1 | #!/usr/bin/env python |
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2 | |
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3 | """Polygon manipulations""" |
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4 | |
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5 | import numpy as num |
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6 | |
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7 | from anuga.utilities.numerical_tools import ensure_numeric |
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8 | from anuga.geospatial_data.geospatial_data import ensure_absolute, \ |
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9 | Geospatial_data |
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10 | import anuga.utilities.log as log |
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11 | |
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12 | from aabb import AABB |
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13 | |
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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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21 | def point_on_line(point, line, rtol=1.0e-5, atol=1.0e-8): |
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22 | """Determine whether a point is on a line segment |
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23 | |
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24 | Input: |
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25 | point is given by [x, y] |
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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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28 | |
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29 | Output: |
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30 | |
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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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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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39 | line[0, 0], line[0, 1], |
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40 | line[1, 0], line[1, 1], |
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41 | rtol, atol) |
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42 | |
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43 | return bool(res) |
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44 | |
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45 | |
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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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50 | |
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51 | # result functions for possible states |
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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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72 | |
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73 | # this function called when an impossible state is found |
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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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77 | |
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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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98 | |
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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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111 | def intersection(line0, line1, rtol=1.0e-5, atol=1.0e-8): |
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112 | """Returns intersecting point between two line segments. |
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113 | |
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114 | However, if parallel lines coincide partly (i.e. share a common segment), |
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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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119 | A line can also be a 2x2 numpy array with each row |
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120 | corresponding to a point. |
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121 | |
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122 | Output: |
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123 | status, value - where status and value is interpreted as follows: |
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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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126 | status == 2: Collinear overlapping lines found. |
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127 | Value takes the form [[x0,y0], [x1,y1]]. |
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128 | status == 3: Collinear non-overlapping lines. Value set to None. |
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129 | status == 4: Lines are parallel. Value set to None. |
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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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134 | line0 = ensure_numeric(line0, num.float) |
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135 | line1 = ensure_numeric(line1, num.float) |
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136 | |
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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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139 | |
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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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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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146 | |
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147 | if num.allclose(denom, 0.0, rtol=rtol, atol=atol): |
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148 | # Lines are parallel - check if they are collinear |
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149 | if num.allclose([u0, u1], 0.0, rtol=rtol, atol=atol): |
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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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155 | |
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156 | return collinear_result[state_tuple]([x0, y0], [x1, y1], |
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157 | [x2, y2], [x3, y3]) |
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158 | else: |
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159 | # Lines are parallel but aren't collinear |
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160 | return 4, None #FIXME (Ole): Add distance here instead of None |
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161 | else: |
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162 | # Lines are not parallel, check if they intersect |
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163 | u0 = u0/denom |
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164 | u1 = u1/denom |
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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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170 | assert num.allclose(x, x2 + u1*(x3-x2), rtol=rtol, atol=atol) |
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171 | assert num.allclose(y, y2 + u1*(y3-y2), rtol=rtol, atol=atol) |
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172 | |
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173 | # Check if point found lies within given line segments |
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174 | if 0.0 <= u0 <= 1.0 and 0.0 <= u1 <= 1.0: |
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175 | # We have intersection |
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176 | return 1, num.array([x, y]) |
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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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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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192 | def NEW_C_intersection(line0, line1): |
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193 | """Returns intersecting point between two line segments. |
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194 | |
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195 | However, if parallel lines coincide partly (i.e. share a common segment), |
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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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200 | A line can also be a 2x2 numpy array with each row |
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201 | corresponding to a point. |
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202 | |
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203 | Output: |
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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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211 | """ |
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212 | |
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213 | line0 = ensure_numeric(line0, num.float) |
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214 | line1 = ensure_numeric(line1, num.float) |
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215 | |
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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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220 | |
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221 | return status, value |
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222 | |
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223 | def polygon_overlap(triangles, polygon, verbose=False): |
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224 | """Determine if a polygon and triangle overlap |
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225 | |
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226 | """ |
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227 | polygon = ensure_numeric(polygon) |
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228 | triangles = ensure_numeric(triangles) |
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229 | |
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230 | M = triangles.shape[0]/3 # Number of triangles |
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231 | |
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232 | indices = num.zeros(M, num.int) |
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233 | |
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234 | count = _polygon_overlap(polygon, triangles, indices) |
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235 | |
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236 | if verbose: |
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237 | log.critical('Found %d triangles (out of %d) that polygon' % (count, M)) |
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238 | |
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239 | return indices[:count] |
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240 | |
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241 | def not_polygon_overlap(triangles, polygon, verbose=False): |
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242 | """Determine if a polygon and triangle overlap |
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243 | |
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244 | """ |
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245 | polygon = ensure_numeric(polygon) |
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246 | triangles = ensure_numeric(triangles) |
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247 | |
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248 | M = triangles.shape[0]/3 # Number of triangles |
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249 | |
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250 | indices = num.zeros(M, num.int) |
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251 | |
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252 | count = _polygon_overlap(polygon, triangles, indices) |
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253 | |
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254 | if verbose: |
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255 | log.critical('Found %d triangles (out of %d) that polygon' % (count, M)) |
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256 | |
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257 | return indices[count:] |
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258 | |
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259 | def is_inside_triangle(point, triangle, |
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260 | closed=True, |
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261 | rtol=1.0e-12, |
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262 | atol=1.0e-12, |
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263 | check_inputs=True): |
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264 | """Determine if one point is inside a triangle |
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265 | |
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266 | This uses the barycentric method: |
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267 | |
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268 | Triangle is A, B, C |
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269 | Point P can then be written as |
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270 | |
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271 | P = A + alpha * (C-A) + beta * (B-A) |
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272 | or if we let |
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273 | v=P-A, v0=C-A, v1=B-A |
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274 | |
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275 | v = alpha*v0 + beta*v1 |
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276 | |
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277 | Dot this equation by v0 and v1 to get two: |
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278 | |
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279 | dot(v0, v) = alpha*dot(v0, v0) + beta*dot(v0, v1) |
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280 | dot(v1, v) = alpha*dot(v1, v0) + beta*dot(v1, v1) |
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281 | |
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282 | or if a_ij = dot(v_i, v_j) and b_i = dot(v_i, v) |
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283 | the matrix equation: |
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284 | |
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285 | a_00 a_01 alpha b_0 |
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286 | = |
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287 | a_10 a_11 beta b_1 |
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288 | |
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289 | Solving for alpha and beta yields: |
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290 | |
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291 | alpha = (b_0*a_11 - b_1*a_01)/denom |
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292 | beta = (b_1*a_00 - b_0*a_10)/denom |
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293 | |
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294 | with denom = a_11*a_00 - a_10*a_01 |
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295 | |
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296 | The point is in the triangle whenever |
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297 | alpha and beta and their sums are in the unit interval. |
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298 | |
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299 | rtol and atol will determine how close the point has to be to the edge |
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300 | before it is deemed to be on the edge. |
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301 | |
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302 | """ |
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303 | |
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304 | triangle = ensure_numeric(triangle) |
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305 | point = ensure_numeric(point, num.float) |
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306 | |
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307 | if check_inputs is True: |
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308 | msg = 'is_inside_triangle must be invoked with one point only' |
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309 | assert num.allclose(point.shape, [2]), msg |
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310 | |
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311 | |
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312 | # Use C-implementation |
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313 | return bool(_is_inside_triangle(point, triangle, int(closed), rtol, atol)) |
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314 | |
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315 | def is_complex(polygon, verbose=False): |
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316 | """Check if a polygon is complex (self-intersecting). |
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317 | Uses a sweep algorithm that is O(n^2) in the worst case, but |
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318 | for most normal looking polygons it'll be O(n log n). |
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319 | |
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320 | polygon is a list of points that define a closed polygon. |
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321 | verbose will print a list of the intersection points if true |
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322 | |
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323 | Return True if polygon is complex. |
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324 | """ |
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325 | |
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326 | def key_xpos(item): |
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327 | """ Return the x coord out of the passed point for sorting key. """ |
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328 | return (item[0][0]) |
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329 | |
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330 | def segments_joined(seg0, seg1): |
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331 | """ See if there are identical segments in the 2 lists. """ |
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332 | for i in seg0: |
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333 | for j in seg1: |
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334 | if i == j: return True |
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335 | return False |
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336 | |
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337 | polygon = ensure_numeric(polygon, num.float) |
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338 | |
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339 | # build a list of discrete segments from the polygon |
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340 | unsorted_segs = [] |
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341 | for i in range(0, len(polygon)-1): |
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342 | unsorted_segs.append([list(polygon[i]), list(polygon[i+1])]) |
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343 | unsorted_segs.append([list(polygon[0]), list(polygon[-1])]) |
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344 | |
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345 | # all segments must point in same direction |
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346 | for val in unsorted_segs: |
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347 | if val[0][0] > val[1][0]: |
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348 | val[0], val[1] = val[1], val[0] |
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349 | |
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350 | l_x = sorted(unsorted_segs, key=key_xpos) |
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351 | |
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352 | comparisons = 0 |
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353 | |
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354 | # loop through, only comparing lines that partially overlap in x |
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355 | for index, leftmost in enumerate(l_x): |
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356 | cmp = index+1 |
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357 | while cmp < len(l_x) and leftmost[1][0] > l_x[cmp][0][0]: |
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358 | if not segments_joined(leftmost, l_x[cmp]): |
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359 | (type, point) = intersection(leftmost, l_x[cmp]) |
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360 | comparisons += 1 |
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361 | if type != 0 and type != 4 or (type == 2 and list(point[0]) !=\ |
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362 | list(point[1])): |
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363 | if verbose: |
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364 | print 'Self-intersecting polygon found, type ', type |
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365 | print 'point', point, |
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366 | print 'vertices: ', leftmost, ' - ', l_x[cmp] |
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367 | return True |
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368 | cmp += 1 |
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369 | |
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370 | return False |
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371 | |
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372 | |
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373 | def is_inside_polygon(point, polygon, closed=True, verbose=False): |
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374 | """Determine if one point is inside a polygon |
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375 | |
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376 | See inside_polygon for more details |
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377 | """ |
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378 | |
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379 | indices = inside_polygon(point, polygon, closed, verbose) |
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380 | |
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381 | if indices.shape[0] == 1: |
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382 | return True |
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383 | elif indices.shape[0] == 0: |
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384 | return False |
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385 | else: |
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386 | msg = 'is_inside_polygon must be invoked with one point only' |
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387 | raise Exception(msg) |
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388 | |
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389 | ## |
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390 | # @brief Determine which of a set of points are inside a polygon. |
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391 | # @param points A set of points (tuple, list or array). |
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392 | # @param polygon A set of points defining a polygon (tuple, list or array). |
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393 | # @param closed True if points on boundary are considered 'inside' polygon. |
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394 | # @param verbose True if this function is to be verbose. |
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395 | # @return A list of indices of points inside the polygon. |
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396 | def inside_polygon(points, polygon, closed=True, verbose=False): |
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397 | """Determine points inside a polygon |
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398 | |
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399 | Functions inside_polygon and outside_polygon have been defined in |
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400 | terms of separate_by_polygon which will put all inside indices in |
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401 | the first part of the indices array and outside indices in the last |
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402 | |
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403 | See separate_points_by_polygon for documentation |
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404 | |
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405 | points and polygon can be a geospatial instance, |
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406 | a list or a numeric array |
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407 | """ |
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408 | |
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409 | try: |
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410 | points = ensure_absolute(points) |
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411 | except NameError, err: |
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412 | raise NameError, err |
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413 | except: |
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414 | # If this fails it is going to be because the points can't be |
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415 | # converted to a numeric array. |
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416 | msg = 'Points could not be converted to numeric array' |
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417 | raise Exception, msg |
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418 | |
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419 | polygon = ensure_absolute(polygon) |
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420 | try: |
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421 | polygon = ensure_absolute(polygon) |
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422 | except NameError, e: |
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423 | raise NameError, e |
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424 | except: |
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425 | # If this fails it is going to be because the points can't be |
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426 | # converted to a numeric array. |
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427 | msg = ('Polygon %s could not be converted to numeric array' |
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428 | % (str(polygon))) |
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429 | raise Exception, msg |
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430 | |
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431 | if len(points.shape) == 1: |
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432 | # Only one point was passed in. Convert to array of points |
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433 | points = num.reshape(points, (1,2)) |
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434 | |
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435 | indices, count = separate_points_by_polygon(points, polygon, |
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436 | closed=closed, |
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437 | verbose=verbose) |
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438 | |
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439 | # Return indices of points inside polygon |
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440 | return indices[:count] |
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441 | |
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442 | ## |
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443 | # @brief Determine if one point is outside a polygon. |
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444 | # @param point The point of interest. |
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445 | # @param polygon The polygon to test inclusion in. |
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446 | # @param closed True if points on boundary are considered 'inside' polygon. |
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447 | # @param verbose True if this function is to be verbose. |
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448 | # @return True if point is outside the polygon. |
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449 | # @note Uses inside_polygon() to do the work. |
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450 | def is_outside_polygon(point, polygon, closed=True, verbose=False, |
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451 | points_geo_ref=None, polygon_geo_ref=None): |
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452 | """Determine if one point is outside a polygon |
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453 | |
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454 | See outside_polygon for more details |
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455 | """ |
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456 | |
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457 | indices = outside_polygon(point, polygon, closed, verbose) |
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458 | |
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459 | if indices.shape[0] == 1: |
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460 | return True |
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461 | elif indices.shape[0] == 0: |
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462 | return False |
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463 | else: |
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464 | msg = 'is_outside_polygon must be invoked with one point only' |
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465 | raise Exception, msg |
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466 | |
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467 | ## |
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468 | # @brief Determine which of a set of points are outside a polygon. |
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469 | # @param points A set of points (tuple, list or array). |
---|
470 | # @param polygon A set of points defining a polygon (tuple, list or array). |
---|
471 | # @param closed True if points on boundary are considered 'inside' polygon. |
---|
472 | # @param verbose True if this function is to be verbose. |
---|
473 | # @return A list of indices of points outside the polygon. |
---|
474 | def outside_polygon(points, polygon, closed = True, verbose = False): |
---|
475 | """Determine points outside a polygon |
---|
476 | |
---|
477 | Functions inside_polygon and outside_polygon have been defined in |
---|
478 | terms of separate_by_polygon which will put all inside indices in |
---|
479 | the first part of the indices array and outside indices in the last |
---|
480 | |
---|
481 | See separate_points_by_polygon for documentation |
---|
482 | """ |
---|
483 | |
---|
484 | try: |
---|
485 | points = ensure_numeric(points, num.float) |
---|
486 | except NameError, e: |
---|
487 | raise NameError, e |
---|
488 | except: |
---|
489 | msg = 'Points could not be converted to numeric array' |
---|
490 | raise Exception, msg |
---|
491 | |
---|
492 | try: |
---|
493 | polygon = ensure_numeric(polygon, num.float) |
---|
494 | except NameError, e: |
---|
495 | raise NameError, e |
---|
496 | except: |
---|
497 | msg = 'Polygon could not be converted to numeric array' |
---|
498 | raise Exception, msg |
---|
499 | |
---|
500 | if len(points.shape) == 1: |
---|
501 | # Only one point was passed in. Convert to array of points |
---|
502 | points = num.reshape(points, (1, 2)) |
---|
503 | |
---|
504 | indices, count = separate_points_by_polygon(points, polygon, |
---|
505 | closed=closed, |
---|
506 | verbose=verbose) |
---|
507 | |
---|
508 | # Return indices of points outside polygon |
---|
509 | if count == len(indices): |
---|
510 | # No points are outside |
---|
511 | return num.array([]) |
---|
512 | else: |
---|
513 | return indices[count:][::-1] #return reversed |
---|
514 | |
---|
515 | ## |
---|
516 | # @brief Separate a list of points into two sets inside+outside a polygon. |
---|
517 | # @param points A set of points (tuple, list or array). |
---|
518 | # @param polygon A set of points defining a polygon (tuple, list or array). |
---|
519 | # @param closed True if points on boundary are considered 'inside' polygon. |
---|
520 | # @param verbose True if this function is to be verbose. |
---|
521 | # @return A tuple (in, out) of point indices for poinst inside amd outside. |
---|
522 | def in_and_outside_polygon(points, polygon, closed=True, verbose=False): |
---|
523 | """Determine points inside and outside a polygon |
---|
524 | |
---|
525 | See separate_points_by_polygon for documentation |
---|
526 | |
---|
527 | Returns an array of points inside and array of points outside the polygon |
---|
528 | """ |
---|
529 | |
---|
530 | try: |
---|
531 | points = ensure_numeric(points, num.float) |
---|
532 | except NameError, e: |
---|
533 | raise NameError, e |
---|
534 | except: |
---|
535 | msg = 'Points could not be converted to numeric array' |
---|
536 | raise Exception, msg |
---|
537 | |
---|
538 | try: |
---|
539 | polygon = ensure_numeric(polygon, num.float) |
---|
540 | except NameError, e: |
---|
541 | raise NameError, e |
---|
542 | except: |
---|
543 | msg = 'Polygon could not be converted to numeric array' |
---|
544 | raise Exception, msg |
---|
545 | |
---|
546 | if len(points.shape) == 1: |
---|
547 | # Only one point was passed in. Convert to array of points |
---|
548 | points = num.reshape(points, (1, 2)) |
---|
549 | |
---|
550 | indices, count = separate_points_by_polygon(points, polygon, |
---|
551 | closed=closed, |
---|
552 | verbose=verbose) |
---|
553 | |
---|
554 | # Returns indices of points inside and indices of points outside |
---|
555 | # the polygon |
---|
556 | if count == len(indices): |
---|
557 | # No points are outside |
---|
558 | return indices[:count], [] |
---|
559 | else: |
---|
560 | return indices[:count], indices[count:][::-1] #return reversed |
---|
561 | |
---|
562 | |
---|
563 | |
---|
564 | def separate_points_by_polygon(points, polygon, |
---|
565 | closed=True, |
---|
566 | check_input=True, |
---|
567 | verbose=False): |
---|
568 | """Determine whether points are inside or outside a polygon |
---|
569 | |
---|
570 | Input: |
---|
571 | points - Tuple of (x, y) coordinates, or list of tuples |
---|
572 | polygon - list of vertices of polygon |
---|
573 | closed - (optional) determine whether points on boundary should be |
---|
574 | regarded as belonging to the polygon (closed = True) |
---|
575 | or not (closed = False) |
---|
576 | check_input: Allows faster execution if set to False |
---|
577 | |
---|
578 | Outputs: |
---|
579 | indices: array of same length as points with indices of points falling |
---|
580 | inside the polygon listed from the beginning and indices of points |
---|
581 | falling outside listed from the end. |
---|
582 | |
---|
583 | count: count of points falling inside the polygon |
---|
584 | |
---|
585 | The indices of points inside are obtained as indices[:count] |
---|
586 | The indices of points outside are obtained as indices[count:] |
---|
587 | |
---|
588 | Examples: |
---|
589 | U = [[0,0], [1,0], [1,1], [0,1]] #Unit square |
---|
590 | |
---|
591 | separate_points_by_polygon( [[0.5, 0.5], [1, -0.5], [0.3, 0.2]], U) |
---|
592 | will return the indices [0, 2, 1] and count == 2 as only the first |
---|
593 | and the last point are inside the unit square |
---|
594 | |
---|
595 | Remarks: |
---|
596 | The vertices may be listed clockwise or counterclockwise and |
---|
597 | the first point may optionally be repeated. |
---|
598 | Polygons do not need to be convex. |
---|
599 | Polygons can have holes in them and points inside a hole is |
---|
600 | regarded as being outside the polygon. |
---|
601 | |
---|
602 | Algorithm is based on work by Darel Finley, |
---|
603 | http://www.alienryderflex.com/polygon/ |
---|
604 | |
---|
605 | Uses underlying C-implementation in polygon_ext.c |
---|
606 | """ |
---|
607 | |
---|
608 | if check_input: |
---|
609 | #Input checks |
---|
610 | assert isinstance(closed, bool), \ |
---|
611 | 'Keyword argument "closed" must be boolean' |
---|
612 | assert isinstance(verbose, bool), \ |
---|
613 | 'Keyword argument "verbose" must be boolean' |
---|
614 | |
---|
615 | try: |
---|
616 | points = ensure_numeric(points, num.float) |
---|
617 | except NameError, e: |
---|
618 | raise NameError, e |
---|
619 | except: |
---|
620 | msg = 'Points could not be converted to numeric array' |
---|
621 | raise Exception(msg) |
---|
622 | |
---|
623 | try: |
---|
624 | polygon = ensure_numeric(polygon, num.float) |
---|
625 | except NameError, e: |
---|
626 | raise NameError(e) |
---|
627 | except: |
---|
628 | msg = 'Polygon could not be converted to numeric array' |
---|
629 | raise Exception(msg) |
---|
630 | |
---|
631 | msg = 'Polygon array must be a 2d array of vertices' |
---|
632 | assert len(polygon.shape) == 2, msg |
---|
633 | |
---|
634 | msg = 'Polygon array must have two columns' |
---|
635 | assert polygon.shape[1] == 2, msg |
---|
636 | |
---|
637 | |
---|
638 | msg = ('Points array must be 1 or 2 dimensional. ' |
---|
639 | 'I got %d dimensions' % len(points.shape)) |
---|
640 | assert 0 < len(points.shape) < 3, msg |
---|
641 | |
---|
642 | if len(points.shape) == 1: |
---|
643 | # Only one point was passed in. Convert to array of points. |
---|
644 | points = num.reshape(points, (1, 2)) |
---|
645 | |
---|
646 | msg = ('Point array must have two columns (x,y), ' |
---|
647 | 'I got points.shape[1]=%d' % points.shape[0]) |
---|
648 | assert points.shape[1]==2, msg |
---|
649 | |
---|
650 | |
---|
651 | msg = ('Points array must be a 2d array. I got %s.' |
---|
652 | % str(points[:30])) |
---|
653 | assert len(points.shape) == 2, msg |
---|
654 | |
---|
655 | msg = 'Points array must have two columns' |
---|
656 | assert points.shape[1] == 2, msg |
---|
657 | |
---|
658 | N = polygon.shape[0] # Number of vertices in polygon |
---|
659 | M = points.shape[0] # Number of points |
---|
660 | |
---|
661 | indices = num.zeros(M, num.int) |
---|
662 | |
---|
663 | count = _separate_points_by_polygon(points, polygon, indices, |
---|
664 | int(closed), int(verbose)) |
---|
665 | |
---|
666 | if verbose: |
---|
667 | log.critical('Found %d points (out of %d) inside polygon' % (count, M)) |
---|
668 | |
---|
669 | return indices, count |
---|
670 | |
---|
671 | |
---|
672 | def polygon_area(input_polygon): |
---|
673 | """ Determine area of arbitrary polygon. |
---|
674 | |
---|
675 | input_polygon The polygon to get area of. |
---|
676 | |
---|
677 | return A scalar value for the polygon area. |
---|
678 | |
---|
679 | Reference: http://mathworld.wolfram.com/PolygonArea.html |
---|
680 | """ |
---|
681 | # Move polygon to origin (0,0) to avoid rounding errors |
---|
682 | # This makes a copy of the polygon to avoid destroying it |
---|
683 | input_polygon = ensure_numeric(input_polygon) |
---|
684 | min_x = min(input_polygon[:, 0]) |
---|
685 | min_y = min(input_polygon[:, 1]) |
---|
686 | polygon = input_polygon - [min_x, min_y] |
---|
687 | |
---|
688 | # Compute area |
---|
689 | n = len(polygon) |
---|
690 | poly_area = 0.0 |
---|
691 | |
---|
692 | for i in range(n): |
---|
693 | pti = polygon[i] |
---|
694 | if i == n-1: |
---|
695 | pt1 = polygon[0] |
---|
696 | else: |
---|
697 | pt1 = polygon[i+1] |
---|
698 | xi = pti[0] |
---|
699 | yi1 = pt1[1] |
---|
700 | xi1 = pt1[0] |
---|
701 | yi = pti[1] |
---|
702 | poly_area += xi*yi1 - xi1*yi |
---|
703 | |
---|
704 | return abs(poly_area/2) |
---|
705 | |
---|
706 | |
---|
707 | def plot_polygons(polygons_points, |
---|
708 | style=None, |
---|
709 | figname=None, |
---|
710 | label=None, |
---|
711 | alpha=None): |
---|
712 | """ Take list of polygons and plot. |
---|
713 | |
---|
714 | Inputs: |
---|
715 | |
---|
716 | polygons - list of polygons |
---|
717 | |
---|
718 | style - style list corresponding to each polygon |
---|
719 | - for a polygon, use 'line' |
---|
720 | - for points falling outside a polygon, use 'outside' |
---|
721 | - style can also be user defined as in normal pylab plot. |
---|
722 | |
---|
723 | figname - name to save figure to |
---|
724 | |
---|
725 | label - title for plotA |
---|
726 | |
---|
727 | alpha - transparency of polygon fill, 0.0=none, 1.0=solid |
---|
728 | if not supplied, no fill. |
---|
729 | |
---|
730 | Outputs: |
---|
731 | |
---|
732 | - plot of polygons |
---|
733 | """ |
---|
734 | |
---|
735 | from pylab import ion, hold, plot, savefig, xlabel, \ |
---|
736 | ylabel, title, close, title, fill |
---|
737 | |
---|
738 | assert type(polygons_points) == list, \ |
---|
739 | 'input must be a list of polygons and/or points' |
---|
740 | |
---|
741 | ion() |
---|
742 | hold(True) |
---|
743 | |
---|
744 | if label is None: |
---|
745 | label = '' |
---|
746 | |
---|
747 | # clamp alpha to sensible range |
---|
748 | if alpha: |
---|
749 | try: |
---|
750 | alpha = float(alpha) |
---|
751 | except ValueError: |
---|
752 | alpha = None |
---|
753 | else: |
---|
754 | alpha = max(0.0, min(1.0, alpha)) |
---|
755 | |
---|
756 | num_points = len(polygons_points) |
---|
757 | colour = [] |
---|
758 | if style is None: |
---|
759 | style_type = 'line' |
---|
760 | style = [] |
---|
761 | for i in range(num_points): |
---|
762 | style.append(style_type) |
---|
763 | colour.append('b-') |
---|
764 | else: |
---|
765 | for style_name in style: |
---|
766 | if style_name == 'line': |
---|
767 | colour.append('b-') |
---|
768 | if style_name == 'outside': |
---|
769 | colour.append('r.') |
---|
770 | if style_name == 'point': |
---|
771 | colour.append('g.') |
---|
772 | if style_name not in ['line', 'outside', 'point']: |
---|
773 | colour.append(style_name) |
---|
774 | |
---|
775 | for i, item in enumerate(polygons_points): |
---|
776 | pt_x, pt_y = _poly_xy(item) |
---|
777 | plot(pt_x, pt_y, colour[i]) |
---|
778 | if alpha: |
---|
779 | fill(pt_x, pt_y, colour[i], alpha=alpha) |
---|
780 | xlabel('x') |
---|
781 | ylabel('y') |
---|
782 | title(label) |
---|
783 | |
---|
784 | if figname is not None: |
---|
785 | savefig(figname) |
---|
786 | else: |
---|
787 | savefig('test_image') |
---|
788 | |
---|
789 | close('all') |
---|
790 | |
---|
791 | |
---|
792 | def _poly_xy(polygon): |
---|
793 | """ this is used within plot_polygons so need to duplicate |
---|
794 | the first point so can have closed polygon in plot |
---|
795 | # @param polygon A set of points defining a polygon. |
---|
796 | # @param verbose True if this function is to be verbose. |
---|
797 | # @return A tuple (x, y) of X and Y coordinates of the polygon. |
---|
798 | # @note We duplicate the first point so can have closed polygon in plot. |
---|
799 | """ |
---|
800 | |
---|
801 | try: |
---|
802 | polygon = ensure_numeric(polygon, num.float) |
---|
803 | except NameError, err: |
---|
804 | raise NameError, err |
---|
805 | except: |
---|
806 | msg = ('Polygon %s could not be converted to numeric array' |
---|
807 | % (str(polygon))) |
---|
808 | raise Exception, msg |
---|
809 | |
---|
810 | pts_x = num.concatenate((polygon[:, 0], [polygon[0, 0]]), axis = 0) |
---|
811 | pts_y = num.concatenate((polygon[:, 1], [polygon[0, 1]]), axis = 0) |
---|
812 | |
---|
813 | return pts_x, pts_y |
---|
814 | |
---|
815 | |
---|
816 | ################################################################################ |
---|
817 | # Functions to read and write polygon information |
---|
818 | ################################################################################ |
---|
819 | |
---|
820 | def read_polygon(filename, delimiter=','): |
---|
821 | """ Read points assumed to form a polygon. |
---|
822 | |
---|
823 | Also checks to make sure polygon is not complex (self-intersecting). |
---|
824 | |
---|
825 | filename Path to file containing polygon data. |
---|
826 | delimiter Delimiter to split polygon data with. |
---|
827 | A list of point data from the polygon file. |
---|
828 | |
---|
829 | There must be exactly two numbers in each line separated by the delimiter. |
---|
830 | No header. |
---|
831 | """ |
---|
832 | |
---|
833 | fid = open(filename) |
---|
834 | lines = fid.readlines() |
---|
835 | fid.close() |
---|
836 | polygon = [] |
---|
837 | for line in lines: |
---|
838 | fields = line.split(delimiter) |
---|
839 | polygon.append([float(fields[0]), float(fields[1])]) |
---|
840 | |
---|
841 | # check this is a valid polygon. |
---|
842 | if is_complex(polygon, verbose=True): |
---|
843 | msg = 'ERROR: Self-intersecting polygon detected in file ' |
---|
844 | msg += filename +'. A complex polygon will not ' |
---|
845 | msg += 'necessarily break the algorithms within ANUGA, but it' |
---|
846 | msg += 'usually signifies pathological data. Please fix this file.' |
---|
847 | raise Exception, msg |
---|
848 | |
---|
849 | return polygon |
---|
850 | |
---|
851 | |
---|
852 | def write_polygon(polygon, filename=None): |
---|
853 | """Write polygon to csv file. |
---|
854 | |
---|
855 | There will be exactly two numbers, easting and northing, in each line |
---|
856 | separated by a comma. |
---|
857 | |
---|
858 | No header. |
---|
859 | """ |
---|
860 | |
---|
861 | fid = open(filename, 'w') |
---|
862 | for point in polygon: |
---|
863 | fid.write('%f, %f\n' % point) |
---|
864 | fid.close() |
---|
865 | |
---|
866 | |
---|
867 | def populate_polygon(polygon, number_of_points, seed=None, exclude=None): |
---|
868 | """Populate given polygon with uniformly distributed points. |
---|
869 | |
---|
870 | Input: |
---|
871 | polygon - list of vertices of polygon |
---|
872 | number_of_points - (optional) number of points |
---|
873 | seed - seed for random number generator (default=None) |
---|
874 | exclude - list of polygons (inside main polygon) from where points |
---|
875 | should be excluded |
---|
876 | |
---|
877 | Output: |
---|
878 | points - list of points inside polygon |
---|
879 | |
---|
880 | Examples: |
---|
881 | populate_polygon( [[0,0], [1,0], [1,1], [0,1]], 5 ) |
---|
882 | will return five randomly selected points inside the unit square |
---|
883 | """ |
---|
884 | |
---|
885 | from random import uniform, seed as seed_function |
---|
886 | |
---|
887 | seed_function(seed) |
---|
888 | |
---|
889 | points = [] |
---|
890 | |
---|
891 | # Find outer extent of polygon |
---|
892 | extents = AABB(polygon) |
---|
893 | |
---|
894 | while len(points) < number_of_points: |
---|
895 | rand_x = uniform(extents.xmin, extents.xmax) |
---|
896 | rand_y = uniform(extents.ymin, extents.ymax) |
---|
897 | |
---|
898 | append = False |
---|
899 | if is_inside_polygon([rand_x, rand_y], polygon): |
---|
900 | append = True |
---|
901 | |
---|
902 | #Check exclusions |
---|
903 | if exclude is not None: |
---|
904 | for ex_poly in exclude: |
---|
905 | if is_inside_polygon([rand_x, rand_y], ex_poly): |
---|
906 | append = False |
---|
907 | |
---|
908 | if append is True: |
---|
909 | points.append([rand_x, rand_y]) |
---|
910 | |
---|
911 | return points |
---|
912 | |
---|
913 | |
---|
914 | def point_in_polygon(polygon, delta=1e-8): |
---|
915 | """Return a point inside a given polygon which will be close to the |
---|
916 | polygon edge. |
---|
917 | |
---|
918 | Input: |
---|
919 | polygon - list of vertices of polygon |
---|
920 | delta - the square root of 2 * delta is the maximum distance from the |
---|
921 | polygon points and the returned point. |
---|
922 | Output: |
---|
923 | points - a point inside polygon |
---|
924 | |
---|
925 | searches in all diagonals and up and down (not left and right). |
---|
926 | """ |
---|
927 | |
---|
928 | polygon = ensure_numeric(polygon) |
---|
929 | |
---|
930 | while True: |
---|
931 | for poly_point in polygon: |
---|
932 | for x_mult in range(-1, 2): |
---|
933 | for y_mult in range(-1, 2): |
---|
934 | pt_x, pt_y = poly_point |
---|
935 | |
---|
936 | if pt_x == 0: |
---|
937 | x_delta = x_mult * delta |
---|
938 | else: |
---|
939 | x_delta = pt_x + x_mult*pt_x*delta |
---|
940 | |
---|
941 | if pt_y == 0: |
---|
942 | y_delta = y_mult * delta |
---|
943 | else: |
---|
944 | y_delta = pt_y + y_mult*pt_y*delta |
---|
945 | |
---|
946 | point = [x_delta, y_delta] |
---|
947 | |
---|
948 | if is_inside_polygon(point, polygon, closed=False): |
---|
949 | return point |
---|
950 | delta = delta * 0.1 |
---|
951 | |
---|
952 | |
---|
953 | def number_mesh_triangles(interior_regions, bounding_poly, remainder_res): |
---|
954 | """Calculate the approximate number of triangles inside the |
---|
955 | bounding polygon and the other interior regions |
---|
956 | |
---|
957 | Polygon areas are converted to square Kms |
---|
958 | |
---|
959 | FIXME: Add tests for this function |
---|
960 | """ |
---|
961 | |
---|
962 | # TO DO check if any of the regions fall inside one another |
---|
963 | |
---|
964 | log.critical('-' * 80) |
---|
965 | log.critical('Polygon Max triangle area (m^2) Total area (km^2) ' |
---|
966 | 'Estimated #triangles') |
---|
967 | log.critical('-' * 80) |
---|
968 | |
---|
969 | no_triangles = 0.0 |
---|
970 | area = polygon_area(bounding_poly) |
---|
971 | |
---|
972 | for poly, resolution in interior_regions: |
---|
973 | this_area = polygon_area(poly) |
---|
974 | this_triangles = this_area/resolution |
---|
975 | no_triangles += this_triangles |
---|
976 | area -= this_area |
---|
977 | |
---|
978 | log.critical('Interior %s%s%d' |
---|
979 | % (('%.0f' % resolution).ljust(25), |
---|
980 | ('%.2f' % (this_area/1000000)).ljust(19), |
---|
981 | this_triangles)) |
---|
982 | #print 'Interior ', |
---|
983 | #print ('%.0f' % resolution).ljust(25), |
---|
984 | #print ('%.2f' % (this_area/1000000)).ljust(19), |
---|
985 | #print '%d' % (this_triangles) |
---|
986 | |
---|
987 | bound_triangles = area/remainder_res |
---|
988 | no_triangles += bound_triangles |
---|
989 | |
---|
990 | log.critical('Bounding %s%s%d' |
---|
991 | % (('%.0f' % remainder_res).ljust(25), |
---|
992 | ('%.2f' % (area/1000000)).ljust(19), |
---|
993 | bound_triangles)) |
---|
994 | #print 'Bounding ', |
---|
995 | #print ('%.0f' % remainder_res).ljust(25), |
---|
996 | #print ('%.2f' % (area/1000000)).ljust(19), |
---|
997 | #print '%d' % (bound_triangles) |
---|
998 | |
---|
999 | total_number_of_triangles = no_triangles/0.7 |
---|
1000 | |
---|
1001 | log.critical('Estimated total number of triangles: %d' |
---|
1002 | % total_number_of_triangles) |
---|
1003 | log.critical('Note: This is generally about 20%% ' |
---|
1004 | 'less than the final amount') |
---|
1005 | |
---|
1006 | return int(total_number_of_triangles) |
---|
1007 | |
---|
1008 | |
---|
1009 | def decimate_polygon(polygon, factor=10): |
---|
1010 | """Reduce number of points in polygon by the specified |
---|
1011 | factor (default=10, hence the name of the function) such that |
---|
1012 | the extrema in both axes are preserved. |
---|
1013 | |
---|
1014 | ## |
---|
1015 | # @brief Reduce number of points in polygon by the specified factor. |
---|
1016 | # @param polygon The polygon to reduce. |
---|
1017 | # @param factor The factor to reduce polygon points by (default 10). |
---|
1018 | # @note The extrema of both axes are preserved. |
---|
1019 | |
---|
1020 | Return reduced polygon |
---|
1021 | """ |
---|
1022 | |
---|
1023 | # FIXME(Ole): This doesn't work at present, |
---|
1024 | # but it isn't critical either |
---|
1025 | |
---|
1026 | # Find outer extent of polygon |
---|
1027 | num_polygon = ensure_numeric(polygon) |
---|
1028 | max_x = max(num_polygon[:, 0]) |
---|
1029 | max_y = max(num_polygon[:, 1]) |
---|
1030 | min_x = min(num_polygon[:, 0]) |
---|
1031 | min_y = min(num_polygon[:, 1]) |
---|
1032 | |
---|
1033 | # Keep only some points making sure extrema are kept |
---|
1034 | reduced_polygon = [] |
---|
1035 | for i, point in enumerate(polygon): |
---|
1036 | if point[0] in [min_x, max_x] and point[1] in [min_y, max_y]: |
---|
1037 | # Keep |
---|
1038 | reduced_polygon.append(point) |
---|
1039 | else: |
---|
1040 | if len(reduced_polygon)*factor < i: |
---|
1041 | reduced_polygon.append(point) |
---|
1042 | |
---|
1043 | return reduced_polygon |
---|
1044 | |
---|
1045 | |
---|
1046 | def interpolate_polyline(data, |
---|
1047 | polyline_nodes, |
---|
1048 | gauge_neighbour_id, |
---|
1049 | interpolation_points=None, |
---|
1050 | rtol=1.0e-6, |
---|
1051 | atol=1.0e-8): |
---|
1052 | """Interpolate linearly between values data on polyline nodes |
---|
1053 | of a polyline to list of interpolation points. |
---|
1054 | |
---|
1055 | data is the data on the polyline nodes. |
---|
1056 | |
---|
1057 | Inputs: |
---|
1058 | data: Vector or array of data at the polyline nodes. |
---|
1059 | polyline_nodes: Location of nodes where data is available. |
---|
1060 | gauge_neighbour_id: ? |
---|
1061 | interpolation_points: Interpolate polyline data to these positions. |
---|
1062 | List of coordinate pairs [x, y] of |
---|
1063 | data points or an nx2 numeric array or a Geospatial_data object |
---|
1064 | rtol, atol: Used to determine whether a point is on the polyline or not. |
---|
1065 | See point_on_line. |
---|
1066 | |
---|
1067 | Output: |
---|
1068 | Interpolated values at interpolation points |
---|
1069 | """ |
---|
1070 | |
---|
1071 | if isinstance(interpolation_points, Geospatial_data): |
---|
1072 | interpolation_points = interpolation_points.\ |
---|
1073 | get_data_points(absolute=True) |
---|
1074 | |
---|
1075 | interpolated_values = num.zeros(len(interpolation_points), num.float) |
---|
1076 | |
---|
1077 | data = ensure_numeric(data, num.float) |
---|
1078 | polyline_nodes = ensure_numeric(polyline_nodes, num.float) |
---|
1079 | interpolation_points = ensure_numeric(interpolation_points, num.float) |
---|
1080 | gauge_neighbour_id = ensure_numeric(gauge_neighbour_id, num.int) |
---|
1081 | |
---|
1082 | num_nodes = polyline_nodes.shape[0] # Number of nodes in polyline |
---|
1083 | |
---|
1084 | # Input sanity check |
---|
1085 | assert_msg = 'interpolation_points are not given (interpolate.py)' |
---|
1086 | assert interpolation_points is not None, assert_msg |
---|
1087 | |
---|
1088 | assert_msg = 'function value must be specified at every interpolation node' |
---|
1089 | assert data.shape[0] == polyline_nodes.shape[0], assert_msg |
---|
1090 | |
---|
1091 | assert_msg = 'Must define function value at one or more nodes' |
---|
1092 | assert data.shape[0] > 0, assert_msg |
---|
1093 | |
---|
1094 | if num_nodes == 1: |
---|
1095 | assert_msg = 'Polyline contained only one point. I need more. ' |
---|
1096 | assert_msg += str(data) |
---|
1097 | raise Exception, assert_msg |
---|
1098 | elif num_nodes > 1: |
---|
1099 | _interpolate_polyline(data, |
---|
1100 | polyline_nodes, |
---|
1101 | gauge_neighbour_id, |
---|
1102 | interpolation_points, |
---|
1103 | interpolated_values, |
---|
1104 | rtol, |
---|
1105 | atol) |
---|
1106 | |
---|
1107 | |
---|
1108 | return interpolated_values |
---|
1109 | |
---|
1110 | |
---|
1111 | def polylist2points_verts(polylist): |
---|
1112 | """ Convert a list of polygons to discrete points and vertices. |
---|
1113 | """ |
---|
1114 | |
---|
1115 | offset = 0 |
---|
1116 | points = [] |
---|
1117 | vertices = [] |
---|
1118 | for poly in polylist: |
---|
1119 | points.extend(poly) |
---|
1120 | vertices.extend([[i, i+1] for i in range(offset, offset+len(poly)-1)]) |
---|
1121 | offset += len(poly) |
---|
1122 | |
---|
1123 | return points, vertices |
---|
1124 | |
---|
1125 | |
---|
1126 | ################################################################################ |
---|
1127 | # Initialise module |
---|
1128 | ################################################################################ |
---|
1129 | |
---|
1130 | from anuga.utilities import compile |
---|
1131 | if compile.can_use_C_extension('polygon_ext.c'): |
---|
1132 | # Underlying C implementations can be accessed |
---|
1133 | from polygon_ext import _point_on_line |
---|
1134 | from polygon_ext import _separate_points_by_polygon |
---|
1135 | from polygon_ext import _interpolate_polyline |
---|
1136 | from polygon_ext import _polygon_overlap |
---|
1137 | from polygon_ext import _is_inside_triangle |
---|
1138 | #from polygon_ext import _intersection |
---|
1139 | |
---|
1140 | else: |
---|
1141 | ERROR_MSG = 'C implementations could not be accessed by %s.\n ' % __file__ |
---|
1142 | ERROR_MSG += 'Make sure compile_all.py has been run as described in ' |
---|
1143 | ERROR_MSG += 'the ANUGA installation guide.' |
---|
1144 | raise Exception(ERROR_MSG) |
---|
1145 | |
---|
1146 | |
---|
1147 | if __name__ == "__main__": |
---|
1148 | pass |
---|