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 | import math |
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7 | |
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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, \ |
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10 | Geospatial_data |
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11 | import anuga.utilities.log as log |
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12 | |
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13 | from aabb import AABB |
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14 | |
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15 | def point_on_line(point, line, rtol=1.0e-5, atol=1.0e-8): |
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16 | """Determine whether a point is on a line segment |
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17 | |
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18 | Input: |
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19 | point is given by [x, y] |
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20 | line is given by [x0, y0], [x1, y1]] or |
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21 | the equivalent 2x2 numeric array with each row corresponding to a point. |
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22 | |
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23 | Output: |
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24 | |
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25 | Note: Line can be degenerate and function still works to discern coinciding |
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26 | points from non-coinciding. |
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27 | """ |
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28 | |
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29 | point = ensure_numeric(point) |
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30 | line = ensure_numeric(line) |
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31 | |
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32 | res = _point_on_line(point[0], point[1], |
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33 | line[0, 0], line[0, 1], |
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34 | line[1, 0], line[1, 1], |
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35 | rtol, atol) |
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36 | |
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37 | return bool(res) |
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38 | |
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39 | |
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40 | ###### |
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41 | # Result functions used in intersection() below for collinear lines. |
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42 | # (p0,p1) defines line 0, (p2,p3) defines line 1. |
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43 | ###### |
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44 | |
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45 | # result functions for possible states |
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46 | def lines_dont_coincide(p0, p1, p2, p3): |
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47 | return (3, None) |
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48 | |
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49 | def lines_0_fully_included_in_1(p0, p1, p2, p3): |
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50 | return (2, num.array([p0, p1])) |
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51 | |
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52 | def lines_1_fully_included_in_0(p0, p1, p2, p3): |
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53 | return (2, num.array([p2, p3])) |
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54 | |
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55 | def lines_overlap_same_direction(p0, p1, p2, p3): |
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56 | return (2, num.array([p0, p3])) |
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57 | |
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58 | def lines_overlap_same_direction2(p0, p1, p2, p3): |
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59 | return (2, num.array([p2, p1])) |
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60 | |
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61 | def lines_overlap_opposite_direction(p0, p1, p2, p3): |
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62 | return (2, num.array([p0, p2])) |
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63 | |
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64 | def lines_overlap_opposite_direction2(p0, p1, p2, p3): |
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65 | return (2, num.array([p3, p1])) |
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66 | |
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67 | # this function called when an impossible state is found |
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68 | def lines_error(p1, p2, p3, p4): |
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69 | raise RuntimeError, ('INTERNAL ERROR: p1=%s, p2=%s, p3=%s, p4=%s' |
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70 | % (str(p1), str(p2), str(p3), str(p4))) |
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71 | |
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72 | collinear_result = { |
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73 | # line 0 starts on 1, 0 ends 1, 1 starts 0, 1 ends 0 |
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74 | # 0s1 0e1 1s0 1e0 |
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75 | (False, False, False, False): lines_dont_coincide, |
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76 | (False, False, False, True ): lines_error, |
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77 | (False, False, True, False): lines_error, |
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78 | (False, False, True, True ): lines_1_fully_included_in_0, |
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79 | (False, True, False, False): lines_error, |
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80 | (False, True, False, True ): lines_overlap_opposite_direction2, |
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81 | (False, True, True, False): lines_overlap_same_direction2, |
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82 | (False, True, True, True ): lines_1_fully_included_in_0, |
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83 | (True, False, False, False): lines_error, |
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84 | (True, False, False, True ): lines_overlap_same_direction, |
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85 | (True, False, True, False): lines_overlap_opposite_direction, |
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86 | (True, False, True, True ): lines_1_fully_included_in_0, |
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87 | (True, True, False, False): lines_0_fully_included_in_1, |
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88 | (True, True, False, True ): lines_0_fully_included_in_1, |
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89 | (True, True, True, False): lines_0_fully_included_in_1, |
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90 | (True, True, True, True ): lines_0_fully_included_in_1 |
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91 | } |
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92 | |
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93 | def intersection(line0, line1, rtol=1.0e-5, atol=1.0e-8): |
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94 | """Returns intersecting point between two line segments. |
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95 | |
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96 | However, if parallel lines coincide partly (i.e. share a common segment), |
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97 | the line segment where lines coincide is returned |
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98 | |
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99 | Inputs: |
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100 | line0, line1: Each defined by two end points as in: [[x0, y0], [x1, y1]] |
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101 | A line can also be a 2x2 numpy array with each row |
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102 | corresponding to a point. |
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103 | |
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104 | Output: |
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105 | status, value - where status and value is interpreted as follows: |
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106 | status == 0: no intersection, value set to None. |
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107 | status == 1: intersection point found and returned in value as [x,y]. |
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108 | status == 2: Collinear overlapping lines found. |
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109 | Value takes the form [[x0,y0], [x1,y1]]. |
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110 | status == 3: Collinear non-overlapping lines. Value set to None. |
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111 | status == 4: Lines are parallel. Value set to None. |
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112 | """ |
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113 | |
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114 | # FIXME (Ole): Write this in C |
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115 | |
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116 | line0 = ensure_numeric(line0, num.float) |
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117 | line1 = ensure_numeric(line1, num.float) |
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118 | |
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119 | x0 = line0[0, 0]; y0 = line0[0, 1] |
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120 | x1 = line0[1, 0]; y1 = line0[1, 1] |
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121 | |
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122 | x2 = line1[0, 0]; y2 = line1[0, 1] |
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123 | x3 = line1[1, 0]; y3 = line1[1, 1] |
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124 | |
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125 | denom = (y3-y2)*(x1-x0) - (x3-x2)*(y1-y0) |
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126 | u0 = (x3-x2)*(y0-y2) - (y3-y2)*(x0-x2) |
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127 | u1 = (x2-x0)*(y1-y0) - (y2-y0)*(x1-x0) |
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128 | |
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129 | if num.allclose(denom, 0.0, rtol=rtol, atol=atol): |
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130 | # Lines are parallel - check if they are collinear |
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131 | if num.allclose([u0, u1], 0.0, rtol=rtol, atol=atol): |
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132 | # We now know that the lines are collinear |
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133 | state_tuple = (point_on_line([x0, y0], line1, rtol=rtol, atol=atol), |
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134 | point_on_line([x1, y1], line1, rtol=rtol, atol=atol), |
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135 | point_on_line([x2, y2], line0, rtol=rtol, atol=atol), |
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136 | point_on_line([x3, y3], line0, rtol=rtol, atol=atol)) |
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137 | |
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138 | return collinear_result[state_tuple]([x0, y0], [x1, y1], |
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139 | [x2, y2], [x3, y3]) |
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140 | else: |
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141 | # Lines are parallel but aren't collinear |
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142 | return 4, None #FIXME (Ole): Add distance here instead of None |
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143 | else: |
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144 | # Lines are not parallel, check if they intersect |
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145 | u0 = u0/denom |
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146 | u1 = u1/denom |
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147 | |
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148 | x = x0 + u0*(x1-x0) |
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149 | y = y0 + u0*(y1-y0) |
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150 | |
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151 | # Sanity check - can be removed to speed up if needed |
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152 | assert num.allclose(x, x2 + u1*(x3-x2), rtol=rtol, atol=atol) |
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153 | assert num.allclose(y, y2 + u1*(y3-y2), rtol=rtol, atol=atol) |
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154 | |
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155 | # Check if point found lies within given line segments |
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156 | if 0.0 <= u0 <= 1.0 and 0.0 <= u1 <= 1.0: |
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157 | # We have intersection |
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158 | return 1, num.array([x, y]) |
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159 | else: |
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160 | # No intersection |
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161 | return 0, None |
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162 | |
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163 | def NEW_C_intersection(line0, line1): |
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164 | """Returns intersecting point between two line segments. |
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165 | |
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166 | However, if parallel lines coincide partly (i.e. share a common segment), |
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167 | the line segment where lines coincide is returned |
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168 | |
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169 | Inputs: |
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170 | line0, line1: Each defined by two end points as in: [[x0, y0], [x1, y1]] |
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171 | A line can also be a 2x2 numpy array with each row |
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172 | corresponding to a point. |
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173 | |
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174 | Output: |
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175 | status, value - where status and value is interpreted as follows: |
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176 | status == 0: no intersection, value set to None. |
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177 | status == 1: intersection point found and returned in value as [x,y]. |
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178 | status == 2: Collinear overlapping lines found. |
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179 | Value takes the form [[x0,y0], [x1,y1]]. |
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180 | status == 3: Collinear non-overlapping lines. Value set to None. |
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181 | status == 4: Lines are parallel. Value set to None. |
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182 | """ |
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183 | |
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184 | line0 = ensure_numeric(line0, num.float) |
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185 | line1 = ensure_numeric(line1, num.float) |
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186 | |
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187 | status, value = _intersection(line0[0, 0], line0[0, 1], |
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188 | line0[1, 0], line0[1, 1], |
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189 | line1[0, 0], line1[0, 1], |
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190 | line1[1, 0], line1[1, 1]) |
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191 | |
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192 | return status, value |
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193 | |
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194 | def polygon_overlap(triangles, polygon, verbose=False): |
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195 | """Determine if a polygon and triangle overlap |
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196 | |
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197 | """ |
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198 | polygon = ensure_numeric(polygon) |
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199 | triangles = ensure_numeric(triangles) |
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200 | |
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201 | M = triangles.shape[0]/3 # Number of triangles |
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202 | |
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203 | indices = num.zeros(M, num.int) |
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204 | |
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205 | count = _polygon_overlap(polygon, triangles, indices) |
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206 | |
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207 | if verbose: |
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208 | log.critical('Found %d triangles (out of %d) that polygon' % (count, M)) |
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209 | |
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210 | return indices[:count] |
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211 | |
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212 | def not_polygon_overlap(triangles, polygon, verbose=False): |
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213 | """Determine if a polygon and triangle overlap |
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214 | |
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215 | """ |
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216 | polygon = ensure_numeric(polygon) |
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217 | triangles = ensure_numeric(triangles) |
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218 | |
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219 | M = triangles.shape[0]/3 # Number of triangles |
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220 | |
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221 | indices = num.zeros(M, num.int) |
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222 | |
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223 | count = _polygon_overlap(polygon, triangles, indices) |
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224 | |
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225 | if verbose: |
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226 | log.critical('Found %d triangles (out of %d) that polygon' % (count, M)) |
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227 | |
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228 | return indices[count:] |
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229 | |
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230 | def line_intersect(triangles, line, verbose=False): |
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231 | """Determine if a polygon and triangle overlap |
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232 | |
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233 | """ |
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234 | line = ensure_numeric(line) |
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235 | triangles = ensure_numeric(triangles) |
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236 | |
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237 | M = triangles.shape[0]/3 # Number of triangles |
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238 | |
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239 | indices = num.zeros(M, num.int) |
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240 | |
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241 | count = _line_intersect(line, triangles, indices) |
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242 | |
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243 | if verbose: |
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244 | log.critical('Found %d triangles (out of %d) that overlap the polygon' % (count, M)) |
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245 | |
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246 | return indices[:count] |
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247 | |
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248 | |
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249 | def line_length(line): |
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250 | """Determine the length of the line |
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251 | """ |
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252 | |
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253 | l12 = line[1]-line[0] |
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254 | |
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255 | return math.sqrt(num.dot(l12,l12)) |
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256 | |
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257 | def not_line_intersect(triangles, line, verbose=False): |
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258 | """Determine if a polyline and triangle overlap |
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259 | |
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260 | """ |
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261 | line = ensure_numeric(line) |
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262 | triangles = ensure_numeric(triangles) |
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263 | |
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264 | M = triangles.shape[0]/3 # Number of triangles |
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265 | |
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266 | indices = num.zeros(M, num.int) |
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267 | |
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268 | count = _line_intersect(line, triangles, indices) |
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269 | |
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270 | if verbose: |
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271 | log.critical('Found %d triangles (out of %d) that intersect the line' % (count, M)) |
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272 | |
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273 | return indices[count:] |
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274 | |
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275 | |
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276 | def is_inside_triangle(point, triangle, |
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277 | closed=True, |
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278 | rtol=1.0e-12, |
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279 | atol=1.0e-12, |
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280 | check_inputs=True): |
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281 | """Determine if one point is inside a triangle |
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282 | |
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283 | This uses the barycentric method: |
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284 | |
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285 | Triangle is A, B, C |
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286 | Point P can then be written as |
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287 | |
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288 | P = A + alpha * (C-A) + beta * (B-A) |
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289 | or if we let |
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290 | v=P-A, v0=C-A, v1=B-A |
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291 | |
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292 | v = alpha*v0 + beta*v1 |
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293 | |
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294 | Dot this equation by v0 and v1 to get two: |
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295 | |
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296 | dot(v0, v) = alpha*dot(v0, v0) + beta*dot(v0, v1) |
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297 | dot(v1, v) = alpha*dot(v1, v0) + beta*dot(v1, v1) |
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298 | |
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299 | or if a_ij = dot(v_i, v_j) and b_i = dot(v_i, v) |
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300 | the matrix equation: |
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301 | |
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302 | a_00 a_01 alpha b_0 |
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303 | = |
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304 | a_10 a_11 beta b_1 |
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305 | |
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306 | Solving for alpha and beta yields: |
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307 | |
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308 | alpha = (b_0*a_11 - b_1*a_01)/denom |
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309 | beta = (b_1*a_00 - b_0*a_10)/denom |
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310 | |
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311 | with denom = a_11*a_00 - a_10*a_01 |
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312 | |
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313 | The point is in the triangle whenever |
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314 | alpha and beta and their sums are in the unit interval. |
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315 | |
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316 | rtol and atol will determine how close the point has to be to the edge |
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317 | before it is deemed to be on the edge. |
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318 | |
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319 | """ |
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320 | |
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321 | triangle = ensure_numeric(triangle) |
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322 | point = ensure_numeric(point, num.float) |
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323 | |
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324 | if check_inputs is True: |
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325 | msg = 'is_inside_triangle must be invoked with one point only' |
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326 | assert num.allclose(point.shape, [2]), msg |
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327 | |
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328 | |
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329 | # Use C-implementation |
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330 | return bool(_is_inside_triangle(point, triangle, int(closed), rtol, atol)) |
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331 | |
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332 | def is_complex(polygon, closed=True, verbose=False): |
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333 | """Check if a polygon is complex (self-intersecting). |
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334 | Uses a sweep algorithm that is O(n^2) in the worst case, but |
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335 | for most normal looking polygons it'll be O(n log n). |
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336 | |
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337 | polygon is a list of points that define a closed polygon. |
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338 | verbose will print a list of the intersection points if true |
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339 | |
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340 | Return True if polygon is complex. |
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341 | """ |
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342 | |
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343 | def key_xpos(item): |
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344 | """ Return the x coord out of the passed point for sorting key. """ |
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345 | return (item[0][0]) |
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346 | |
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347 | def segments_joined(seg0, seg1): |
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348 | """ See if there are identical segments in the 2 lists. """ |
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349 | for i in seg0: |
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350 | for j in seg1: |
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351 | if i == j: return True |
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352 | return False |
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353 | |
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354 | polygon = ensure_numeric(polygon, num.float) |
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355 | |
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356 | # build a list of discrete segments from the polygon |
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357 | unsorted_segs = [] |
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358 | for i in range(0, len(polygon)-1): |
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359 | unsorted_segs.append([list(polygon[i]), list(polygon[i+1])]) |
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360 | |
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361 | if closed: |
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362 | unsorted_segs.append([list(polygon[0]), list(polygon[-1])]) |
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363 | |
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364 | # all segments must point in same direction |
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365 | for val in unsorted_segs: |
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366 | if val[0][0] > val[1][0]: |
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367 | val[0], val[1] = val[1], val[0] |
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368 | |
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369 | l_x = sorted(unsorted_segs, key=key_xpos) |
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370 | |
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371 | comparisons = 0 |
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372 | |
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373 | # loop through, only comparing lines that partially overlap in x |
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374 | for index, leftmost in enumerate(l_x): |
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375 | cmp = index+1 |
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376 | while cmp < len(l_x) and leftmost[1][0] > l_x[cmp][0][0]: |
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377 | if not segments_joined(leftmost, l_x[cmp]): |
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378 | (type, point) = intersection(leftmost, l_x[cmp]) |
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379 | comparisons += 1 |
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380 | if type != 0 and type != 4 or (type == 2 and list(point[0]) !=\ |
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381 | list(point[1])): |
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382 | if verbose: |
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383 | print 'Self-intersecting polygon found, type ', type |
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384 | print 'point', point, |
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385 | print 'vertices: ', leftmost, ' - ', l_x[cmp] |
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386 | return True |
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387 | cmp += 1 |
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388 | |
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389 | return False |
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390 | |
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391 | |
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392 | def is_inside_polygon(point, polygon, closed=True, verbose=False): |
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393 | """Determine if one point is inside a polygon |
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394 | |
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395 | See inside_polygon for more details |
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396 | """ |
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397 | |
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398 | indices = inside_polygon(point, polygon, closed, verbose) |
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399 | |
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400 | if indices.shape[0] == 1: |
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401 | return True |
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402 | elif indices.shape[0] == 0: |
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403 | return False |
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404 | else: |
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405 | msg = 'is_inside_polygon must be invoked with one point only' |
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406 | raise Exception(msg) |
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407 | |
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408 | def inside_polygon(points, polygon, closed=True, verbose=False): |
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409 | """Determine points inside a polygon |
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410 | |
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411 | Functions inside_polygon and outside_polygon have been defined in |
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412 | terms of separate_by_polygon which will put all inside indices in |
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413 | the first part of the indices array and outside indices in the last |
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414 | |
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415 | See separate_points_by_polygon for documentation |
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416 | |
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417 | points and polygon can be a geospatial instance, |
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418 | a list or a numeric array |
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419 | """ |
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420 | |
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421 | try: |
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422 | points = ensure_absolute(points) |
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423 | except NameError, err: |
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424 | raise NameError, err |
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425 | except: |
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426 | # If this fails it is going to be because the points can't be |
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427 | # converted to a numeric array. |
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428 | msg = 'Points could not be converted to numeric array' |
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429 | raise Exception, msg |
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430 | |
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431 | polygon = ensure_absolute(polygon) |
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432 | try: |
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433 | polygon = ensure_absolute(polygon) |
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434 | except NameError, e: |
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435 | raise NameError, e |
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436 | except: |
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437 | # If this fails it is going to be because the points can't be |
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438 | # converted to a numeric array. |
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439 | msg = ('Polygon %s could not be converted to numeric array' |
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440 | % (str(polygon))) |
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441 | raise Exception, msg |
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442 | |
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443 | if len(points.shape) == 1: |
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444 | # Only one point was passed in. Convert to array of points |
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445 | points = num.reshape(points, (1,2)) |
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446 | |
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447 | indices, count = separate_points_by_polygon(points, polygon, |
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448 | closed=closed, |
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449 | verbose=verbose) |
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450 | |
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451 | # Return indices of points inside polygon |
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452 | return indices[:count] |
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453 | |
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454 | def is_outside_polygon(point, polygon, closed=True, verbose=False, |
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455 | points_geo_ref=None, polygon_geo_ref=None): |
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456 | """Determine if one point is outside a polygon |
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457 | |
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458 | See outside_polygon for more details |
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459 | """ |
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460 | |
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461 | indices = outside_polygon(point, polygon, closed, verbose) |
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462 | |
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463 | if indices.shape[0] == 1: |
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464 | return True |
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465 | elif indices.shape[0] == 0: |
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466 | return False |
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467 | else: |
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468 | msg = 'is_outside_polygon must be invoked with one point only' |
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469 | raise Exception, msg |
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470 | |
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471 | def outside_polygon(points, polygon, closed = True, verbose = False): |
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472 | """Determine points outside a polygon |
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473 | |
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474 | Functions inside_polygon and outside_polygon have been defined in |
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475 | terms of separate_by_polygon which will put all inside indices in |
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476 | the first part of the indices array and outside indices in the last |
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477 | |
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478 | See separate_points_by_polygon for documentation |
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479 | """ |
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480 | |
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481 | try: |
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482 | points = ensure_numeric(points, num.float) |
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483 | except NameError, e: |
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484 | raise NameError, e |
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485 | except: |
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486 | msg = 'Points could not be converted to numeric array' |
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487 | raise Exception, msg |
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488 | |
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489 | try: |
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490 | polygon = ensure_numeric(polygon, num.float) |
---|
491 | except NameError, e: |
---|
492 | raise NameError, e |
---|
493 | except: |
---|
494 | msg = 'Polygon could not be converted to numeric array' |
---|
495 | raise Exception, msg |
---|
496 | |
---|
497 | if len(points.shape) == 1: |
---|
498 | # Only one point was passed in. Convert to array of points |
---|
499 | points = num.reshape(points, (1, 2)) |
---|
500 | |
---|
501 | indices, count = separate_points_by_polygon(points, polygon, |
---|
502 | closed=closed, |
---|
503 | verbose=verbose) |
---|
504 | |
---|
505 | # Return indices of points outside polygon |
---|
506 | if count == len(indices): |
---|
507 | # No points are outside |
---|
508 | return num.array([]) |
---|
509 | else: |
---|
510 | return indices[count:][::-1] #return reversed |
---|
511 | |
---|
512 | def in_and_outside_polygon(points, polygon, closed=True, verbose=False): |
---|
513 | """Determine points inside and outside a polygon |
---|
514 | |
---|
515 | See separate_points_by_polygon for documentation |
---|
516 | |
---|
517 | Returns an array of points inside and array of points outside the polygon |
---|
518 | """ |
---|
519 | |
---|
520 | try: |
---|
521 | points = ensure_numeric(points, num.float) |
---|
522 | except NameError, e: |
---|
523 | raise NameError, e |
---|
524 | except: |
---|
525 | msg = 'Points could not be converted to numeric array' |
---|
526 | raise Exception, msg |
---|
527 | |
---|
528 | try: |
---|
529 | polygon = ensure_numeric(polygon, num.float) |
---|
530 | except NameError, e: |
---|
531 | raise NameError, e |
---|
532 | except: |
---|
533 | msg = 'Polygon could not be converted to numeric array' |
---|
534 | raise Exception, msg |
---|
535 | |
---|
536 | if len(points.shape) == 1: |
---|
537 | # Only one point was passed in. Convert to array of points |
---|
538 | points = num.reshape(points, (1, 2)) |
---|
539 | |
---|
540 | indices, count = separate_points_by_polygon(points, polygon, |
---|
541 | closed=closed, |
---|
542 | verbose=verbose) |
---|
543 | |
---|
544 | # Returns indices of points inside and indices of points outside |
---|
545 | # the polygon |
---|
546 | if count == len(indices): |
---|
547 | # No points are outside |
---|
548 | return indices[:count], [] |
---|
549 | else: |
---|
550 | return indices[:count], indices[count:][::-1] #return reversed |
---|
551 | |
---|
552 | |
---|
553 | |
---|
554 | def separate_points_by_polygon(points, polygon, |
---|
555 | closed=True, |
---|
556 | check_input=True, |
---|
557 | verbose=False): |
---|
558 | """Determine whether points are inside or outside a polygon |
---|
559 | |
---|
560 | Input: |
---|
561 | points - Tuple of (x, y) coordinates, or list of tuples |
---|
562 | polygon - list of vertices of polygon |
---|
563 | closed - (optional) determine whether points on boundary should be |
---|
564 | regarded as belonging to the polygon (closed = True) |
---|
565 | or not (closed = False) |
---|
566 | check_input: Allows faster execution if set to False |
---|
567 | |
---|
568 | Outputs: |
---|
569 | indices: array of same length as points with indices of points falling |
---|
570 | inside the polygon listed from the beginning and indices of points |
---|
571 | falling outside listed from the end. |
---|
572 | |
---|
573 | count: count of points falling inside the polygon |
---|
574 | |
---|
575 | The indices of points inside are obtained as indices[:count] |
---|
576 | The indices of points outside are obtained as indices[count:] |
---|
577 | |
---|
578 | Examples: |
---|
579 | U = [[0,0], [1,0], [1,1], [0,1]] #Unit square |
---|
580 | |
---|
581 | separate_points_by_polygon( [[0.5, 0.5], [1, -0.5], [0.3, 0.2]], U) |
---|
582 | will return the indices [0, 2, 1] and count == 2 as only the first |
---|
583 | and the last point are inside the unit square |
---|
584 | |
---|
585 | Remarks: |
---|
586 | The vertices may be listed clockwise or counterclockwise and |
---|
587 | the first point may optionally be repeated. |
---|
588 | Polygons do not need to be convex. |
---|
589 | Polygons can have holes in them and points inside a hole is |
---|
590 | regarded as being outside the polygon. |
---|
591 | |
---|
592 | Algorithm is based on work by Darel Finley, |
---|
593 | http://www.alienryderflex.com/polygon/ |
---|
594 | |
---|
595 | Uses underlying C-implementation in polygon_ext.c |
---|
596 | """ |
---|
597 | |
---|
598 | if check_input: |
---|
599 | #Input checks |
---|
600 | assert isinstance(closed, bool), \ |
---|
601 | 'Keyword argument "closed" must be boolean' |
---|
602 | assert isinstance(verbose, bool), \ |
---|
603 | 'Keyword argument "verbose" must be boolean' |
---|
604 | |
---|
605 | try: |
---|
606 | points = ensure_numeric(points, num.float) |
---|
607 | except NameError, e: |
---|
608 | raise NameError, e |
---|
609 | except: |
---|
610 | msg = 'Points could not be converted to numeric array' |
---|
611 | raise Exception(msg) |
---|
612 | |
---|
613 | try: |
---|
614 | polygon = ensure_numeric(polygon, num.float) |
---|
615 | except NameError, e: |
---|
616 | raise NameError(e) |
---|
617 | except: |
---|
618 | msg = 'Polygon could not be converted to numeric array' |
---|
619 | raise Exception(msg) |
---|
620 | |
---|
621 | msg = 'Polygon array must be a 2d array of vertices' |
---|
622 | assert len(polygon.shape) == 2, msg |
---|
623 | |
---|
624 | msg = 'Polygon array must have two columns' |
---|
625 | assert polygon.shape[1] == 2, msg |
---|
626 | |
---|
627 | |
---|
628 | msg = ('Points array must be 1 or 2 dimensional. ' |
---|
629 | 'I got %d dimensions' % len(points.shape)) |
---|
630 | assert 0 < len(points.shape) < 3, msg |
---|
631 | |
---|
632 | if len(points.shape) == 1: |
---|
633 | # Only one point was passed in. Convert to array of points. |
---|
634 | points = num.reshape(points, (1, 2)) |
---|
635 | |
---|
636 | msg = ('Point array must have two columns (x,y), ' |
---|
637 | 'I got points.shape[1]=%d' % points.shape[0]) |
---|
638 | assert points.shape[1]==2, msg |
---|
639 | |
---|
640 | |
---|
641 | msg = ('Points array must be a 2d array. I got %s.' |
---|
642 | % str(points[:30])) |
---|
643 | assert len(points.shape) == 2, msg |
---|
644 | |
---|
645 | msg = 'Points array must have two columns' |
---|
646 | assert points.shape[1] == 2, msg |
---|
647 | |
---|
648 | N = polygon.shape[0] # Number of vertices in polygon |
---|
649 | M = points.shape[0] # Number of points |
---|
650 | |
---|
651 | indices = num.zeros(M, num.int) |
---|
652 | |
---|
653 | count = _separate_points_by_polygon(points, polygon, indices, |
---|
654 | int(closed), int(verbose)) |
---|
655 | |
---|
656 | if verbose: |
---|
657 | log.critical('Found %d points (out of %d) inside polygon' % (count, M)) |
---|
658 | |
---|
659 | return indices, count |
---|
660 | |
---|
661 | |
---|
662 | def polygon_area(input_polygon): |
---|
663 | """ Determine area of arbitrary polygon. |
---|
664 | |
---|
665 | input_polygon The polygon to get area of. |
---|
666 | |
---|
667 | return A scalar value for the polygon area. |
---|
668 | |
---|
669 | Reference: http://mathworld.wolfram.com/PolygonArea.html |
---|
670 | """ |
---|
671 | # Move polygon to origin (0,0) to avoid rounding errors |
---|
672 | # This makes a copy of the polygon to avoid destroying it |
---|
673 | input_polygon = ensure_numeric(input_polygon) |
---|
674 | min_x = min(input_polygon[:, 0]) |
---|
675 | min_y = min(input_polygon[:, 1]) |
---|
676 | polygon = input_polygon - [min_x, min_y] |
---|
677 | |
---|
678 | # Compute area |
---|
679 | n = len(polygon) |
---|
680 | poly_area = 0.0 |
---|
681 | |
---|
682 | for i in range(n): |
---|
683 | pti = polygon[i] |
---|
684 | if i == n-1: |
---|
685 | pt1 = polygon[0] |
---|
686 | else: |
---|
687 | pt1 = polygon[i+1] |
---|
688 | xi = pti[0] |
---|
689 | yi1 = pt1[1] |
---|
690 | xi1 = pt1[0] |
---|
691 | yi = pti[1] |
---|
692 | poly_area += xi*yi1 - xi1*yi |
---|
693 | |
---|
694 | return abs(poly_area/2) |
---|
695 | |
---|
696 | |
---|
697 | def plot_polygons(polygons_points, |
---|
698 | style=None, |
---|
699 | figname=None, |
---|
700 | label=None, |
---|
701 | alpha=None): |
---|
702 | """ Take list of polygons and plot. |
---|
703 | |
---|
704 | Inputs: |
---|
705 | |
---|
706 | polygons - list of polygons |
---|
707 | |
---|
708 | style - style list corresponding to each polygon |
---|
709 | - for a polygon, use 'line' |
---|
710 | - for points falling outside a polygon, use 'outside' |
---|
711 | - style can also be user defined as in normal pylab plot. |
---|
712 | |
---|
713 | figname - name to save figure to |
---|
714 | |
---|
715 | label - title for plotA |
---|
716 | |
---|
717 | alpha - transparency of polygon fill, 0.0=none, 1.0=solid |
---|
718 | if not supplied, no fill. |
---|
719 | |
---|
720 | Outputs: |
---|
721 | |
---|
722 | - plot of polygons |
---|
723 | """ |
---|
724 | |
---|
725 | from pylab import ion, hold, plot, savefig, xlabel, \ |
---|
726 | ylabel, title, close, title, fill |
---|
727 | |
---|
728 | assert type(polygons_points) == list, \ |
---|
729 | 'input must be a list of polygons and/or points' |
---|
730 | |
---|
731 | ion() |
---|
732 | hold(True) |
---|
733 | |
---|
734 | if label is None: |
---|
735 | label = '' |
---|
736 | |
---|
737 | # clamp alpha to sensible range |
---|
738 | if alpha: |
---|
739 | try: |
---|
740 | alpha = float(alpha) |
---|
741 | except ValueError: |
---|
742 | alpha = None |
---|
743 | else: |
---|
744 | alpha = max(0.0, min(1.0, alpha)) |
---|
745 | |
---|
746 | num_points = len(polygons_points) |
---|
747 | colour = [] |
---|
748 | if style is None: |
---|
749 | style_type = 'line' |
---|
750 | style = [] |
---|
751 | for i in range(num_points): |
---|
752 | style.append(style_type) |
---|
753 | colour.append('b-') |
---|
754 | else: |
---|
755 | for style_name in style: |
---|
756 | if style_name == 'line': |
---|
757 | colour.append('b-') |
---|
758 | if style_name == 'outside': |
---|
759 | colour.append('r.') |
---|
760 | if style_name == 'point': |
---|
761 | colour.append('g.') |
---|
762 | if style_name not in ['line', 'outside', 'point']: |
---|
763 | colour.append(style_name) |
---|
764 | |
---|
765 | for i, item in enumerate(polygons_points): |
---|
766 | pt_x, pt_y = _poly_xy(item) |
---|
767 | plot(pt_x, pt_y, colour[i]) |
---|
768 | if alpha: |
---|
769 | fill(pt_x, pt_y, colour[i], alpha=alpha) |
---|
770 | xlabel('x') |
---|
771 | ylabel('y') |
---|
772 | title(label) |
---|
773 | |
---|
774 | if figname is not None: |
---|
775 | savefig(figname) |
---|
776 | else: |
---|
777 | savefig('test_image') |
---|
778 | |
---|
779 | close('all') |
---|
780 | |
---|
781 | |
---|
782 | def _poly_xy(polygon): |
---|
783 | """ this is used within plot_polygons so need to duplicate |
---|
784 | the first point so can have closed polygon in plot |
---|
785 | |
---|
786 | polygon A set of points defining a polygon. |
---|
787 | verbose True if this function is to be verbose. |
---|
788 | |
---|
789 | Returns a tuple (x, y) of X and Y coordinates of the polygon. |
---|
790 | We duplicate the first point so can have closed polygon in plot. |
---|
791 | """ |
---|
792 | |
---|
793 | try: |
---|
794 | polygon = ensure_numeric(polygon, num.float) |
---|
795 | except NameError, err: |
---|
796 | raise NameError, err |
---|
797 | except: |
---|
798 | msg = ('Polygon %s could not be converted to numeric array' |
---|
799 | % (str(polygon))) |
---|
800 | raise Exception, msg |
---|
801 | |
---|
802 | pts_x = num.concatenate((polygon[:, 0], [polygon[0, 0]]), axis = 0) |
---|
803 | pts_y = num.concatenate((polygon[:, 1], [polygon[0, 1]]), axis = 0) |
---|
804 | |
---|
805 | return pts_x, pts_y |
---|
806 | |
---|
807 | |
---|
808 | ################################################################################ |
---|
809 | # Functions to read and write polygon information |
---|
810 | ################################################################################ |
---|
811 | |
---|
812 | def read_polygon(filename, delimiter=',', closed=True, verbose=False): |
---|
813 | """ Read points assumed to form a (closed) polygon. |
---|
814 | Can also be used to read in a polyline (closed=False) |
---|
815 | |
---|
816 | Also checks to make sure polygon (polyline) |
---|
817 | is not complex (self-intersecting). |
---|
818 | |
---|
819 | filename Path to file containing polygon data. |
---|
820 | delimiter Delimiter to split polygon data with. |
---|
821 | A list of point data from the polygon file. |
---|
822 | |
---|
823 | There must be exactly two numbers in each line |
---|
824 | separated by the delimiter. |
---|
825 | No header. |
---|
826 | """ |
---|
827 | |
---|
828 | fid = open(filename) |
---|
829 | lines = fid.readlines() |
---|
830 | fid.close() |
---|
831 | polygon = [] |
---|
832 | for line in lines: |
---|
833 | fields = line.split(delimiter) |
---|
834 | polygon.append([float(fields[0]), float(fields[1])]) |
---|
835 | |
---|
836 | # check this is a valid polygon (polyline). |
---|
837 | if is_complex(polygon, closed, verbose=verbose): |
---|
838 | msg = 'ERROR: Self-intersecting polygon detected in file ' |
---|
839 | msg += filename +'. A complex polygon will not ' |
---|
840 | msg += 'necessarily break the algorithms within ANUGA, but it' |
---|
841 | msg += 'usually signifies pathological data. Please fix this file.' |
---|
842 | raise Exception, msg |
---|
843 | |
---|
844 | return polygon |
---|
845 | |
---|
846 | |
---|
847 | def write_polygon(polygon, filename=None): |
---|
848 | """Write polygon to csv file. |
---|
849 | |
---|
850 | There will be exactly two numbers, easting and northing, in each line |
---|
851 | separated by a comma. |
---|
852 | |
---|
853 | No header. |
---|
854 | """ |
---|
855 | |
---|
856 | fid = open(filename, 'w') |
---|
857 | for point in polygon: |
---|
858 | fid.write('%f, %f\n' % point) |
---|
859 | fid.close() |
---|
860 | |
---|
861 | |
---|
862 | def populate_polygon(polygon, number_of_points, seed=None, exclude=None): |
---|
863 | """Populate given polygon with uniformly distributed points. |
---|
864 | |
---|
865 | Input: |
---|
866 | polygon - list of vertices of polygon |
---|
867 | number_of_points - (optional) number of points |
---|
868 | seed - seed for random number generator (default=None) |
---|
869 | exclude - list of polygons (inside main polygon) from where points |
---|
870 | should be excluded |
---|
871 | |
---|
872 | Output: |
---|
873 | points - list of points inside polygon |
---|
874 | |
---|
875 | Examples: |
---|
876 | populate_polygon( [[0,0], [1,0], [1,1], [0,1]], 5 ) |
---|
877 | will return five randomly selected points inside the unit square |
---|
878 | """ |
---|
879 | |
---|
880 | from random import uniform, seed as seed_function |
---|
881 | |
---|
882 | seed_function(seed) |
---|
883 | |
---|
884 | points = [] |
---|
885 | |
---|
886 | # Find outer extent of polygon |
---|
887 | extents = AABB(polygon) |
---|
888 | |
---|
889 | while len(points) < number_of_points: |
---|
890 | rand_x = uniform(extents.xmin, extents.xmax) |
---|
891 | rand_y = uniform(extents.ymin, extents.ymax) |
---|
892 | |
---|
893 | append = False |
---|
894 | if is_inside_polygon([rand_x, rand_y], polygon): |
---|
895 | append = True |
---|
896 | |
---|
897 | #Check exclusions |
---|
898 | if exclude is not None: |
---|
899 | for ex_poly in exclude: |
---|
900 | if is_inside_polygon([rand_x, rand_y], ex_poly): |
---|
901 | append = False |
---|
902 | |
---|
903 | if append is True: |
---|
904 | points.append([rand_x, rand_y]) |
---|
905 | |
---|
906 | return points |
---|
907 | |
---|
908 | |
---|
909 | def point_in_polygon(polygon, delta=1e-8): |
---|
910 | """Return a point inside a given polygon which will be close to the |
---|
911 | polygon edge. |
---|
912 | |
---|
913 | Input: |
---|
914 | polygon - list of vertices of polygon |
---|
915 | delta - the square root of 2 * delta is the maximum distance from the |
---|
916 | polygon points and the returned point. |
---|
917 | Output: |
---|
918 | points - a point inside polygon |
---|
919 | |
---|
920 | searches in all diagonals and up and down (not left and right). |
---|
921 | """ |
---|
922 | |
---|
923 | polygon = ensure_numeric(polygon) |
---|
924 | |
---|
925 | while True: |
---|
926 | for poly_point in polygon: |
---|
927 | for x_mult in range(-1, 2): |
---|
928 | for y_mult in range(-1, 2): |
---|
929 | pt_x, pt_y = poly_point |
---|
930 | |
---|
931 | if pt_x == 0: |
---|
932 | x_delta = x_mult * delta |
---|
933 | else: |
---|
934 | x_delta = pt_x + x_mult*pt_x*delta |
---|
935 | |
---|
936 | if pt_y == 0: |
---|
937 | y_delta = y_mult * delta |
---|
938 | else: |
---|
939 | y_delta = pt_y + y_mult*pt_y*delta |
---|
940 | |
---|
941 | point = [x_delta, y_delta] |
---|
942 | |
---|
943 | if is_inside_polygon(point, polygon, closed=False): |
---|
944 | return point |
---|
945 | delta = delta * 0.1 |
---|
946 | |
---|
947 | |
---|
948 | def number_mesh_triangles(interior_regions, bounding_poly, remainder_res): |
---|
949 | """Calculate the approximate number of triangles inside the |
---|
950 | bounding polygon and the other interior regions |
---|
951 | |
---|
952 | Polygon areas are converted to square Kms |
---|
953 | |
---|
954 | FIXME: Add tests for this function |
---|
955 | """ |
---|
956 | |
---|
957 | # TO DO check if any of the regions fall inside one another |
---|
958 | |
---|
959 | log.info('-' * 80) |
---|
960 | log.info('Polygon Max triangle area (m^2) Total area (km^2) ' |
---|
961 | 'Estimated #triangles') |
---|
962 | log.info('-' * 80) |
---|
963 | |
---|
964 | no_triangles = 0.0 |
---|
965 | area = polygon_area(bounding_poly) |
---|
966 | |
---|
967 | for poly, resolution in interior_regions: |
---|
968 | this_area = polygon_area(poly) |
---|
969 | this_triangles = this_area/resolution |
---|
970 | no_triangles += this_triangles |
---|
971 | area -= this_area |
---|
972 | |
---|
973 | log.info('Interior %s%s%d' |
---|
974 | % (('%.0f' % resolution).ljust(25), |
---|
975 | ('%.2f' % (this_area/1000000)).ljust(19), |
---|
976 | this_triangles)) |
---|
977 | |
---|
978 | bound_triangles = area/remainder_res |
---|
979 | no_triangles += bound_triangles |
---|
980 | |
---|
981 | log.info('Bounding %s%s%d' |
---|
982 | % (('%.0f' % remainder_res).ljust(25), |
---|
983 | ('%.2f' % (area/1000000)).ljust(19), |
---|
984 | bound_triangles)) |
---|
985 | |
---|
986 | total_number_of_triangles = no_triangles/0.7 |
---|
987 | |
---|
988 | log.info('Estimated total number of triangles: %d' |
---|
989 | % total_number_of_triangles) |
---|
990 | log.info('Note: This is generally about 20% less than the final amount') |
---|
991 | |
---|
992 | return int(total_number_of_triangles) |
---|
993 | |
---|
994 | |
---|
995 | def decimate_polygon(polygon, factor=10): |
---|
996 | """Reduce number of points in polygon by the specified |
---|
997 | factor (default=10, hence the name of the function) such that |
---|
998 | the extrema in both axes are preserved. |
---|
999 | |
---|
1000 | Reduce number of points in polygon by the specified factor. |
---|
1001 | polygon The polygon to reduce. |
---|
1002 | factor The factor to reduce polygon points by (default 10). |
---|
1003 | |
---|
1004 | The extrema of both axes are preserved. |
---|
1005 | |
---|
1006 | Return reduced polygon |
---|
1007 | """ |
---|
1008 | |
---|
1009 | # FIXME(Ole): This doesn't work at present, |
---|
1010 | # but it isn't critical either |
---|
1011 | |
---|
1012 | # Find outer extent of polygon |
---|
1013 | num_polygon = ensure_numeric(polygon) |
---|
1014 | max_x = max(num_polygon[:, 0]) |
---|
1015 | max_y = max(num_polygon[:, 1]) |
---|
1016 | min_x = min(num_polygon[:, 0]) |
---|
1017 | min_y = min(num_polygon[:, 1]) |
---|
1018 | |
---|
1019 | # Keep only some points making sure extrema are kept |
---|
1020 | reduced_polygon = [] |
---|
1021 | for i, point in enumerate(polygon): |
---|
1022 | if point[0] in [min_x, max_x] and point[1] in [min_y, max_y]: |
---|
1023 | # Keep |
---|
1024 | reduced_polygon.append(point) |
---|
1025 | else: |
---|
1026 | if len(reduced_polygon)*factor < i: |
---|
1027 | reduced_polygon.append(point) |
---|
1028 | |
---|
1029 | return reduced_polygon |
---|
1030 | |
---|
1031 | |
---|
1032 | def interpolate_polyline(data, |
---|
1033 | polyline_nodes, |
---|
1034 | gauge_neighbour_id, |
---|
1035 | interpolation_points=None, |
---|
1036 | rtol=1.0e-6, |
---|
1037 | atol=1.0e-8): |
---|
1038 | """Interpolate linearly between values data on polyline nodes |
---|
1039 | of a polyline to list of interpolation points. |
---|
1040 | |
---|
1041 | data is the data on the polyline nodes. |
---|
1042 | |
---|
1043 | Inputs: |
---|
1044 | data: Vector or array of data at the polyline nodes. |
---|
1045 | polyline_nodes: Location of nodes where data is available. |
---|
1046 | gauge_neighbour_id: ? |
---|
1047 | interpolation_points: Interpolate polyline data to these positions. |
---|
1048 | List of coordinate pairs [x, y] of |
---|
1049 | data points or an nx2 numeric array or a Geospatial_data object |
---|
1050 | rtol, atol: Used to determine whether a point is on the polyline or not. |
---|
1051 | See point_on_line. |
---|
1052 | |
---|
1053 | Output: |
---|
1054 | Interpolated values at interpolation points |
---|
1055 | """ |
---|
1056 | |
---|
1057 | if isinstance(interpolation_points, Geospatial_data): |
---|
1058 | interpolation_points = interpolation_points.\ |
---|
1059 | get_data_points(absolute=True) |
---|
1060 | |
---|
1061 | interpolated_values = num.zeros(len(interpolation_points), num.float) |
---|
1062 | |
---|
1063 | data = ensure_numeric(data, num.float) |
---|
1064 | polyline_nodes = ensure_numeric(polyline_nodes, num.float) |
---|
1065 | interpolation_points = ensure_numeric(interpolation_points, num.float) |
---|
1066 | gauge_neighbour_id = ensure_numeric(gauge_neighbour_id, num.int) |
---|
1067 | |
---|
1068 | num_nodes = polyline_nodes.shape[0] # Number of nodes in polyline |
---|
1069 | |
---|
1070 | # Input sanity check |
---|
1071 | assert_msg = 'interpolation_points are not given (interpolate.py)' |
---|
1072 | assert interpolation_points is not None, assert_msg |
---|
1073 | |
---|
1074 | assert_msg = 'function value must be specified at every interpolation node' |
---|
1075 | assert data.shape[0] == polyline_nodes.shape[0], assert_msg |
---|
1076 | |
---|
1077 | assert_msg = 'Must define function value at one or more nodes' |
---|
1078 | assert data.shape[0] > 0, assert_msg |
---|
1079 | |
---|
1080 | if num_nodes == 1: |
---|
1081 | assert_msg = 'Polyline contained only one point. I need more. ' |
---|
1082 | assert_msg += str(data) |
---|
1083 | raise Exception, assert_msg |
---|
1084 | elif num_nodes > 1: |
---|
1085 | _interpolate_polyline(data, |
---|
1086 | polyline_nodes, |
---|
1087 | gauge_neighbour_id, |
---|
1088 | interpolation_points, |
---|
1089 | interpolated_values, |
---|
1090 | rtol, |
---|
1091 | atol) |
---|
1092 | |
---|
1093 | |
---|
1094 | return interpolated_values |
---|
1095 | |
---|
1096 | |
---|
1097 | def polylist2points_verts(polylist): |
---|
1098 | """ Convert a list of polygons to discrete points and vertices. |
---|
1099 | """ |
---|
1100 | |
---|
1101 | offset = 0 |
---|
1102 | points = [] |
---|
1103 | vertices = [] |
---|
1104 | for poly in polylist: |
---|
1105 | points.extend(poly) |
---|
1106 | vertices.extend([[i, i+1] for i in range(offset, offset+len(poly)-1)]) |
---|
1107 | offset += len(poly) |
---|
1108 | |
---|
1109 | return points, vertices |
---|
1110 | |
---|
1111 | |
---|
1112 | ################################################################################ |
---|
1113 | # Initialise module |
---|
1114 | ################################################################################ |
---|
1115 | |
---|
1116 | from anuga.utilities import compile |
---|
1117 | if compile.can_use_C_extension('polygon_ext.c'): |
---|
1118 | # Underlying C implementations can be accessed |
---|
1119 | from polygon_ext import _point_on_line |
---|
1120 | from polygon_ext import _separate_points_by_polygon |
---|
1121 | from polygon_ext import _interpolate_polyline |
---|
1122 | from polygon_ext import _polygon_overlap |
---|
1123 | from polygon_ext import _line_intersect |
---|
1124 | from polygon_ext import _is_inside_triangle |
---|
1125 | #from polygon_ext import _intersection |
---|
1126 | |
---|
1127 | else: |
---|
1128 | ERROR_MSG = 'C implementations could not be accessed by %s.\n ' % __file__ |
---|
1129 | ERROR_MSG += 'Make sure compile_all.py has been run as described in ' |
---|
1130 | ERROR_MSG += 'the ANUGA installation guide.' |
---|
1131 | raise Exception(ERROR_MSG) |
---|
1132 | |
---|
1133 | |
---|
1134 | if __name__ == "__main__": |
---|
1135 | pass |
---|