1 | // Python - C extension for polygon module. |
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2 | // |
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3 | // To compile (Python2.3): |
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4 | // gcc -c polygon_ext.c -I/usr/include/python2.3 -o polygon_ext.o -Wall -O |
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5 | // gcc -shared polygon_ext.o -o polygon_ext.so |
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6 | // |
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7 | // See the module polygon.py |
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8 | // |
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9 | // |
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10 | // Ole Nielsen, GA 2004 |
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11 | // |
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12 | // NOTE: We use long* instead of int* for Numeric arrays as this will work both |
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13 | // for 64 as well as 32 bit systems |
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14 | |
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15 | |
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16 | #include "Python.h" |
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17 | #include "Numeric/arrayobject.h" |
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18 | #include "math.h" |
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19 | |
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20 | double dist(double x, |
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21 | double y) { |
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22 | |
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23 | return sqrt(x*x + y*y); |
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24 | } |
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25 | |
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26 | |
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27 | int __point_on_line(double x, double y, |
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28 | double x0, double y0, |
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29 | double x1, double y1, |
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30 | double rtol, |
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31 | double atol) { |
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32 | /*Determine whether a point is on a line segment |
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33 | |
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34 | Input: x, y, x0, x0, x1, y1: where |
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35 | point is given by x, y |
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36 | line is given by (x0, y0) and (x1, y1) |
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37 | |
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38 | */ |
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39 | |
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40 | double a0, a1, a_normal0, a_normal1, b0, b1, len_a, len_b; |
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41 | double nominator, denominator; |
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42 | int is_parallel; |
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43 | |
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44 | a0 = x - x0; |
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45 | a1 = y - y0; |
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46 | |
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47 | a_normal0 = a1; |
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48 | a_normal1 = -a0; |
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49 | |
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50 | b0 = x1 - x0; |
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51 | b1 = y1 - y0; |
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52 | |
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53 | nominator = fabs(a_normal0*b0 + a_normal1*b1); |
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54 | denominator = b0*b0 + b1*b1; |
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55 | |
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56 | // Determine if line is parallel to point vector up to a tolerance |
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57 | is_parallel = 0; |
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58 | if (denominator == 0.0) { |
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59 | // Use absolute tolerance |
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60 | if (nominator <= atol) { |
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61 | is_parallel = 1; |
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62 | } |
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63 | } else { |
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64 | // Denominator is positive - use relative tolerance |
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65 | if (nominator/denominator <= rtol) { |
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66 | is_parallel = 1; |
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67 | } |
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68 | } |
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69 | |
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70 | if (is_parallel) { |
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71 | // Point is somewhere on the infinite extension of the line |
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72 | // subject to specified absolute tolerance |
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73 | |
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74 | len_a = dist(a0, a1); //sqrt(a0*a0 + a1*a1); |
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75 | len_b = dist(b0, b1); //sqrt(b0*b0 + b1*b1); |
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76 | |
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77 | if (a0*b0 + a1*b1 >= 0 && len_a <= len_b) { |
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78 | return 1; |
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79 | } else { |
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80 | return 0; |
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81 | } |
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82 | } else { |
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83 | return 0; |
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84 | } |
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85 | } |
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86 | |
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87 | |
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88 | |
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89 | /* |
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90 | WORK IN PROGRESS TO OPTIMISE INTERSECTION |
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91 | int __intersection(double x0, double y0, |
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92 | double x1, double y1) { |
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93 | |
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94 | |
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95 | x0 = line0[0,0]; y0 = line0[0,1] |
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96 | x1 = line0[1,0]; y1 = line0[1,1] |
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97 | |
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98 | x2 = line1[0,0]; y2 = line1[0,1] |
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99 | x3 = line1[1,0]; y3 = line1[1,1] |
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100 | |
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101 | denom = (y3-y2)*(x1-x0) - (x3-x2)*(y1-y0) |
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102 | u0 = (x3-x2)*(y0-y2) - (y3-y2)*(x0-x2) |
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103 | u1 = (x2-x0)*(y1-y0) - (y2-y0)*(x1-x0) |
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104 | |
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105 | if allclose(denom, 0.0): |
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106 | # Lines are parallel - check if they coincide on a shared a segment |
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107 | |
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108 | if allclose( [u0, u1], 0.0 ): |
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109 | # We now know that the lines if continued coincide |
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110 | # The remaining check will establish if the finite lines share a segment |
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111 | |
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112 | line0_starts_on_line1 = line0_ends_on_line1 =\ |
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113 | line1_starts_on_line0 = line1_ends_on_line0 = False |
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114 | |
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115 | if point_on_line([x0, y0], line1): |
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116 | line0_starts_on_line1 = True |
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117 | |
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118 | if point_on_line([x1, y1], line1): |
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119 | line0_ends_on_line1 = True |
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120 | |
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121 | if point_on_line([x2, y2], line0): |
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122 | line1_starts_on_line0 = True |
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123 | |
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124 | if point_on_line([x3, y3], line0): |
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125 | line1_ends_on_line0 = True |
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126 | |
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127 | if not(line0_starts_on_line1 or line0_ends_on_line1\ |
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128 | or line1_starts_on_line0 or line1_ends_on_line0): |
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129 | # Lines are parallel and would coincide if extended, but not as they are. |
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130 | return 3, None |
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131 | |
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132 | |
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133 | # One line fully included in the other. Use direction of included line |
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134 | if line0_starts_on_line1 and line0_ends_on_line1: |
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135 | # Shared segment is line0 fully included in line1 |
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136 | segment = array([[x0, y0], [x1, y1]]) |
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137 | |
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138 | if line1_starts_on_line0 and line1_ends_on_line0: |
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139 | # Shared segment is line1 fully included in line0 |
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140 | segment = array([[x2, y2], [x3, y3]]) |
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141 | |
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142 | |
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143 | # Overlap with lines are oriented the same way |
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144 | if line0_starts_on_line1 and line1_ends_on_line0: |
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145 | # Shared segment from line0 start to line 1 end |
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146 | segment = array([[x0, y0], [x3, y3]]) |
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147 | |
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148 | if line1_starts_on_line0 and line0_ends_on_line1: |
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149 | # Shared segment from line1 start to line 0 end |
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150 | segment = array([[x2, y2], [x1, y1]]) |
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151 | |
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152 | |
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153 | # Overlap in opposite directions - use direction of line0 |
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154 | if line0_starts_on_line1 and line1_starts_on_line0: |
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155 | # Shared segment from line0 start to line 1 end |
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156 | segment = array([[x0, y0], [x2, y2]]) |
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157 | |
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158 | if line0_ends_on_line1 and line1_ends_on_line0: |
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159 | # Shared segment from line0 start to line 1 end |
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160 | segment = array([[x3, y3], [x1, y1]]) |
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161 | |
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162 | |
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163 | return 2, segment |
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164 | else: |
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165 | # Lines are parallel but they do not coincide |
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166 | return 4, None #FIXME (Ole): Add distance here instead of None |
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167 | |
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168 | else: |
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169 | # Lines are not parallel or coinciding |
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170 | u0 = u0/denom |
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171 | u1 = u1/denom |
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172 | |
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173 | x = x0 + u0*(x1-x0) |
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174 | y = y0 + u0*(y1-y0) |
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175 | |
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176 | # Sanity check - can be removed to speed up if needed |
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177 | assert allclose(x, x2 + u1*(x3-x2)) |
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178 | assert allclose(y, y2 + u1*(y3-y2)) |
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179 | |
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180 | # Check if point found lies within given line segments |
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181 | if 0.0 <= u0 <= 1.0 and 0.0 <= u1 <= 1.0: |
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182 | # We have intersection |
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183 | |
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184 | return 1, array([x, y]) |
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185 | else: |
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186 | # No intersection |
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187 | return 0, None |
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188 | |
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189 | |
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190 | } |
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191 | */ |
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192 | |
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193 | |
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194 | |
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195 | int __interpolate_polyline(int number_of_nodes, |
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196 | int number_of_points, |
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197 | double* data, |
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198 | double* polyline_nodes, |
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199 | long* gauge_neighbour_id, |
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200 | double* interpolation_points, |
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201 | double* interpolated_values, |
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202 | double rtol, |
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203 | double atol) { |
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204 | |
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205 | int j, i, neighbour_id; |
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206 | double x0, y0, x1, y1, x, y; |
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207 | double segment_len, segment_delta, slope, alpha; |
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208 | |
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209 | for (j=0; j<number_of_nodes; j++) { |
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210 | |
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211 | neighbour_id = gauge_neighbour_id[j]; |
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212 | |
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213 | // FIXME(Ole): I am convinced that gauge_neighbour_id can be discarded, but need to check with John J. |
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214 | // Keep it for now (17 Jan 2009) |
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215 | // When gone, we can simply interpolate between neighbouring nodes, i.e. neighbour_id = j+1. |
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216 | // and the test below becomes something like: if j < number_of_nodes... |
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217 | |
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218 | if (neighbour_id >= 0) { |
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219 | x0 = polyline_nodes[2*j]; |
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220 | y0 = polyline_nodes[2*j+1]; |
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221 | |
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222 | x1 = polyline_nodes[2*neighbour_id]; |
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223 | y1 = polyline_nodes[2*neighbour_id+1]; |
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224 | |
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225 | |
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226 | segment_len = dist(x1-x0, y1-y0); |
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227 | segment_delta = data[neighbour_id] - data[j]; |
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228 | slope = segment_delta/segment_len; |
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229 | |
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230 | for (i=0; i<number_of_points; i++) { |
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231 | x = interpolation_points[2*i]; |
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232 | y = interpolation_points[2*i+1]; |
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233 | |
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234 | if (__point_on_line(x, y, x0, y0, x1, y1, rtol, atol)) { |
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235 | alpha = dist(x-x0, y-y0); |
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236 | interpolated_values[i] = slope*alpha + data[j]; |
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237 | } |
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238 | } |
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239 | } |
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240 | } |
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241 | |
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242 | return 0; |
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243 | } |
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244 | |
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245 | |
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246 | int __separate_points_by_polygon(int M, // Number of points |
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247 | int N, // Number of polygon vertices |
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248 | double* points, |
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249 | double* polygon, |
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250 | long* indices, // M-Array for storage indices |
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251 | int closed, |
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252 | int verbose) { |
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253 | |
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254 | double minpx, maxpx, minpy, maxpy, x, y, px_i, py_i, px_j, py_j, rtol=0.0, atol=0.0; |
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255 | int i, j, k, outside_index, inside_index, inside; |
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256 | |
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257 | //Find min and max of poly used for optimisation when points |
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258 | //are far away from polygon |
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259 | |
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260 | //FIXME(Ole): Pass in rtol and atol from Python |
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261 | |
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262 | minpx = polygon[0]; maxpx = minpx; |
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263 | minpy = polygon[1]; maxpy = minpy; |
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264 | |
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265 | for (i=0; i<N; i++) { |
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266 | px_i = polygon[2*i]; |
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267 | py_i = polygon[2*i + 1]; |
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268 | |
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269 | if (px_i < minpx) minpx = px_i; |
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270 | if (px_i > maxpx) maxpx = px_i; |
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271 | if (py_i < minpy) minpy = py_i; |
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272 | if (py_i > maxpy) maxpy = py_i; |
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273 | } |
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274 | |
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275 | //Begin main loop (for each point) |
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276 | inside_index = 0; //Keep track of points inside |
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277 | outside_index = M-1; //Keep track of points outside (starting from end) |
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278 | if (verbose){ |
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279 | printf("Separating %d points\n", M); |
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280 | } |
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281 | for (k=0; k<M; k++) { |
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282 | if (verbose){ |
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283 | if (k %((M+10)/10)==0) printf("Doing %d of %d\n", k, M); |
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284 | } |
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285 | |
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286 | x = points[2*k]; |
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287 | y = points[2*k + 1]; |
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288 | |
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289 | inside = 0; |
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290 | |
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291 | //Optimisation |
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292 | if ((x > maxpx) || (x < minpx) || (y > maxpy) || (y < minpy)) { |
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293 | //Nothing |
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294 | } else { |
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295 | //Check polygon |
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296 | for (i=0; i<N; i++) { |
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297 | //printf("k,i=%d,%d\n", k, i); |
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298 | j = (i+1)%N; |
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299 | |
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300 | px_i = polygon[2*i]; |
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301 | py_i = polygon[2*i+1]; |
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302 | px_j = polygon[2*j]; |
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303 | py_j = polygon[2*j+1]; |
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304 | |
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305 | //Check for case where point is contained in line segment |
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306 | if (__point_on_line(x, y, px_i, py_i, px_j, py_j, rtol, atol)) { |
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307 | if (closed == 1) { |
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308 | inside = 1; |
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309 | } else { |
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310 | inside = 0; |
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311 | } |
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312 | break; |
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313 | } else { |
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314 | //Check if truly inside polygon |
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315 | if ( ((py_i < y) && (py_j >= y)) || |
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316 | ((py_j < y) && (py_i >= y)) ) { |
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317 | if (px_i + (y-py_i)/(py_j-py_i)*(px_j-px_i) < x) |
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318 | inside = 1-inside; |
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319 | } |
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320 | } |
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321 | } |
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322 | } |
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323 | if (inside == 1) { |
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324 | indices[inside_index] = k; |
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325 | inside_index += 1; |
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326 | } else { |
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327 | indices[outside_index] = k; |
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328 | outside_index -= 1; |
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329 | } |
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330 | } // End k |
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331 | |
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332 | return inside_index; |
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333 | } |
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334 | |
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335 | |
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336 | |
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337 | // Gateways to Python |
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338 | PyObject *_point_on_line(PyObject *self, PyObject *args) { |
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339 | // |
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340 | // point_on_line(x, y, x0, y0, x1, y1) |
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341 | // |
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342 | |
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343 | double x, y, x0, y0, x1, y1, rtol, atol; |
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344 | int res; |
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345 | PyObject *result; |
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346 | |
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347 | // Convert Python arguments to C |
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348 | if (!PyArg_ParseTuple(args, "dddddddd", &x, &y, &x0, &y0, &x1, &y1, &rtol, &atol)) { |
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349 | PyErr_SetString(PyExc_RuntimeError, |
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350 | "point_on_line could not parse input"); |
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351 | return NULL; |
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352 | } |
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353 | |
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354 | |
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355 | // Call underlying routine |
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356 | res = __point_on_line(x, y, x0, y0, x1, y1, rtol, atol); |
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357 | |
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358 | // Return values a and b |
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359 | result = Py_BuildValue("i", res); |
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360 | return result; |
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361 | } |
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362 | |
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363 | |
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364 | |
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365 | // Gateways to Python |
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366 | PyObject *_interpolate_polyline(PyObject *self, PyObject *args) { |
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367 | // |
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368 | // _interpolate_polyline(data, polyline_nodes, gauge_neighbour_id, interpolation_points |
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369 | // interpolated_values): |
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370 | // |
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371 | |
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372 | |
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373 | PyArrayObject |
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374 | *data, |
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375 | *polyline_nodes, |
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376 | *gauge_neighbour_id, |
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377 | *interpolation_points, |
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378 | *interpolated_values; |
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379 | |
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380 | double rtol, atol; |
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381 | int number_of_nodes, number_of_points, res; |
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382 | |
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383 | // Convert Python arguments to C |
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384 | if (!PyArg_ParseTuple(args, "OOOOOdd", |
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385 | &data, |
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386 | &polyline_nodes, |
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387 | &gauge_neighbour_id, |
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388 | &interpolation_points, |
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389 | &interpolated_values, |
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390 | &rtol, |
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391 | &atol)) { |
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392 | |
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393 | PyErr_SetString(PyExc_RuntimeError, |
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394 | "_interpolate_polyline could not parse input"); |
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395 | return NULL; |
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396 | } |
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397 | |
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398 | number_of_nodes = polyline_nodes -> dimensions[0]; // Number of nodes in polyline |
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399 | number_of_points = interpolation_points -> dimensions[0]; //Number of points |
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400 | |
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401 | |
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402 | // Call underlying routine |
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403 | res = __interpolate_polyline(number_of_nodes, |
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404 | number_of_points, |
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405 | (double*) data -> data, |
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406 | (double*) polyline_nodes -> data, |
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407 | (long*) gauge_neighbour_id -> data, |
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408 | (double*) interpolation_points -> data, |
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409 | (double*) interpolated_values -> data, |
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410 | rtol, |
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411 | atol); |
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412 | |
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413 | // Return |
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414 | return Py_BuildValue(""); |
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415 | } |
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416 | |
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417 | |
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418 | |
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419 | /* |
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420 | PyObject *_intersection(PyObject *self, PyObject *args) { |
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421 | // |
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422 | // intersection(x0, y0, x1, y1) |
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423 | // |
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424 | |
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425 | double x, y, x0, y0, x1, y1; |
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426 | int res; |
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427 | PyObject *result; |
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428 | |
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429 | // Convert Python arguments to C |
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430 | if (!PyArg_ParseTuple(args, "dddddd", &x, &y, &x0, &y0, &x1, &y1)) { |
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431 | PyErr_SetString(PyExc_RuntimeError, |
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432 | "point_on_line could not parse input"); |
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433 | return NULL; |
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434 | } |
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435 | |
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436 | |
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437 | // Call underlying routine |
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438 | res = __intersection(x, y, x0, y0, x1, y1); |
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439 | |
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440 | // Return values a and b |
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441 | result = Py_BuildValue("i", res); |
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442 | return result; |
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443 | } |
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444 | */ |
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445 | |
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446 | |
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447 | PyObject *_separate_points_by_polygon(PyObject *self, PyObject *args) { |
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448 | //def separate_points_by_polygon(points, polygon, closed, verbose, one_point): |
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449 | // """Determine whether points are inside or outside a polygon |
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450 | // |
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451 | // Input: |
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452 | // point - Tuple of (x, y) coordinates, or list of tuples |
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453 | // polygon - list of vertices of polygon |
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454 | // closed - (optional) determine whether points on boundary should be |
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455 | // regarded as belonging to the polygon (closed = True) |
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456 | // or not (closed = False) |
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457 | |
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458 | // |
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459 | // Output: |
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460 | // indices: array of same length as points with indices of points falling |
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461 | // inside the polygon listed from the beginning and indices of points |
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462 | // falling outside listed from the end. |
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463 | // |
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464 | // count: count of points falling inside the polygon |
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465 | // |
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466 | // The indices of points inside are obtained as indices[:count] |
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467 | // The indices of points outside are obtained as indices[count:] |
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468 | // |
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469 | // Examples: |
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470 | // separate_polygon( [[0.5, 0.5], [1, -0.5], [0.3, 0.2]] ) |
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471 | // will return the indices [0, 2, 1] as only the first and the last point |
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472 | // is inside the unit square |
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473 | // |
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474 | // Remarks: |
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475 | // The vertices may be listed clockwise or counterclockwise and |
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476 | // the first point may optionally be repeated. |
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477 | // Polygons do not need to be convex. |
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478 | // Polygons can have holes in them and points inside a hole is |
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479 | // regarded as being outside the polygon. |
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480 | // |
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481 | // |
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482 | // Algorithm is based on work by Darel Finley, |
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483 | // http://www.alienryderflex.com/polygon/ |
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484 | // |
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485 | // |
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486 | |
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487 | PyArrayObject |
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488 | *points, |
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489 | *polygon, |
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490 | *indices; |
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491 | |
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492 | int closed, verbose; //Flags |
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493 | int count, M, N; |
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494 | |
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495 | // Convert Python arguments to C |
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496 | if (!PyArg_ParseTuple(args, "OOOii", |
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497 | &points, |
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498 | &polygon, |
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499 | &indices, |
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500 | &closed, |
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501 | &verbose)) { |
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502 | |
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503 | |
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504 | PyErr_SetString(PyExc_RuntimeError, |
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505 | "separate_points_by_polygon could not parse input"); |
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506 | return NULL; |
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507 | } |
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508 | |
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509 | M = points -> dimensions[0]; //Number of points |
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510 | N = polygon -> dimensions[0]; //Number of vertices in polygon |
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511 | |
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512 | //FIXME (Ole): This isn't send to Python's sys.stdout |
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513 | if (verbose) printf("Got %d points and %d polygon vertices\n", M, N); |
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514 | |
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515 | //Call underlying routine |
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516 | count = __separate_points_by_polygon(M, N, |
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517 | (double*) points -> data, |
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518 | (double*) polygon -> data, |
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519 | (long*) indices -> data, |
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520 | closed, verbose); |
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521 | |
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522 | //NOTE: return number of points inside.. |
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523 | return Py_BuildValue("i", count); |
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524 | } |
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525 | |
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526 | |
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527 | |
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528 | // Method table for python module |
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529 | static struct PyMethodDef MethodTable[] = { |
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530 | /* The cast of the function is necessary since PyCFunction values |
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531 | * only take two PyObject* parameters, and rotate() takes |
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532 | * three. |
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533 | */ |
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534 | |
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535 | {"_point_on_line", _point_on_line, METH_VARARGS, "Print out"}, |
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536 | //{"_intersection", _intersection, METH_VARARGS, "Print out"}, |
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537 | {"_separate_points_by_polygon", _separate_points_by_polygon, |
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538 | METH_VARARGS, "Print out"}, |
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539 | {"_interpolate_polyline", _interpolate_polyline, |
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540 | METH_VARARGS, "Print out"}, |
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541 | {NULL, NULL, 0, NULL} /* sentinel */ |
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542 | }; |
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543 | |
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544 | |
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545 | |
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546 | // Module initialisation |
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547 | void initpolygon_ext(void){ |
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548 | Py_InitModule("polygon_ext", MethodTable); |
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549 | |
---|
550 | import_array(); //Necessary for handling of NumPY structures |
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551 | } |
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552 | |
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553 | |
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554 | |
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