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