) ' |
---|
| 929 | 'Estimated #triangles') |
---|
| 930 | log.critical('-' * 80) |
---|
[5897] | 931 | |
---|
| 932 | no_triangles = 0.0 |
---|
| 933 | area = polygon_area(bounding_poly) |
---|
[7276] | 934 | |
---|
[5897] | 935 | for poly, resolution in interior_regions: |
---|
| 936 | this_area = polygon_area(poly) |
---|
| 937 | this_triangles = this_area/resolution |
---|
| 938 | no_triangles += this_triangles |
---|
| 939 | area -= this_area |
---|
[7276] | 940 | |
---|
[7317] | 941 | log.critical('Interior %s%s%d' |
---|
| 942 | % (('%.0f' % resolution).ljust(25), |
---|
| 943 | ('%.2f' % (this_area/1000000)).ljust(19), |
---|
| 944 | this_triangles)) |
---|
| 945 | #print 'Interior ', |
---|
| 946 | #print ('%.0f' % resolution).ljust(25), |
---|
| 947 | #print ('%.2f' % (this_area/1000000)).ljust(19), |
---|
| 948 | #print '%d' % (this_triangles) |
---|
[7276] | 949 | |
---|
[5897] | 950 | bound_triangles = area/remainder_res |
---|
| 951 | no_triangles += bound_triangles |
---|
| 952 | |
---|
[7317] | 953 | log.critical('Bounding %s%s%d' |
---|
| 954 | % (('%.0f' % remainder_res).ljust(25), |
---|
| 955 | ('%.2f' % (area/1000000)).ljust(19), |
---|
| 956 | bound_triangles)) |
---|
| 957 | #print 'Bounding ', |
---|
| 958 | #print ('%.0f' % remainder_res).ljust(25), |
---|
| 959 | #print ('%.2f' % (area/1000000)).ljust(19), |
---|
| 960 | #print '%d' % (bound_triangles) |
---|
[5897] | 961 | |
---|
| 962 | total_number_of_triangles = no_triangles/0.7 |
---|
| 963 | |
---|
[7317] | 964 | log.critical('Estimated total number of triangles: %d' |
---|
| 965 | % total_number_of_triangles) |
---|
| 966 | log.critical('Note: This is generally about 20%% ' |
---|
| 967 | 'less than the final amount') |
---|
[5897] | 968 | |
---|
| 969 | return int(total_number_of_triangles) |
---|
| 970 | |
---|
[7778] | 971 | |
---|
| 972 | def decimate_polygon(polygon, factor=10): |
---|
| 973 | """Reduce number of points in polygon by the specified |
---|
| 974 | factor (default=10, hence the name of the function) such that |
---|
| 975 | the extrema in both axes are preserved. |
---|
| 976 | |
---|
[7276] | 977 | ## |
---|
| 978 | # @brief Reduce number of points in polygon by the specified factor. |
---|
| 979 | # @param polygon The polygon to reduce. |
---|
| 980 | # @param factor The factor to reduce polygon points by (default 10). |
---|
| 981 | # @note The extrema of both axes are preserved. |
---|
[5897] | 982 | |
---|
| 983 | Return reduced polygon |
---|
| 984 | """ |
---|
| 985 | |
---|
| 986 | # FIXME(Ole): This doesn't work at present, |
---|
| 987 | # but it isn't critical either |
---|
| 988 | |
---|
| 989 | # Find outer extent of polygon |
---|
| 990 | num_polygon = ensure_numeric(polygon) |
---|
[7841] | 991 | max_x = max(num_polygon[:, 0]) |
---|
| 992 | max_y = max(num_polygon[:, 1]) |
---|
| 993 | min_x = min(num_polygon[:, 0]) |
---|
| 994 | min_y = min(num_polygon[:, 1]) |
---|
[5897] | 995 | |
---|
| 996 | # Keep only some points making sure extrema are kept |
---|
[7276] | 997 | reduced_polygon = [] |
---|
[5897] | 998 | for i, point in enumerate(polygon): |
---|
[7858] | 999 | if point[0] in [min_x, max_x] and point[1] in [min_y, max_y]: |
---|
[5897] | 1000 | # Keep |
---|
| 1001 | reduced_polygon.append(point) |
---|
| 1002 | else: |
---|
| 1003 | if len(reduced_polygon)*factor < i: |
---|
[7276] | 1004 | reduced_polygon.append(point) |
---|
[5897] | 1005 | |
---|
| 1006 | return reduced_polygon |
---|
| 1007 | |
---|
[7778] | 1008 | |
---|
[6189] | 1009 | def interpolate_polyline(data, |
---|
| 1010 | polyline_nodes, |
---|
| 1011 | gauge_neighbour_id, |
---|
| 1012 | interpolation_points=None, |
---|
| 1013 | rtol=1.0e-6, |
---|
[7841] | 1014 | atol=1.0e-8): |
---|
[6189] | 1015 | """Interpolate linearly between values data on polyline nodes |
---|
[7276] | 1016 | of a polyline to list of interpolation points. |
---|
[6189] | 1017 | |
---|
| 1018 | data is the data on the polyline nodes. |
---|
| 1019 | |
---|
| 1020 | Inputs: |
---|
| 1021 | data: Vector or array of data at the polyline nodes. |
---|
[7276] | 1022 | polyline_nodes: Location of nodes where data is available. |
---|
[6189] | 1023 | gauge_neighbour_id: ? |
---|
| 1024 | interpolation_points: Interpolate polyline data to these positions. |
---|
| 1025 | List of coordinate pairs [x, y] of |
---|
[7276] | 1026 | data points or an nx2 numeric array or a Geospatial_data object |
---|
| 1027 | rtol, atol: Used to determine whether a point is on the polyline or not. |
---|
| 1028 | See point_on_line. |
---|
[6189] | 1029 | |
---|
| 1030 | Output: |
---|
| 1031 | Interpolated values at interpolation points |
---|
| 1032 | """ |
---|
[7276] | 1033 | |
---|
[6189] | 1034 | if isinstance(interpolation_points, Geospatial_data): |
---|
[7276] | 1035 | interpolation_points = interpolation_points.\ |
---|
| 1036 | get_data_points(absolute=True) |
---|
[6189] | 1037 | |
---|
[7276] | 1038 | interpolated_values = num.zeros(len(interpolation_points), num.float) |
---|
[6189] | 1039 | |
---|
[7276] | 1040 | data = ensure_numeric(data, num.float) |
---|
| 1041 | polyline_nodes = ensure_numeric(polyline_nodes, num.float) |
---|
| 1042 | interpolation_points = ensure_numeric(interpolation_points, num.float) |
---|
| 1043 | gauge_neighbour_id = ensure_numeric(gauge_neighbour_id, num.int) |
---|
[6189] | 1044 | |
---|
[7841] | 1045 | num_nodes = polyline_nodes.shape[0] # Number of nodes in polyline |
---|
[7276] | 1046 | |
---|
[6189] | 1047 | # Input sanity check |
---|
[7841] | 1048 | assert_msg = 'interpolation_points are not given (interpolate.py)' |
---|
| 1049 | assert interpolation_points is not None, assert_msg |
---|
[7276] | 1050 | |
---|
[7841] | 1051 | assert_msg = 'function value must be specified at every interpolation node' |
---|
| 1052 | assert data.shape[0] == polyline_nodes.shape[0], assert_msg |
---|
[7276] | 1053 | |
---|
[7841] | 1054 | assert_msg = 'Must define function value at one or more nodes' |
---|
| 1055 | assert data.shape[0] > 0, assert_msg |
---|
[6189] | 1056 | |
---|
[7841] | 1057 | if num_nodes == 1: |
---|
| 1058 | assert_msg = 'Polyline contained only one point. I need more. ' |
---|
| 1059 | assert_msg += str(data) |
---|
| 1060 | raise Exception, assert_msg |
---|
| 1061 | elif num_nodes > 1: |
---|
[6189] | 1062 | _interpolate_polyline(data, |
---|
| 1063 | polyline_nodes, |
---|
| 1064 | gauge_neighbour_id, |
---|
[7276] | 1065 | interpolation_points, |
---|
[6189] | 1066 | interpolated_values, |
---|
| 1067 | rtol, |
---|
| 1068 | atol) |
---|
[7276] | 1069 | |
---|
[7699] | 1070 | |
---|
[6189] | 1071 | return interpolated_values |
---|
| 1072 | |
---|
[7699] | 1073 | |
---|
| 1074 | def polylist2points_verts(polylist): |
---|
| 1075 | """ Convert a list of polygons to discrete points and vertices. |
---|
| 1076 | """ |
---|
| 1077 | |
---|
| 1078 | offset = 0 |
---|
| 1079 | points = [] |
---|
| 1080 | vertices = [] |
---|
| 1081 | for poly in polylist: |
---|
| 1082 | points.extend(poly) |
---|
| 1083 | vertices.extend([[i, i+1] for i in range(offset, offset+len(poly)-1)]) |
---|
| 1084 | offset += len(poly) |
---|
| 1085 | |
---|
| 1086 | return points, vertices |
---|
[7276] | 1087 | |
---|
| 1088 | |
---|
| 1089 | ################################################################################ |
---|
| 1090 | # Initialise module |
---|
| 1091 | ################################################################################ |
---|
[5897] | 1092 | |
---|
[6119] | 1093 | from anuga.utilities import compile |
---|
| 1094 | if compile.can_use_C_extension('polygon_ext.c'): |
---|
[5897] | 1095 | # Underlying C implementations can be accessed |
---|
| 1096 | from polygon_ext import _point_on_line |
---|
| 1097 | from polygon_ext import _separate_points_by_polygon |
---|
[6189] | 1098 | from polygon_ext import _interpolate_polyline |
---|
[6535] | 1099 | from polygon_ext import _is_inside_triangle |
---|
[5897] | 1100 | #from polygon_ext import _intersection |
---|
| 1101 | |
---|
| 1102 | else: |
---|
[7858] | 1103 | ERROR_MSG = 'C implementations could not be accessed by %s.\n ' % __file__ |
---|
| 1104 | ERROR_MSG += 'Make sure compile_all.py has been run as described in ' |
---|
| 1105 | ERROR_MSG += 'the ANUGA installation guide.' |
---|
| 1106 | raise Exception(ERROR_MSG) |
---|
[5897] | 1107 | |
---|
| 1108 | |
---|
| 1109 | if __name__ == "__main__": |
---|
| 1110 | pass |
---|