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