[5897] | 1 | #!/usr/bin/env python |
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| 2 | |
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[6410] | 3 | """Polygon manipulations""" |
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| 4 | |
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[6304] | 5 | import numpy as num |
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[5897] | 6 | |
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| 7 | from math import sqrt |
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| 8 | from anuga.utilities.numerical_tools import ensure_numeric |
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[6189] | 9 | from anuga.geospatial_data.geospatial_data import ensure_absolute, Geospatial_data |
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[6304] | 10 | from anuga.config import netcdf_float |
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[5897] | 11 | |
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| 12 | |
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[6410] | 13 | ## |
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| 14 | # @brief Determine whether a point is on a line segment. |
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| 15 | # @param point (x, y) of point in question (tuple, list or array). |
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| 16 | # @param line ((x1,y1), (x2,y2)) for line (tuple, list or array). |
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| 17 | # @param rtol Relative error for 'close'. |
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| 18 | # @param atol Absolute error for 'close'. |
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| 19 | # @return True or False. |
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[5932] | 20 | def point_on_line(point, line, rtol=1.0e-5, atol=1.0e-8): |
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[5897] | 21 | """Determine whether a point is on a line segment |
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| 22 | |
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[6410] | 23 | Input: |
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[5897] | 24 | point is given by [x, y] |
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[6304] | 25 | line is given by [x0, y0], [x1, y1]] or |
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| 26 | the equivalent 2x2 numeric array with each row corresponding to a point. |
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[5897] | 27 | |
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| 28 | Output: |
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| 29 | |
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[6410] | 30 | Note: Line can be degenerate and function still works to discern coinciding |
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| 31 | points from non-coinciding. |
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[5897] | 32 | """ |
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| 33 | |
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| 34 | point = ensure_numeric(point) |
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| 35 | line = ensure_numeric(line) |
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| 36 | |
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| 37 | res = _point_on_line(point[0], point[1], |
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| 38 | line[0,0], line[0,1], |
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| 39 | line[1,0], line[1,1], |
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| 40 | rtol, atol) |
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[6410] | 41 | |
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[5897] | 42 | return bool(res) |
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| 43 | |
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| 44 | |
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[5942] | 45 | ###### |
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| 46 | # Result functions used in intersection() below for collinear lines. |
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| 47 | # (p0,p1) defines line 0, (p2,p3) defines line 1. |
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| 48 | ###### |
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[5897] | 49 | |
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[5942] | 50 | # result functions for possible states |
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| 51 | def lines_dont_coincide(p0,p1,p2,p3): return (3, None) |
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[6410] | 52 | def lines_0_fully_included_in_1(p0,p1,p2,p3): return (2, |
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| 53 | num.array([p0,p1])) |
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| 54 | def lines_1_fully_included_in_0(p0,p1,p2,p3): return (2, |
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| 55 | num.array([p2,p3])) |
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| 56 | def lines_overlap_same_direction(p0,p1,p2,p3): return (2, |
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| 57 | num.array([p0,p3])) |
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| 58 | def lines_overlap_same_direction2(p0,p1,p2,p3): return (2, |
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| 59 | num.array([p2,p1])) |
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| 60 | def lines_overlap_opposite_direction(p0,p1,p2,p3): return (2, |
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| 61 | num.array([p0,p2])) |
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| 62 | def lines_overlap_opposite_direction2(p0,p1,p2,p3): return (2, |
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| 63 | num.array([p3,p1])) |
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[5897] | 64 | |
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[5942] | 65 | # this function called when an impossible state is found |
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[6410] | 66 | def lines_error(p1, p2, p3, p4): |
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| 67 | raise RuntimeError, ('INTERNAL ERROR: p1=%s, p2=%s, p3=%s, p4=%s' |
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| 68 | % (str(p1), str(p2), str(p3), str(p4))) |
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[5897] | 69 | |
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[5942] | 70 | # 0s1 0e1 1s0 1e0 # line 0 starts on 1, 0 ends 1, 1 starts 0, 1 ends 0 |
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| 71 | collinear_result = { (False, False, False, False): lines_dont_coincide, |
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| 72 | (False, False, False, True ): lines_error, |
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| 73 | (False, False, True, False): lines_error, |
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| 74 | (False, False, True, True ): lines_1_fully_included_in_0, |
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| 75 | (False, True, False, False): lines_error, |
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| 76 | (False, True, False, True ): lines_overlap_opposite_direction2, |
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| 77 | (False, True, True, False): lines_overlap_same_direction2, |
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| 78 | (False, True, True, True ): lines_1_fully_included_in_0, |
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| 79 | (True, False, False, False): lines_error, |
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| 80 | (True, False, False, True ): lines_overlap_same_direction, |
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| 81 | (True, False, True, False): lines_overlap_opposite_direction, |
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| 82 | (True, False, True, True ): lines_1_fully_included_in_0, |
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| 83 | (True, True, False, False): lines_0_fully_included_in_1, |
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| 84 | (True, True, False, True ): lines_0_fully_included_in_1, |
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| 85 | (True, True, True, False): lines_0_fully_included_in_1, |
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| 86 | (True, True, True, True ): lines_0_fully_included_in_1 |
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| 87 | } |
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| 88 | |
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[6410] | 89 | ## |
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| 90 | # @brief Finds intersection point of two line segments. |
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| 91 | # @param line0 First line ((x1,y1), (x2,y2)). |
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| 92 | # @param line1 Second line ((x1,y1), (x2,y2)). |
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| 93 | # @param rtol Relative error for 'close'. |
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| 94 | # @param atol Absolute error for 'close'. |
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| 95 | # @return (status, value) where: |
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| 96 | # status = 0 - no intersection, value set to None |
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| 97 | # 1 - intersection found, value=(x,y) |
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| 98 | # 2 - lines collienar, overlap, value=overlap segment |
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| 99 | # 3 - lines collinear, no overlap, value is None |
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| 100 | # 4 - lines parallel, value is None |
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[5932] | 101 | def intersection(line0, line1, rtol=1.0e-5, atol=1.0e-8): |
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[6410] | 102 | """Returns intersecting point between two line segments. |
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[5897] | 103 | |
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[6410] | 104 | However, if parallel lines coincide partly (i.e. share a common segment), |
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[5897] | 105 | the line segment where lines coincide is returned |
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| 106 | |
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| 107 | Inputs: |
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| 108 | line0, line1: Each defined by two end points as in: [[x0, y0], [x1, y1]] |
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[5942] | 109 | A line can also be a 2x2 numpy array with each row |
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[5897] | 110 | corresponding to a point. |
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| 111 | |
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| 112 | Output: |
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[6410] | 113 | status, value - where status and value is interpreted as follows: |
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[5942] | 114 | status == 0: no intersection, value set to None. |
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| 115 | status == 1: intersection point found and returned in value as [x,y]. |
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[6410] | 116 | status == 2: Collinear overlapping lines found. |
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| 117 | Value takes the form [[x0,y0], [x1,y1]]. |
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[5942] | 118 | status == 3: Collinear non-overlapping lines. Value set to None. |
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[6410] | 119 | status == 4: Lines are parallel. Value set to None. |
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[5897] | 120 | """ |
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| 121 | |
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| 122 | # FIXME (Ole): Write this in C |
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| 123 | |
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[6304] | 124 | line0 = ensure_numeric(line0, num.float) |
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[6410] | 125 | line1 = ensure_numeric(line1, num.float) |
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[5897] | 126 | |
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| 127 | x0 = line0[0,0]; y0 = line0[0,1] |
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| 128 | x1 = line0[1,0]; y1 = line0[1,1] |
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| 129 | |
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| 130 | x2 = line1[0,0]; y2 = line1[0,1] |
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| 131 | x3 = line1[1,0]; y3 = line1[1,1] |
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| 132 | |
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| 133 | denom = (y3-y2)*(x1-x0) - (x3-x2)*(y1-y0) |
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| 134 | u0 = (x3-x2)*(y0-y2) - (y3-y2)*(x0-x2) |
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| 135 | u1 = (x2-x0)*(y1-y0) - (y2-y0)*(x1-x0) |
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[6410] | 136 | |
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[6158] | 137 | if num.allclose(denom, 0.0, rtol=rtol, atol=atol): |
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[5942] | 138 | # Lines are parallel - check if they are collinear |
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[6158] | 139 | if num.allclose([u0, u1], 0.0, rtol=rtol, atol=atol): |
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[5942] | 140 | # We now know that the lines are collinear |
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| 141 | state_tuple = (point_on_line([x0, y0], line1, rtol=rtol, atol=atol), |
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| 142 | point_on_line([x1, y1], line1, rtol=rtol, atol=atol), |
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| 143 | point_on_line([x2, y2], line0, rtol=rtol, atol=atol), |
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| 144 | point_on_line([x3, y3], line0, rtol=rtol, atol=atol)) |
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[5897] | 145 | |
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[6410] | 146 | return collinear_result[state_tuple]([x0,y0], [x1,y1], |
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| 147 | [x2,y2], [x3,y3]) |
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[5897] | 148 | else: |
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[5942] | 149 | # Lines are parallel but aren't collinear |
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[6410] | 150 | return 4, None #FIXME (Ole): Add distance here instead of None |
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[5897] | 151 | else: |
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[5942] | 152 | # Lines are not parallel, check if they intersect |
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[5897] | 153 | u0 = u0/denom |
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[6410] | 154 | u1 = u1/denom |
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[5897] | 155 | |
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| 156 | x = x0 + u0*(x1-x0) |
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| 157 | y = y0 + u0*(y1-y0) |
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| 158 | |
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| 159 | # Sanity check - can be removed to speed up if needed |
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[6158] | 160 | assert num.allclose(x, x2 + u1*(x3-x2), rtol=rtol, atol=atol) |
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[6410] | 161 | assert num.allclose(y, y2 + u1*(y3-y2), rtol=rtol, atol=atol) |
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[5897] | 162 | |
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| 163 | # Check if point found lies within given line segments |
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[6410] | 164 | if 0.0 <= u0 <= 1.0 and 0.0 <= u1 <= 1.0: |
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[5897] | 165 | # We have intersection |
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[6158] | 166 | return 1, num.array([x, y]) |
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[5897] | 167 | else: |
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| 168 | # No intersection |
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| 169 | return 0, None |
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| 170 | |
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[6410] | 171 | ## |
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| 172 | # @brief Finds intersection point of two line segments. |
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| 173 | # @param line0 First line ((x1,y1), (x2,y2)). |
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| 174 | # @param line1 Second line ((x1,y1), (x2,y2)). |
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| 175 | # @return (status, value) where: |
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| 176 | # status = 0 - no intersection, value set to None |
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| 177 | # 1 - intersection found, value=(x,y) |
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| 178 | # 2 - lines collienar, overlap, value=overlap segment |
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| 179 | # 3 - lines collinear, no overlap, value is None |
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| 180 | # 4 - lines parallel, value is None |
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| 181 | # @note Wrapper for C function. |
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[5897] | 182 | def NEW_C_intersection(line0, line1): |
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[6410] | 183 | """Returns intersecting point between two line segments. |
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[5897] | 184 | |
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[6410] | 185 | However, if parallel lines coincide partly (i.e. share a common segment), |
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[5897] | 186 | the line segment where lines coincide is returned |
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| 187 | |
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| 188 | Inputs: |
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| 189 | line0, line1: Each defined by two end points as in: [[x0, y0], [x1, y1]] |
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[6410] | 190 | A line can also be a 2x2 numpy array with each row |
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[5897] | 191 | corresponding to a point. |
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| 192 | |
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| 193 | Output: |
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[6410] | 194 | status, value - where status and value is interpreted as follows: |
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| 195 | status == 0: no intersection, value set to None. |
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| 196 | status == 1: intersection point found and returned in value as [x,y]. |
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| 197 | status == 2: Collinear overlapping lines found. |
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| 198 | Value takes the form [[x0,y0], [x1,y1]]. |
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| 199 | status == 3: Collinear non-overlapping lines. Value set to None. |
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| 200 | status == 4: Lines are parallel. Value set to None. |
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[5897] | 201 | """ |
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| 202 | |
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[6304] | 203 | line0 = ensure_numeric(line0, num.float) |
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[6410] | 204 | line1 = ensure_numeric(line1, num.float) |
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[5897] | 205 | |
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| 206 | status, value = _intersection(line0[0,0], line0[0,1], |
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| 207 | line0[1,0], line0[1,1], |
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| 208 | line1[0,0], line1[0,1], |
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| 209 | line1[1,0], line1[1,1]) |
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| 210 | |
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| 211 | return status, value |
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| 212 | |
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[6553] | 213 | def is_inside_triangle(point, triangle, |
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| 214 | closed=True, |
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| 215 | rtol=1.0e-12, |
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| 216 | atol=1.0e-12, |
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| 217 | check_inputs=True, |
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| 218 | verbose=False): |
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| 219 | """Determine if one point is inside a triangle |
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| 220 | |
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| 221 | This uses the barycentric method: |
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| 222 | |
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| 223 | Triangle is A, B, C |
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| 224 | Point P can then be written as |
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| 225 | |
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| 226 | P = A + alpha * (C-A) + beta * (B-A) |
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| 227 | or if we let |
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| 228 | v=P-A, v0=C-A, v1=B-A |
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| 229 | |
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| 230 | v = alpha*v0 + beta*v1 |
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| 231 | |
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| 232 | Dot this equation by v0 and v1 to get two: |
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| 233 | |
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| 234 | dot(v0, v) = alpha*dot(v0, v0) + beta*dot(v0, v1) |
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| 235 | dot(v1, v) = alpha*dot(v1, v0) + beta*dot(v1, v1) |
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| 236 | |
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| 237 | or if a_ij = dot(v_i, v_j) and b_i = dot(v_i, v) |
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| 238 | the matrix equation: |
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| 239 | |
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| 240 | a_00 a_01 alpha b_0 |
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| 241 | = |
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| 242 | a_10 a_11 beta b_1 |
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| 243 | |
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| 244 | Solving for alpha and beta yields: |
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| 245 | |
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| 246 | alpha = (b_0*a_11 - b_1*a_01)/denom |
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| 247 | beta = (b_1*a_00 - b_0*a_10)/denom |
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| 248 | |
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| 249 | with denom = a_11*a_00 - a_10*a_01 |
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| 250 | |
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| 251 | The point is in the triangle whenever |
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| 252 | alpha and beta and their sums are in the unit interval. |
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| 253 | |
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| 254 | rtol and atol will determine how close the point has to be to the edge |
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| 255 | before it is deemed to be on the edge. |
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| 256 | |
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| 257 | """ |
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| 258 | |
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| 259 | triangle = ensure_numeric(triangle) |
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| 260 | point = ensure_numeric(point, num.float) |
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| 261 | |
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| 262 | if check_inputs is True: |
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| 263 | msg = 'is_inside_triangle must be invoked with one point only' |
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| 264 | assert num.allclose(point.shape, [2]), msg |
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| 265 | |
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| 266 | |
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| 267 | # Use C-implementation |
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| 268 | return bool(_is_inside_triangle(point, triangle, int(closed), rtol, atol)) |
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| 269 | |
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| 270 | |
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| 271 | |
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| 272 | # FIXME (Ole): The rest of this function has been made |
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| 273 | # obsolete by the C extension. |
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| 274 | |
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| 275 | # Quickly reject points that are clearly outside |
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| 276 | if point[0] < min(triangle[:,0]): return False |
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| 277 | if point[0] > max(triangle[:,0]): return False |
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| 278 | if point[1] < min(triangle[:,1]): return False |
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| 279 | if point[1] > max(triangle[:,1]): return False |
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| 280 | |
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| 281 | |
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| 282 | # Start search |
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| 283 | A = triangle[0, :] |
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| 284 | B = triangle[1, :] |
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| 285 | C = triangle[2, :] |
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| 286 | |
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| 287 | # Now check if point lies wholly inside triangle |
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| 288 | v0 = C-A |
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| 289 | v1 = B-A |
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| 290 | |
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| 291 | a00 = num.inner(v0, v0) |
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| 292 | a10 = a01 = num.inner(v0, v1) |
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| 293 | a11 = num.inner(v1, v1) |
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| 294 | |
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| 295 | denom = a11*a00 - a01*a10 |
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| 296 | |
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| 297 | if abs(denom) > 0.0: |
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| 298 | v = point-A |
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| 299 | b0 = num.inner(v0, v) |
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| 300 | b1 = num.inner(v1, v) |
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| 301 | |
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| 302 | alpha = (b0*a11 - b1*a01)/denom |
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| 303 | beta = (b1*a00 - b0*a10)/denom |
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| 304 | |
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| 305 | if (alpha > 0.0) and (beta > 0.0) and (alpha+beta < 1.0): |
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| 306 | return True |
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| 307 | |
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| 308 | |
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| 309 | if closed is True: |
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| 310 | # Check if point lies on one of the edges |
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| 311 | |
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| 312 | for X, Y in [[A,B], [B,C], [C,A]]: |
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| 313 | res = _point_on_line(point[0], point[1], |
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| 314 | X[0], X[1], |
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| 315 | Y[0], Y[1], |
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| 316 | rtol, atol) |
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| 317 | |
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| 318 | if res: |
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| 319 | return True |
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| 320 | |
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| 321 | return False |
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| 322 | |
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| 323 | def is_inside_polygon_quick(point, polygon, closed=True, verbose=False): |
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| 324 | """Determine if one point is inside a polygon |
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| 325 | Both point and polygon are assumed to be numeric arrays or lists and |
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| 326 | no georeferencing etc or other checks will take place. |
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| 327 | |
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| 328 | As such it is faster than is_inside_polygon |
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| 329 | """ |
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| 330 | |
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| 331 | # FIXME(Ole): This function isn't being used |
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| 332 | polygon = ensure_numeric(polygon, num.float) |
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| 333 | points = ensure_numeric(point, num.float) # Convert point to array of points |
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| 334 | points = num.ascontiguousarray(points[num.newaxis, :]) |
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| 335 | msg = ('is_inside_polygon() must be invoked with one point only.\n' |
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| 336 | 'I got %s and converted to %s' % (str(point), str(points.shape))) |
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| 337 | assert points.shape[0] == 1 and points.shape[1] == 2, msg |
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| 338 | |
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| 339 | indices = num.zeros(1, num.int) |
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| 340 | |
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| 341 | count = _separate_points_by_polygon(points, polygon, indices, |
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| 342 | int(closed), int(verbose)) |
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| 343 | |
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| 344 | return count > 0 |
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| 345 | |
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| 346 | |
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[5897] | 347 | def is_inside_polygon(point, polygon, closed=True, verbose=False): |
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| 348 | """Determine if one point is inside a polygon |
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| 349 | |
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| 350 | See inside_polygon for more details |
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| 351 | """ |
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| 352 | |
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| 353 | indices = inside_polygon(point, polygon, closed, verbose) |
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| 354 | |
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| 355 | if indices.shape[0] == 1: |
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| 356 | return True |
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| 357 | elif indices.shape[0] == 0: |
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| 358 | return False |
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| 359 | else: |
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| 360 | msg = 'is_inside_polygon must be invoked with one point only' |
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[6553] | 361 | raise msg |
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[5897] | 362 | |
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[6410] | 363 | ## |
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| 364 | # @brief Determine which of a set of points are inside a polygon. |
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| 365 | # @param points A set of points (tuple, list or array). |
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| 366 | # @param polygon A set of points defining a polygon (tuple, list or array). |
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| 367 | # @param closed True if points on boundary are considered 'inside' polygon. |
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| 368 | # @param verbose True if this function is to be verbose. |
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| 369 | # @return A list of indices of points inside the polygon. |
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[5897] | 370 | def inside_polygon(points, polygon, closed=True, verbose=False): |
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| 371 | """Determine points inside a polygon |
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| 372 | |
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| 373 | Functions inside_polygon and outside_polygon have been defined in |
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[6410] | 374 | terms of separate_by_polygon which will put all inside indices in |
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[5897] | 375 | the first part of the indices array and outside indices in the last |
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| 376 | |
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| 377 | See separate_points_by_polygon for documentation |
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| 378 | |
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| 379 | points and polygon can be a geospatial instance, |
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| 380 | a list or a numeric array |
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| 381 | """ |
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| 382 | |
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| 383 | try: |
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| 384 | points = ensure_absolute(points) |
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| 385 | except NameError, e: |
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| 386 | raise NameError, e |
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| 387 | except: |
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| 388 | # If this fails it is going to be because the points can't be |
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| 389 | # converted to a numeric array. |
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[6553] | 390 | msg = 'Points could not be converted to Numeric array' |
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[6304] | 391 | raise Exception, msg |
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[5897] | 392 | |
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[6553] | 393 | polygon = ensure_absolute(polygon) |
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[5897] | 394 | try: |
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| 395 | polygon = ensure_absolute(polygon) |
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| 396 | except NameError, e: |
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| 397 | raise NameError, e |
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| 398 | except: |
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| 399 | # If this fails it is going to be because the points can't be |
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| 400 | # converted to a numeric array. |
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[6410] | 401 | msg = ('Polygon %s could not be converted to numeric array' |
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| 402 | % (str(polygon))) |
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[6304] | 403 | raise Exception, msg |
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[5897] | 404 | |
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| 405 | if len(points.shape) == 1: |
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| 406 | # Only one point was passed in. Convert to array of points |
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[6304] | 407 | points = num.reshape(points, (1,2)) |
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[5897] | 408 | |
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| 409 | indices, count = separate_points_by_polygon(points, polygon, |
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| 410 | closed=closed, |
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| 411 | verbose=verbose) |
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| 412 | |
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| 413 | # Return indices of points inside polygon |
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| 414 | return indices[:count] |
---|
| 415 | |
---|
[6410] | 416 | ## |
---|
| 417 | # @brief Determine if one point is outside a polygon. |
---|
| 418 | # @param point The point of interest. |
---|
| 419 | # @param polygon The polygon to test inclusion in. |
---|
| 420 | # @param closed True if points on boundary are considered 'inside' polygon. |
---|
| 421 | # @param verbose True if this function is to be verbose. |
---|
| 422 | # @return True if point is outside the polygon. |
---|
| 423 | # @note Uses inside_polygon() to do the work. |
---|
[5897] | 424 | def is_outside_polygon(point, polygon, closed=True, verbose=False, |
---|
| 425 | points_geo_ref=None, polygon_geo_ref=None): |
---|
| 426 | """Determine if one point is outside a polygon |
---|
| 427 | |
---|
| 428 | See outside_polygon for more details |
---|
| 429 | """ |
---|
| 430 | |
---|
| 431 | indices = outside_polygon(point, polygon, closed, verbose) |
---|
| 432 | |
---|
| 433 | if indices.shape[0] == 1: |
---|
| 434 | return True |
---|
| 435 | elif indices.shape[0] == 0: |
---|
| 436 | return False |
---|
| 437 | else: |
---|
| 438 | msg = 'is_outside_polygon must be invoked with one point only' |
---|
[6304] | 439 | raise Exception, msg |
---|
[5897] | 440 | |
---|
[6410] | 441 | ## |
---|
| 442 | # @brief Determine which of a set of points are outside a polygon. |
---|
| 443 | # @param points A set of points (tuple, list or array). |
---|
| 444 | # @param polygon A set of points defining a polygon (tuple, list or array). |
---|
| 445 | # @param closed True if points on boundary are considered 'inside' polygon. |
---|
| 446 | # @param verbose True if this function is to be verbose. |
---|
| 447 | # @return A list of indices of points outside the polygon. |
---|
[5897] | 448 | def outside_polygon(points, polygon, closed = True, verbose = False): |
---|
| 449 | """Determine points outside a polygon |
---|
| 450 | |
---|
| 451 | Functions inside_polygon and outside_polygon have been defined in |
---|
[6410] | 452 | terms of separate_by_polygon which will put all inside indices in |
---|
[5897] | 453 | the first part of the indices array and outside indices in the last |
---|
| 454 | |
---|
| 455 | See separate_points_by_polygon for documentation |
---|
| 456 | """ |
---|
| 457 | |
---|
| 458 | try: |
---|
[6304] | 459 | points = ensure_numeric(points, num.float) |
---|
[5897] | 460 | except NameError, e: |
---|
| 461 | raise NameError, e |
---|
| 462 | except: |
---|
[6304] | 463 | msg = 'Points could not be converted to numeric array' |
---|
| 464 | raise Exception, msg |
---|
[5897] | 465 | |
---|
| 466 | try: |
---|
[6304] | 467 | polygon = ensure_numeric(polygon, num.float) |
---|
[5897] | 468 | except NameError, e: |
---|
| 469 | raise NameError, e |
---|
| 470 | except: |
---|
[6304] | 471 | msg = 'Polygon could not be converted to numeric array' |
---|
| 472 | raise Exception, msg |
---|
[5897] | 473 | |
---|
| 474 | if len(points.shape) == 1: |
---|
| 475 | # Only one point was passed in. Convert to array of points |
---|
[6304] | 476 | points = num.reshape(points, (1,2)) |
---|
[5897] | 477 | |
---|
| 478 | indices, count = separate_points_by_polygon(points, polygon, |
---|
| 479 | closed=closed, |
---|
| 480 | verbose=verbose) |
---|
| 481 | |
---|
| 482 | # Return indices of points outside polygon |
---|
| 483 | if count == len(indices): |
---|
| 484 | # No points are outside |
---|
[6158] | 485 | return num.array([]) |
---|
[5897] | 486 | else: |
---|
| 487 | return indices[count:][::-1] #return reversed |
---|
| 488 | |
---|
[6410] | 489 | ## |
---|
| 490 | # @brief Separate a list of points into two sets inside+outside a polygon. |
---|
| 491 | # @param points A set of points (tuple, list or array). |
---|
| 492 | # @param polygon A set of points defining a polygon (tuple, list or array). |
---|
| 493 | # @param closed True if points on boundary are considered 'inside' polygon. |
---|
| 494 | # @param verbose True if this function is to be verbose. |
---|
| 495 | # @return A tuple (in, out) of point indices for poinst inside amd outside. |
---|
| 496 | def in_and_outside_polygon(points, polygon, closed=True, verbose=False): |
---|
[5897] | 497 | """Determine points inside and outside a polygon |
---|
| 498 | |
---|
| 499 | See separate_points_by_polygon for documentation |
---|
| 500 | |
---|
[6410] | 501 | Returns an array of points inside and array of points outside the polygon |
---|
[5897] | 502 | """ |
---|
| 503 | |
---|
| 504 | try: |
---|
[6304] | 505 | points = ensure_numeric(points, num.float) |
---|
[5897] | 506 | except NameError, e: |
---|
| 507 | raise NameError, e |
---|
| 508 | except: |
---|
[6304] | 509 | msg = 'Points could not be converted to numeric array' |
---|
| 510 | raise Exception, msg |
---|
[5897] | 511 | |
---|
| 512 | try: |
---|
[6304] | 513 | polygon = ensure_numeric(polygon, num.float) |
---|
[5897] | 514 | except NameError, e: |
---|
| 515 | raise NameError, e |
---|
| 516 | except: |
---|
[6304] | 517 | msg = 'Polygon could not be converted to numeric array' |
---|
| 518 | raise Exception, msg |
---|
[5897] | 519 | |
---|
| 520 | if len(points.shape) == 1: |
---|
| 521 | # Only one point was passed in. Convert to array of points |
---|
[6304] | 522 | points = num.reshape(points, (1,2)) |
---|
[5897] | 523 | |
---|
| 524 | indices, count = separate_points_by_polygon(points, polygon, |
---|
| 525 | closed=closed, |
---|
| 526 | verbose=verbose) |
---|
[6410] | 527 | |
---|
[5897] | 528 | # Returns indices of points inside and indices of points outside |
---|
| 529 | # the polygon |
---|
| 530 | if count == len(indices): |
---|
| 531 | # No points are outside |
---|
| 532 | return indices[:count],[] |
---|
| 533 | else: |
---|
| 534 | return indices[:count], indices[count:][::-1] #return reversed |
---|
| 535 | |
---|
[6410] | 536 | ## |
---|
| 537 | # @brief Sort a list of points into contiguous points inside+outside a polygon. |
---|
| 538 | # @param points A set of points (tuple, list or array). |
---|
| 539 | # @param polygon A set of points defining a polygon (tuple, list or array). |
---|
| 540 | # @param closed True if points on boundary are considered 'inside' polygon. |
---|
| 541 | # @param verbose True if this function is to be verbose. |
---|
| 542 | # @return (indices, count) where indices are point indices and count is the |
---|
| 543 | # delimiter index between point inside (on left) and others. |
---|
[6553] | 544 | def separate_points_by_polygon(points, polygon, |
---|
| 545 | closed=True, |
---|
| 546 | check_input=True, |
---|
| 547 | verbose=False): |
---|
[5897] | 548 | """Determine whether points are inside or outside a polygon |
---|
| 549 | |
---|
| 550 | Input: |
---|
| 551 | points - Tuple of (x, y) coordinates, or list of tuples |
---|
| 552 | polygon - list of vertices of polygon |
---|
| 553 | closed - (optional) determine whether points on boundary should be |
---|
| 554 | regarded as belonging to the polygon (closed = True) |
---|
| 555 | or not (closed = False) |
---|
[6553] | 556 | check_input: Allows faster execution if set to False |
---|
[5897] | 557 | |
---|
| 558 | Outputs: |
---|
| 559 | indices: array of same length as points with indices of points falling |
---|
| 560 | inside the polygon listed from the beginning and indices of points |
---|
| 561 | falling outside listed from the end. |
---|
| 562 | |
---|
| 563 | count: count of points falling inside the polygon |
---|
| 564 | |
---|
| 565 | The indices of points inside are obtained as indices[:count] |
---|
| 566 | The indices of points outside are obtained as indices[count:] |
---|
| 567 | |
---|
| 568 | Examples: |
---|
| 569 | U = [[0,0], [1,0], [1,1], [0,1]] #Unit square |
---|
| 570 | |
---|
| 571 | separate_points_by_polygon( [[0.5, 0.5], [1, -0.5], [0.3, 0.2]], U) |
---|
| 572 | will return the indices [0, 2, 1] and count == 2 as only the first |
---|
| 573 | and the last point are inside the unit square |
---|
| 574 | |
---|
| 575 | Remarks: |
---|
| 576 | The vertices may be listed clockwise or counterclockwise and |
---|
| 577 | the first point may optionally be repeated. |
---|
| 578 | Polygons do not need to be convex. |
---|
| 579 | Polygons can have holes in them and points inside a hole is |
---|
| 580 | regarded as being outside the polygon. |
---|
| 581 | |
---|
| 582 | Algorithm is based on work by Darel Finley, |
---|
| 583 | http://www.alienryderflex.com/polygon/ |
---|
| 584 | |
---|
| 585 | Uses underlying C-implementation in polygon_ext.c |
---|
| 586 | """ |
---|
| 587 | |
---|
[6553] | 588 | if check_input: |
---|
| 589 | #Input checks |
---|
| 590 | assert isinstance(closed, bool), 'Keyword argument "closed" must be boolean' |
---|
| 591 | assert isinstance(verbose, bool), 'Keyword argument "verbose" must be boolean' |
---|
[5897] | 592 | |
---|
[6553] | 593 | try: |
---|
| 594 | points = ensure_numeric(points, num.float) |
---|
| 595 | except NameError, e: |
---|
| 596 | raise NameError, e |
---|
| 597 | except: |
---|
| 598 | msg = 'Points could not be converted to numeric array' |
---|
| 599 | raise msg |
---|
[5897] | 600 | |
---|
[6553] | 601 | try: |
---|
| 602 | polygon = ensure_numeric(polygon, num.float) |
---|
| 603 | except NameError, e: |
---|
| 604 | raise NameError, e |
---|
| 605 | except: |
---|
| 606 | msg = 'Polygon could not be converted to numeric array' |
---|
| 607 | raise msg |
---|
[5897] | 608 | |
---|
[6553] | 609 | msg = 'Polygon array must be a 2d array of vertices' |
---|
| 610 | assert len(polygon.shape) == 2, msg |
---|
[5897] | 611 | |
---|
[6553] | 612 | msg = 'Polygon array must have two columns' |
---|
| 613 | assert polygon.shape[1]==2, msg |
---|
[5897] | 614 | |
---|
[6553] | 615 | msg = ('Points array must be 1 or 2 dimensional. ' |
---|
| 616 | 'I got %d dimensions' % len(points.shape)) |
---|
| 617 | assert 0 < len(points.shape) < 3, msg |
---|
[5897] | 618 | |
---|
[6553] | 619 | if len(points.shape) == 1: |
---|
| 620 | # Only one point was passed in. Convert to array of points. |
---|
| 621 | points = num.reshape(points, (1,2)) |
---|
| 622 | |
---|
| 623 | msg = ('Point array must have two columns (x,y), ' |
---|
| 624 | 'I got points.shape[1]=%d' % points.shape[0]) |
---|
| 625 | assert points.shape[1]==2, msg |
---|
[5897] | 626 | |
---|
[6553] | 627 | |
---|
| 628 | msg = ('Points array must be a 2d array. I got %s.' |
---|
| 629 | % str(points[:30])) |
---|
| 630 | assert len(points.shape)==2, msg |
---|
[5897] | 631 | |
---|
[6553] | 632 | msg = 'Points array must have two columns' |
---|
| 633 | assert points.shape[1]==2, msg |
---|
[5897] | 634 | |
---|
[6553] | 635 | N = polygon.shape[0] # Number of vertices in polygon |
---|
| 636 | M = points.shape[0] # Number of points |
---|
[5897] | 637 | |
---|
[6553] | 638 | indices = num.zeros(M, num.int) |
---|
[5897] | 639 | |
---|
| 640 | count = _separate_points_by_polygon(points, polygon, indices, |
---|
| 641 | int(closed), int(verbose)) |
---|
| 642 | |
---|
[6553] | 643 | if verbose: |
---|
| 644 | print 'Found %d points (out of %d) inside polygon' % (count, M) |
---|
[6410] | 645 | |
---|
[5897] | 646 | return indices, count |
---|
| 647 | |
---|
[6410] | 648 | ## |
---|
| 649 | # @brief Determine area of a polygon. |
---|
| 650 | # @param input_polygon The polygon to get area of. |
---|
| 651 | # @return A scalar value for the polygon area. |
---|
| 652 | def polygon_area(input_polygon): |
---|
| 653 | """ Determine area of arbitrary polygon. |
---|
[5897] | 654 | |
---|
[6410] | 655 | Reference: http://mathworld.wolfram.com/PolygonArea.html |
---|
[5897] | 656 | """ |
---|
[6410] | 657 | |
---|
[6000] | 658 | # Move polygon to origin (0,0) to avoid rounding errors |
---|
[6001] | 659 | # This makes a copy of the polygon to avoid destroying it |
---|
| 660 | input_polygon = ensure_numeric(input_polygon) |
---|
| 661 | min_x = min(input_polygon[:,0]) |
---|
[6410] | 662 | min_y = min(input_polygon[:,1]) |
---|
[6001] | 663 | polygon = input_polygon - [min_x, min_y] |
---|
[6000] | 664 | |
---|
[6410] | 665 | # Compute area |
---|
[5897] | 666 | n = len(polygon) |
---|
| 667 | poly_area = 0.0 |
---|
| 668 | |
---|
| 669 | for i in range(n): |
---|
| 670 | pti = polygon[i] |
---|
| 671 | if i == n-1: |
---|
| 672 | pt1 = polygon[0] |
---|
| 673 | else: |
---|
| 674 | pt1 = polygon[i+1] |
---|
| 675 | xi = pti[0] |
---|
| 676 | yi1 = pt1[1] |
---|
| 677 | xi1 = pt1[0] |
---|
| 678 | yi = pti[1] |
---|
| 679 | poly_area += xi*yi1 - xi1*yi |
---|
[6410] | 680 | |
---|
[5897] | 681 | return abs(poly_area/2) |
---|
| 682 | |
---|
[6410] | 683 | ## |
---|
| 684 | # @brief Plot a set of polygons. |
---|
| 685 | # @param polygons_points List of polygons to plot. |
---|
| 686 | # @param style List of styles for each polygon. |
---|
| 687 | # @param figname Name to save figure to. |
---|
| 688 | # @param label Title for the plot. |
---|
| 689 | # @param verbose True if this function is to be verbose. |
---|
| 690 | # @return A list of min/max x and y values [minx, maxx, miny, maxy]. |
---|
| 691 | # @note A style value is 'line' for polygons, 'outside' for points outside. |
---|
| 692 | def plot_polygons(polygons_points, |
---|
| 693 | style=None, |
---|
| 694 | figname=None, |
---|
| 695 | label=None, |
---|
| 696 | verbose=False): |
---|
[5897] | 697 | """ Take list of polygons and plot. |
---|
| 698 | |
---|
| 699 | Inputs: |
---|
| 700 | |
---|
| 701 | polygons - list of polygons |
---|
| 702 | |
---|
| 703 | style - style list corresponding to each polygon |
---|
| 704 | - for a polygon, use 'line' |
---|
| 705 | - for points falling outside a polygon, use 'outside' |
---|
[6410] | 706 | |
---|
[5897] | 707 | figname - name to save figure to |
---|
| 708 | |
---|
| 709 | label - title for plot |
---|
| 710 | |
---|
| 711 | Outputs: |
---|
| 712 | |
---|
| 713 | - list of min and max of x and y coordinates |
---|
| 714 | - plot of polygons |
---|
[6410] | 715 | """ |
---|
[5897] | 716 | |
---|
[6410] | 717 | from pylab import ion, hold, plot, axis, figure, legend, savefig, xlabel, \ |
---|
| 718 | ylabel, title, close, title |
---|
[5897] | 719 | |
---|
[6410] | 720 | assert type(polygons_points) == list, \ |
---|
| 721 | 'input must be a list of polygons and/or points' |
---|
| 722 | |
---|
[5897] | 723 | ion() |
---|
| 724 | hold(True) |
---|
| 725 | |
---|
| 726 | minx = 1e10 |
---|
| 727 | maxx = 0.0 |
---|
| 728 | miny = 1e10 |
---|
| 729 | maxy = 0.0 |
---|
| 730 | |
---|
[6410] | 731 | if label is None: |
---|
| 732 | label = '' |
---|
[5897] | 733 | |
---|
| 734 | n = len(polygons_points) |
---|
| 735 | colour = [] |
---|
| 736 | if style is None: |
---|
[6410] | 737 | style_type = 'line' |
---|
[5897] | 738 | style = [] |
---|
| 739 | for i in range(n): |
---|
| 740 | style.append(style_type) |
---|
| 741 | colour.append('b-') |
---|
| 742 | else: |
---|
| 743 | for s in style: |
---|
[6410] | 744 | if s == 'line': colour.append('b-') |
---|
[5897] | 745 | if s == 'outside': colour.append('r.') |
---|
| 746 | if s <> 'line': |
---|
| 747 | if s <> 'outside': |
---|
| 748 | colour.append('g.') |
---|
[6410] | 749 | |
---|
[5897] | 750 | for i, item in enumerate(polygons_points): |
---|
| 751 | x, y = poly_xy(item) |
---|
| 752 | if min(x) < minx: minx = min(x) |
---|
| 753 | if max(x) > maxx: maxx = max(x) |
---|
| 754 | if min(y) < miny: miny = min(y) |
---|
| 755 | if max(y) > maxy: maxy = max(y) |
---|
| 756 | plot(x,y,colour[i]) |
---|
| 757 | xlabel('x') |
---|
| 758 | ylabel('y') |
---|
| 759 | title(label) |
---|
| 760 | |
---|
| 761 | #raw_input('wait 1') |
---|
| 762 | #FIXME(Ole): This makes for some strange scalings sometimes. |
---|
| 763 | #if minx <> 0: |
---|
| 764 | # axis([minx*0.9,maxx*1.1,miny*0.9,maxy*1.1]) |
---|
| 765 | #else: |
---|
| 766 | # if miny == 0: |
---|
| 767 | # axis([-maxx*.01,maxx*1.1,-maxy*0.01,maxy*1.1]) |
---|
| 768 | # else: |
---|
| 769 | # axis([-maxx*.01,maxx*1.1,miny*0.9,maxy*1.1]) |
---|
| 770 | |
---|
| 771 | if figname is not None: |
---|
| 772 | savefig(figname) |
---|
| 773 | else: |
---|
| 774 | savefig('test_image') |
---|
| 775 | |
---|
| 776 | close('all') |
---|
| 777 | |
---|
[6410] | 778 | vec = [minx, maxx, miny, maxy] |
---|
[5897] | 779 | return vec |
---|
| 780 | |
---|
[6410] | 781 | ## |
---|
| 782 | # @brief |
---|
| 783 | # @param polygon A set of points defining a polygon. |
---|
| 784 | # @param verbose True if this function is to be verbose. |
---|
| 785 | # @return A tuple (x, y) of X and Y coordinates of the polygon. |
---|
| 786 | # @note We duplicate the first point so can have closed polygon in plot. |
---|
[5897] | 787 | def poly_xy(polygon, verbose=False): |
---|
| 788 | """ this is used within plot_polygons so need to duplicate |
---|
| 789 | the first point so can have closed polygon in plot |
---|
| 790 | """ |
---|
| 791 | |
---|
| 792 | try: |
---|
[6304] | 793 | polygon = ensure_numeric(polygon, num.float) |
---|
[5897] | 794 | except NameError, e: |
---|
| 795 | raise NameError, e |
---|
| 796 | except: |
---|
[6410] | 797 | msg = ('Polygon %s could not be converted to numeric array' |
---|
| 798 | % (str(polygon))) |
---|
[6304] | 799 | raise Exception, msg |
---|
[5897] | 800 | |
---|
| 801 | x = polygon[:,0] |
---|
| 802 | y = polygon[:,1] |
---|
[6158] | 803 | x = num.concatenate((x, [polygon[0,0]]), axis = 0) |
---|
| 804 | y = num.concatenate((y, [polygon[0,1]]), axis = 0) |
---|
[6410] | 805 | |
---|
[5897] | 806 | return x, y |
---|
| 807 | |
---|
| 808 | |
---|
[6410] | 809 | ## |
---|
| 810 | # @brief Define a class that defines a callable object for a polygon. |
---|
| 811 | # @note Object created is function: f: x,y -> z |
---|
| 812 | # where x, y and z are vectors and z depends on whether x,y belongs |
---|
| 813 | # to specified polygons. |
---|
[5897] | 814 | class Polygon_function: |
---|
| 815 | """Create callable object f: x,y -> z, where a,y,z are vectors and |
---|
| 816 | where f will return different values depending on whether x,y belongs |
---|
| 817 | to specified polygons. |
---|
| 818 | |
---|
| 819 | To instantiate: |
---|
| 820 | |
---|
| 821 | Polygon_function(polygons) |
---|
| 822 | |
---|
| 823 | where polygons is a list of tuples of the form |
---|
| 824 | |
---|
| 825 | [ (P0, v0), (P1, v1), ...] |
---|
| 826 | |
---|
| 827 | with Pi being lists of vertices defining polygons and vi either |
---|
| 828 | constants or functions of x,y to be applied to points with the polygon. |
---|
| 829 | |
---|
| 830 | The function takes an optional argument, default which is the value |
---|
| 831 | (or function) to used for points not belonging to any polygon. |
---|
| 832 | For example: |
---|
| 833 | |
---|
| 834 | Polygon_function(polygons, default = 0.03) |
---|
| 835 | |
---|
| 836 | If omitted the default value will be 0.0 |
---|
| 837 | |
---|
| 838 | Note: If two polygons overlap, the one last in the list takes precedence |
---|
| 839 | |
---|
| 840 | Coordinates specified in the call are assumed to be relative to the |
---|
| 841 | origin (georeference) e.g. used by domain. |
---|
| 842 | By specifying the optional argument georeference, |
---|
| 843 | all points are made relative. |
---|
| 844 | |
---|
| 845 | FIXME: This should really work with geo_spatial point sets. |
---|
| 846 | """ |
---|
| 847 | |
---|
[6410] | 848 | ## |
---|
| 849 | # @brief Create instance of a polygon function. |
---|
| 850 | # @param regions A list of (x,y) tuples defining a polygon. |
---|
| 851 | # @param default Value or function returning value for points outside poly. |
---|
| 852 | # @param geo_reference ?? |
---|
| 853 | def __init__(self, regions, default=0.0, geo_reference=None): |
---|
[6304] | 854 | try: |
---|
| 855 | len(regions) |
---|
| 856 | except: |
---|
[6410] | 857 | msg = ('Polygon_function takes a list of pairs (polygon, value).' |
---|
| 858 | 'Got %s' % str(regions)) |
---|
[6304] | 859 | raise Exception, msg |
---|
[5897] | 860 | |
---|
| 861 | T = regions[0] |
---|
| 862 | |
---|
| 863 | if isinstance(T, basestring): |
---|
[6410] | 864 | msg = ('You passed in a list of text values into polygon_function ' |
---|
| 865 | 'instead of a list of pairs (polygon, value): "%s"' |
---|
| 866 | % str(T)) |
---|
[5897] | 867 | raise Exception, msg |
---|
[6410] | 868 | |
---|
[6304] | 869 | try: |
---|
[5897] | 870 | a = len(T) |
---|
[6304] | 871 | except: |
---|
[6410] | 872 | msg = ('Polygon_function takes a list of pairs (polygon, value). ' |
---|
| 873 | 'Got %s' % str(T)) |
---|
[6304] | 874 | raise Exception, msg |
---|
[5897] | 875 | |
---|
[6410] | 876 | msg = ('Each entry in regions have two components: (polygon, value). ' |
---|
| 877 | 'I got %s' % str(T)) |
---|
[6304] | 878 | assert a == 2, msg |
---|
[5897] | 879 | |
---|
| 880 | if geo_reference is None: |
---|
| 881 | from anuga.coordinate_transforms.geo_reference import Geo_reference |
---|
| 882 | geo_reference = Geo_reference() |
---|
| 883 | |
---|
| 884 | self.default = default |
---|
| 885 | |
---|
| 886 | # Make points in polygons relative to geo_reference |
---|
| 887 | self.regions = [] |
---|
| 888 | for polygon, value in regions: |
---|
| 889 | P = geo_reference.change_points_geo_ref(polygon) |
---|
[6223] | 890 | self.regions.append((P, value)) |
---|
[5897] | 891 | |
---|
[6410] | 892 | ## |
---|
| 893 | # @brief Implement the 'callable' property of Polygon_function. |
---|
| 894 | # @param x List of x coordinates of points ot interest. |
---|
| 895 | # @param y List of y coordinates of points ot interest. |
---|
[5897] | 896 | def __call__(self, x, y): |
---|
[6304] | 897 | x = num.array(x, num.float) |
---|
| 898 | y = num.array(y, num.float) |
---|
[5897] | 899 | |
---|
[6304] | 900 | # x and y must be one-dimensional and same length |
---|
| 901 | assert len(x.shape) == 1 and len(y.shape) == 1 |
---|
| 902 | N = x.shape[0] |
---|
| 903 | assert y.shape[0] == N |
---|
[5897] | 904 | |
---|
[6304] | 905 | points = num.ascontiguousarray(num.concatenate((x[:,num.newaxis], |
---|
| 906 | y[:,num.newaxis]), |
---|
| 907 | axis=1 )) |
---|
[5897] | 908 | |
---|
[6304] | 909 | if callable(self.default): |
---|
[6410] | 910 | z = self.default(x, y) |
---|
[6304] | 911 | else: |
---|
| 912 | z = num.ones(N, num.float) * self.default |
---|
[5897] | 913 | |
---|
[6304] | 914 | for polygon, value in self.regions: |
---|
| 915 | indices = inside_polygon(points, polygon) |
---|
[5897] | 916 | |
---|
[6304] | 917 | # FIXME: This needs to be vectorised |
---|
| 918 | if callable(value): |
---|
| 919 | for i in indices: |
---|
| 920 | xx = num.array([x[i]]) |
---|
| 921 | yy = num.array([y[i]]) |
---|
[5897] | 922 | z[i] = value(xx, yy)[0] |
---|
[6304] | 923 | else: |
---|
| 924 | for i in indices: |
---|
| 925 | z[i] = value |
---|
[5897] | 926 | |
---|
[6223] | 927 | if len(z) == 0: |
---|
[6410] | 928 | msg = ('Warning: points provided to Polygon function did not fall ' |
---|
| 929 | 'within its regions in [%.2f, %.2f], y in [%.2f, %.2f]' |
---|
| 930 | % (min(x), max(x), min(y), max(y))) |
---|
[6223] | 931 | print msg |
---|
| 932 | |
---|
[5897] | 933 | return z |
---|
| 934 | |
---|
[6410] | 935 | ################################################################################ |
---|
| 936 | # Functions to read and write polygon information |
---|
| 937 | ################################################################################ |
---|
[5897] | 938 | |
---|
[6410] | 939 | ## |
---|
| 940 | # @brief Read polygon data from a file. |
---|
| 941 | # @param filename Path to file containing polygon data. |
---|
| 942 | # @param delimiter Delimiter to split polygon data with. |
---|
| 943 | # @return A list of point data from the polygon file. |
---|
| 944 | def read_polygon(filename, delimiter=','): |
---|
[5897] | 945 | """Read points assumed to form a polygon. |
---|
[6410] | 946 | |
---|
| 947 | There must be exactly two numbers in each line separated by the delimiter. |
---|
| 948 | No header. |
---|
[5897] | 949 | """ |
---|
| 950 | |
---|
| 951 | fid = open(filename) |
---|
| 952 | lines = fid.readlines() |
---|
| 953 | fid.close() |
---|
| 954 | polygon = [] |
---|
| 955 | for line in lines: |
---|
[6410] | 956 | fields = line.split(delimiter) |
---|
| 957 | polygon.append([float(fields[0]), float(fields[1])]) |
---|
[5897] | 958 | |
---|
| 959 | return polygon |
---|
| 960 | |
---|
[6410] | 961 | ## |
---|
| 962 | # @brief Write polygon data to a file. |
---|
| 963 | # @param polygon Polygon points to write to file. |
---|
| 964 | # @param filename Path to file to write. |
---|
| 965 | # @note Delimiter is assumed to be a comma. |
---|
[5897] | 966 | def write_polygon(polygon, filename=None): |
---|
| 967 | """Write polygon to csv file. |
---|
[6410] | 968 | |
---|
| 969 | There will be exactly two numbers, easting and northing, in each line |
---|
| 970 | separated by a comma. |
---|
| 971 | |
---|
| 972 | No header. |
---|
[5897] | 973 | """ |
---|
| 974 | |
---|
| 975 | fid = open(filename, 'w') |
---|
| 976 | for point in polygon: |
---|
[6410] | 977 | fid.write('%f, %f\n' % point) |
---|
[5897] | 978 | fid.close() |
---|
| 979 | |
---|
[6410] | 980 | ## |
---|
| 981 | # @brief Unimplemented. |
---|
[6116] | 982 | def read_tagged_polygons(filename): |
---|
| 983 | """ |
---|
| 984 | """ |
---|
| 985 | pass |
---|
[6410] | 986 | |
---|
| 987 | ## |
---|
| 988 | # @brief Populate given polygon with uniformly distributed points. |
---|
| 989 | # @param polygon Polygon to uniformly fill. |
---|
| 990 | # @param number_of_points Number of points required in polygon. |
---|
| 991 | # @param seed Seed for random number generator. |
---|
| 992 | # @param exclude List of polygons inside main where points should be excluded. |
---|
| 993 | # @return List of random points inside input polygon. |
---|
| 994 | # @note Delimiter is assumed to be a comma. |
---|
[5897] | 995 | def populate_polygon(polygon, number_of_points, seed=None, exclude=None): |
---|
| 996 | """Populate given polygon with uniformly distributed points. |
---|
| 997 | |
---|
| 998 | Input: |
---|
| 999 | polygon - list of vertices of polygon |
---|
| 1000 | number_of_points - (optional) number of points |
---|
| 1001 | seed - seed for random number generator (default=None) |
---|
[6410] | 1002 | exclude - list of polygons (inside main polygon) from where points |
---|
| 1003 | should be excluded |
---|
[5897] | 1004 | |
---|
| 1005 | Output: |
---|
| 1006 | points - list of points inside polygon |
---|
| 1007 | |
---|
| 1008 | Examples: |
---|
| 1009 | populate_polygon( [[0,0], [1,0], [1,1], [0,1]], 5 ) |
---|
| 1010 | will return five randomly selected points inside the unit square |
---|
| 1011 | """ |
---|
| 1012 | |
---|
| 1013 | from random import uniform, seed as seed_function |
---|
| 1014 | |
---|
| 1015 | seed_function(seed) |
---|
| 1016 | |
---|
| 1017 | points = [] |
---|
| 1018 | |
---|
| 1019 | # Find outer extent of polygon |
---|
| 1020 | max_x = min_x = polygon[0][0] |
---|
| 1021 | max_y = min_y = polygon[0][1] |
---|
| 1022 | for point in polygon[1:]: |
---|
| 1023 | x = point[0] |
---|
| 1024 | if x > max_x: max_x = x |
---|
| 1025 | if x < min_x: min_x = x |
---|
| 1026 | y = point[1] |
---|
| 1027 | if y > max_y: max_y = y |
---|
| 1028 | if y < min_y: min_y = y |
---|
| 1029 | |
---|
| 1030 | while len(points) < number_of_points: |
---|
| 1031 | x = uniform(min_x, max_x) |
---|
| 1032 | y = uniform(min_y, max_y) |
---|
| 1033 | |
---|
| 1034 | append = False |
---|
| 1035 | if is_inside_polygon([x,y], polygon): |
---|
| 1036 | append = True |
---|
| 1037 | |
---|
| 1038 | #Check exclusions |
---|
| 1039 | if exclude is not None: |
---|
| 1040 | for ex_poly in exclude: |
---|
| 1041 | if is_inside_polygon([x,y], ex_poly): |
---|
| 1042 | append = False |
---|
| 1043 | |
---|
| 1044 | if append is True: |
---|
| 1045 | points.append([x,y]) |
---|
| 1046 | |
---|
| 1047 | return points |
---|
| 1048 | |
---|
[6410] | 1049 | ## |
---|
| 1050 | # @brief Get a point inside a polygon that is close to an edge. |
---|
| 1051 | # @param polygon List of vertices of polygon. |
---|
| 1052 | # @param delta Maximum distance from an edge is delta * sqrt(2). |
---|
| 1053 | # @return A point that is inside polgon and close to the polygon edge. |
---|
[5897] | 1054 | def point_in_polygon(polygon, delta=1e-8): |
---|
| 1055 | """Return a point inside a given polygon which will be close to the |
---|
| 1056 | polygon edge. |
---|
| 1057 | |
---|
| 1058 | Input: |
---|
| 1059 | polygon - list of vertices of polygon |
---|
| 1060 | delta - the square root of 2 * delta is the maximum distance from the |
---|
| 1061 | polygon points and the returned point. |
---|
| 1062 | Output: |
---|
| 1063 | points - a point inside polygon |
---|
| 1064 | |
---|
[6410] | 1065 | searches in all diagonals and up and down (not left and right). |
---|
[5897] | 1066 | """ |
---|
[6410] | 1067 | |
---|
[5897] | 1068 | import exceptions |
---|
[6410] | 1069 | |
---|
[5897] | 1070 | class Found(exceptions.Exception): pass |
---|
| 1071 | |
---|
[6689] | 1072 | polygon = ensure_numeric(polygon) |
---|
| 1073 | |
---|
[5897] | 1074 | point_in = False |
---|
| 1075 | while not point_in: |
---|
| 1076 | try: |
---|
[6410] | 1077 | for poly_point in polygon: # [1:]: |
---|
| 1078 | for x_mult in range(-1, 2): |
---|
| 1079 | for y_mult in range(-1, 2): |
---|
[5897] | 1080 | x = poly_point[0] |
---|
| 1081 | y = poly_point[1] |
---|
[6410] | 1082 | |
---|
[5897] | 1083 | if x == 0: |
---|
[6410] | 1084 | x_delta = x_mult * delta |
---|
[5897] | 1085 | else: |
---|
[6410] | 1086 | x_delta = x + x_mult*x*delta |
---|
[5897] | 1087 | |
---|
| 1088 | if y == 0: |
---|
[6410] | 1089 | y_delta = y_mult * delta |
---|
[5897] | 1090 | else: |
---|
[6410] | 1091 | y_delta = y + y_mult*y*delta |
---|
[5897] | 1092 | |
---|
| 1093 | point = [x_delta, y_delta] |
---|
[6410] | 1094 | |
---|
[5897] | 1095 | if is_inside_polygon(point, polygon, closed=False): |
---|
| 1096 | raise Found |
---|
| 1097 | except Found: |
---|
| 1098 | point_in = True |
---|
| 1099 | else: |
---|
[6410] | 1100 | delta = delta * 0.1 |
---|
| 1101 | |
---|
[5897] | 1102 | return point |
---|
| 1103 | |
---|
[6410] | 1104 | ## |
---|
| 1105 | # @brief Calculate approximate number of triangles inside a bounding polygon. |
---|
| 1106 | # @param interior_regions |
---|
| 1107 | # @param bounding_poly |
---|
| 1108 | # @param remainder_res |
---|
| 1109 | # @return The number of triangles. |
---|
[5897] | 1110 | def number_mesh_triangles(interior_regions, bounding_poly, remainder_res): |
---|
| 1111 | """Calculate the approximate number of triangles inside the |
---|
| 1112 | bounding polygon and the other interior regions |
---|
| 1113 | |
---|
[6410] | 1114 | Polygon areas are converted to square Kms |
---|
[5897] | 1115 | |
---|
| 1116 | FIXME: Add tests for this function |
---|
| 1117 | """ |
---|
[6410] | 1118 | |
---|
[5897] | 1119 | from anuga.utilities.polygon import polygon_area |
---|
| 1120 | |
---|
| 1121 | # TO DO check if any of the regions fall inside one another |
---|
| 1122 | |
---|
[6689] | 1123 | print '----------------------------------------------------------------------------' |
---|
| 1124 | print 'Polygon Max triangle area (m^2) Total area (km^2) Estimated #triangles' |
---|
| 1125 | print '----------------------------------------------------------------------------' |
---|
| 1126 | |
---|
[5897] | 1127 | no_triangles = 0.0 |
---|
| 1128 | area = polygon_area(bounding_poly) |
---|
[6410] | 1129 | |
---|
[5897] | 1130 | for poly, resolution in interior_regions: |
---|
| 1131 | this_area = polygon_area(poly) |
---|
| 1132 | this_triangles = this_area/resolution |
---|
| 1133 | no_triangles += this_triangles |
---|
| 1134 | area -= this_area |
---|
[6410] | 1135 | |
---|
[5897] | 1136 | print 'Interior ', |
---|
[6410] | 1137 | print ('%.0f' % resolution).ljust(25), |
---|
| 1138 | print ('%.2f' % (this_area/1000000)).ljust(19), |
---|
| 1139 | print '%d' % (this_triangles) |
---|
| 1140 | |
---|
[5897] | 1141 | bound_triangles = area/remainder_res |
---|
| 1142 | no_triangles += bound_triangles |
---|
| 1143 | |
---|
| 1144 | print 'Bounding ', |
---|
[6410] | 1145 | print ('%.0f' % remainder_res).ljust(25), |
---|
| 1146 | print ('%.2f' % (area/1000000)).ljust(19), |
---|
| 1147 | print '%d' % (bound_triangles) |
---|
[5897] | 1148 | |
---|
| 1149 | total_number_of_triangles = no_triangles/0.7 |
---|
| 1150 | |
---|
| 1151 | print 'Estimated total number of triangles: %d' %total_number_of_triangles |
---|
[6410] | 1152 | print 'Note: This is generally about 20% less than the final amount' |
---|
[5897] | 1153 | |
---|
| 1154 | return int(total_number_of_triangles) |
---|
| 1155 | |
---|
[6410] | 1156 | ## |
---|
| 1157 | # @brief Reduce number of points in polygon by the specified factor. |
---|
| 1158 | # @param polygon The polygon to reduce. |
---|
| 1159 | # @param factor The factor to reduce polygon points by (default 10). |
---|
| 1160 | # @return The reduced polygon points list. |
---|
| 1161 | # @note The extrema of both axes are preserved. |
---|
[5897] | 1162 | def decimate_polygon(polygon, factor=10): |
---|
| 1163 | """Reduce number of points in polygon by the specified |
---|
| 1164 | factor (default=10, hence the name of the function) such that |
---|
| 1165 | the extrema in both axes are preserved. |
---|
| 1166 | |
---|
| 1167 | Return reduced polygon |
---|
| 1168 | """ |
---|
| 1169 | |
---|
| 1170 | # FIXME(Ole): This doesn't work at present, |
---|
| 1171 | # but it isn't critical either |
---|
| 1172 | |
---|
| 1173 | # Find outer extent of polygon |
---|
| 1174 | num_polygon = ensure_numeric(polygon) |
---|
| 1175 | max_x = max(num_polygon[:,0]) |
---|
| 1176 | max_y = max(num_polygon[:,1]) |
---|
| 1177 | min_x = min(num_polygon[:,0]) |
---|
[6410] | 1178 | min_y = min(num_polygon[:,1]) |
---|
[5897] | 1179 | |
---|
| 1180 | # Keep only some points making sure extrema are kept |
---|
[6410] | 1181 | reduced_polygon = [] |
---|
[5897] | 1182 | for i, point in enumerate(polygon): |
---|
| 1183 | x = point[0] |
---|
[6410] | 1184 | y = point[1] |
---|
[5897] | 1185 | if x in [min_x, max_x] and y in [min_y, max_y]: |
---|
| 1186 | # Keep |
---|
| 1187 | reduced_polygon.append(point) |
---|
| 1188 | else: |
---|
| 1189 | if len(reduced_polygon)*factor < i: |
---|
[6410] | 1190 | reduced_polygon.append(point) |
---|
[5897] | 1191 | |
---|
| 1192 | return reduced_polygon |
---|
| 1193 | |
---|
[6189] | 1194 | ## |
---|
| 1195 | # @brief Interpolate linearly from polyline nodes to midpoints of triangles. |
---|
| 1196 | # @param data The data on the polyline nodes. |
---|
| 1197 | # @param polyline_nodes ?? |
---|
| 1198 | # @param gauge_neighbour_id ?? FIXME(Ole): I want to get rid of this |
---|
| 1199 | # @param point_coordinates ?? |
---|
| 1200 | # @param verbose True if this function is to be verbose. |
---|
| 1201 | def interpolate_polyline(data, |
---|
| 1202 | polyline_nodes, |
---|
| 1203 | gauge_neighbour_id, |
---|
| 1204 | interpolation_points=None, |
---|
| 1205 | rtol=1.0e-6, |
---|
| 1206 | atol=1.0e-8, |
---|
| 1207 | verbose=False): |
---|
| 1208 | """Interpolate linearly between values data on polyline nodes |
---|
[6410] | 1209 | of a polyline to list of interpolation points. |
---|
[6189] | 1210 | |
---|
| 1211 | data is the data on the polyline nodes. |
---|
| 1212 | |
---|
| 1213 | Inputs: |
---|
| 1214 | data: Vector or array of data at the polyline nodes. |
---|
[6410] | 1215 | polyline_nodes: Location of nodes where data is available. |
---|
[6189] | 1216 | gauge_neighbour_id: ? |
---|
| 1217 | interpolation_points: Interpolate polyline data to these positions. |
---|
| 1218 | List of coordinate pairs [x, y] of |
---|
[6304] | 1219 | data points or an nx2 numeric array or a Geospatial_data object |
---|
[6410] | 1220 | rtol, atol: Used to determine whether a point is on the polyline or not. |
---|
| 1221 | See point_on_line. |
---|
[6189] | 1222 | |
---|
| 1223 | Output: |
---|
| 1224 | Interpolated values at interpolation points |
---|
| 1225 | """ |
---|
[6410] | 1226 | |
---|
[6189] | 1227 | if isinstance(interpolation_points, Geospatial_data): |
---|
[6410] | 1228 | interpolation_points = interpolation_points.\ |
---|
| 1229 | get_data_points(absolute=True) |
---|
[6189] | 1230 | |
---|
[6304] | 1231 | interpolated_values = num.zeros(len(interpolation_points), num.float) |
---|
[6189] | 1232 | |
---|
[6304] | 1233 | data = ensure_numeric(data, num.float) |
---|
| 1234 | polyline_nodes = ensure_numeric(polyline_nodes, num.float) |
---|
| 1235 | interpolation_points = ensure_numeric(interpolation_points, num.float) |
---|
| 1236 | gauge_neighbour_id = ensure_numeric(gauge_neighbour_id, num.int) |
---|
[6189] | 1237 | |
---|
[6410] | 1238 | n = polyline_nodes.shape[0] # Number of nodes in polyline |
---|
| 1239 | |
---|
[6189] | 1240 | # Input sanity check |
---|
| 1241 | msg = 'interpolation_points are not given (interpolate.py)' |
---|
| 1242 | assert interpolation_points is not None, msg |
---|
[6410] | 1243 | |
---|
[6189] | 1244 | msg = 'function value must be specified at every interpolation node' |
---|
[6410] | 1245 | assert data.shape[0] == polyline_nodes.shape[0], msg |
---|
| 1246 | |
---|
[6189] | 1247 | msg = 'Must define function value at one or more nodes' |
---|
[6410] | 1248 | assert data.shape[0] > 0, msg |
---|
[6189] | 1249 | |
---|
| 1250 | if n == 1: |
---|
| 1251 | msg = 'Polyline contained only one point. I need more. ' + str(data) |
---|
| 1252 | raise Exception, msg |
---|
| 1253 | elif n > 1: |
---|
| 1254 | _interpolate_polyline(data, |
---|
| 1255 | polyline_nodes, |
---|
| 1256 | gauge_neighbour_id, |
---|
[6410] | 1257 | interpolation_points, |
---|
[6189] | 1258 | interpolated_values, |
---|
| 1259 | rtol, |
---|
| 1260 | atol) |
---|
[6410] | 1261 | |
---|
[6189] | 1262 | return interpolated_values |
---|
| 1263 | |
---|
[6410] | 1264 | ## |
---|
| 1265 | # @brief |
---|
| 1266 | # @param data |
---|
| 1267 | # @param polyline_nodes |
---|
| 1268 | # @param gauge_neighbour_id |
---|
| 1269 | # @param interpolation_points |
---|
| 1270 | # @param interpolated_values |
---|
| 1271 | # @param rtol |
---|
| 1272 | # @param atol |
---|
| 1273 | # @return |
---|
| 1274 | # @note OBSOLETED BY C-EXTENSION |
---|
[6189] | 1275 | def _interpolate_polyline(data, |
---|
[6410] | 1276 | polyline_nodes, |
---|
| 1277 | gauge_neighbour_id, |
---|
| 1278 | interpolation_points, |
---|
[6189] | 1279 | interpolated_values, |
---|
| 1280 | rtol=1.0e-6, |
---|
| 1281 | atol=1.0e-8): |
---|
| 1282 | """Auxiliary function used by interpolate_polyline |
---|
[6410] | 1283 | |
---|
[6189] | 1284 | NOTE: OBSOLETED BY C-EXTENSION |
---|
| 1285 | """ |
---|
[6410] | 1286 | |
---|
| 1287 | number_of_nodes = len(polyline_nodes) |
---|
[6189] | 1288 | number_of_points = len(interpolation_points) |
---|
[6410] | 1289 | |
---|
| 1290 | for j in range(number_of_nodes): |
---|
[6189] | 1291 | neighbour_id = gauge_neighbour_id[j] |
---|
[6410] | 1292 | |
---|
| 1293 | # FIXME(Ole): I am convinced that gauge_neighbour_id can be discarded, |
---|
| 1294 | # but need to check with John J. |
---|
[6189] | 1295 | # Keep it for now (17 Jan 2009) |
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[6410] | 1296 | # When gone, we can simply interpolate between neighbouring nodes, |
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| 1297 | # i.e. neighbour_id = j+1. |
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| 1298 | # and the test below becomes something like: if j < number_of_nodes... |
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| 1299 | |
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[6189] | 1300 | if neighbour_id >= 0: |
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| 1301 | x0, y0 = polyline_nodes[j,:] |
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| 1302 | x1, y1 = polyline_nodes[neighbour_id,:] |
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[6410] | 1303 | |
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[6189] | 1304 | segment_len = sqrt((x1-x0)**2 + (y1-y0)**2) |
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[6410] | 1305 | segment_delta = data[neighbour_id] - data[j] |
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[6189] | 1306 | slope = segment_delta/segment_len |
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[6410] | 1307 | |
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| 1308 | for i in range(number_of_points): |
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[6189] | 1309 | x, y = interpolation_points[i,:] |
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[6410] | 1310 | if point_on_line([x, y], [[x0, y0], [x1, y1]], |
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| 1311 | rtol=rtol, atol=atol): |
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[6189] | 1312 | dist = sqrt((x-x0)**2 + (y-y0)**2) |
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| 1313 | interpolated_values[i] = slope*dist + data[j] |
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| 1314 | |
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| 1315 | |
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[6410] | 1316 | ################################################################################ |
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| 1317 | # Initialise module |
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| 1318 | ################################################################################ |
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[5897] | 1319 | |
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[6119] | 1320 | from anuga.utilities import compile |
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| 1321 | if compile.can_use_C_extension('polygon_ext.c'): |
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[5897] | 1322 | # Underlying C implementations can be accessed |
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| 1323 | from polygon_ext import _point_on_line |
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| 1324 | from polygon_ext import _separate_points_by_polygon |
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[6553] | 1325 | from polygon_ext import _interpolate_polyline |
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| 1326 | from polygon_ext import _is_inside_triangle |
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[5897] | 1327 | #from polygon_ext import _intersection |
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| 1328 | |
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| 1329 | else: |
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| 1330 | msg = 'C implementations could not be accessed by %s.\n ' %__file__ |
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| 1331 | msg += 'Make sure compile_all.py has been run as described in ' |
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| 1332 | msg += 'the ANUGA installation guide.' |
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| 1333 | raise Exception, msg |
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| 1334 | |
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| 1335 | |
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| 1336 | if __name__ == "__main__": |
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| 1337 | pass |
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