1 | //---------------------------------------------------------------------- |
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2 | // File: kd_util.cpp |
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3 | // Programmer: Sunil Arya and David Mount |
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4 | // Description: Common utilities for kd-trees |
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5 | // Last modified: 01/04/05 (Version 1.0) |
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6 | //---------------------------------------------------------------------- |
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7 | // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and |
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8 | // David Mount. All Rights Reserved. |
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9 | // |
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10 | // This software and related documentation is part of the Approximate |
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11 | // Nearest Neighbor Library (ANN). This software is provided under |
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12 | // the provisions of the Lesser GNU Public License (LGPL). See the |
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13 | // file ../ReadMe.txt for further information. |
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14 | // |
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15 | // The University of Maryland (U.M.) and the authors make no |
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16 | // representations about the suitability or fitness of this software for |
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17 | // any purpose. It is provided "as is" without express or implied |
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18 | // warranty. |
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19 | //---------------------------------------------------------------------- |
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20 | // History: |
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21 | // Revision 0.1 03/04/98 |
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22 | // Initial release |
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23 | //---------------------------------------------------------------------- |
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24 | |
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25 | #include "kd_util.h" // kd-utility declarations |
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26 | |
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27 | #include <ANN/ANNperf.h> // performance evaluation |
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28 | |
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29 | //---------------------------------------------------------------------- |
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30 | // The following routines are utility functions for manipulating |
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31 | // points sets, used in determining splitting planes for kd-tree |
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32 | // construction. |
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33 | //---------------------------------------------------------------------- |
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34 | |
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35 | //---------------------------------------------------------------------- |
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36 | // NOTE: Virtually all point indexing is done through an index (i.e. |
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37 | // permutation) array pidx. Consequently, a reference to the d-th |
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38 | // coordinate of the i-th point is pa[pidx[i]][d]. The macro PA(i,d) |
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39 | // is a shorthand for this. |
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40 | //---------------------------------------------------------------------- |
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41 | // standard 2-d indirect indexing |
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42 | #define PA(i,d) (pa[pidx[(i)]][(d)]) |
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43 | // accessing a single point |
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44 | #define PP(i) (pa[pidx[(i)]]) |
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45 | |
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46 | //---------------------------------------------------------------------- |
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47 | // annAspectRatio |
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48 | // Compute the aspect ratio (ratio of longest to shortest side) |
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49 | // of a rectangle. |
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50 | //---------------------------------------------------------------------- |
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51 | |
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52 | double annAspectRatio( |
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53 | int dim, // dimension |
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54 | const ANNorthRect &bnd_box) // bounding cube |
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55 | { |
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56 | ANNcoord length = bnd_box.hi[0] - bnd_box.lo[0]; |
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57 | ANNcoord min_length = length; // min side length |
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58 | ANNcoord max_length = length; // max side length |
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59 | for (int d = 0; d < dim; d++) { |
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60 | length = bnd_box.hi[d] - bnd_box.lo[d]; |
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61 | if (length < min_length) min_length = length; |
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62 | if (length > max_length) max_length = length; |
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63 | } |
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64 | return max_length/min_length; |
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65 | } |
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66 | |
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67 | //---------------------------------------------------------------------- |
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68 | // annEnclRect, annEnclCube |
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69 | // These utilities compute the smallest rectangle and cube enclosing |
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70 | // a set of points, respectively. |
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71 | //---------------------------------------------------------------------- |
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72 | |
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73 | void annEnclRect( |
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74 | ANNpointArray pa, // point array |
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75 | ANNidxArray pidx, // point indices |
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76 | int n, // number of points |
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77 | int dim, // dimension |
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78 | ANNorthRect &bnds) // bounding cube (returned) |
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79 | { |
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80 | for (int d = 0; d < dim; d++) { // find smallest enclosing rectangle |
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81 | ANNcoord lo_bnd = PA(0,d); // lower bound on dimension d |
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82 | ANNcoord hi_bnd = PA(0,d); // upper bound on dimension d |
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83 | for (int i = 0; i < n; i++) { |
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84 | if (PA(i,d) < lo_bnd) lo_bnd = PA(i,d); |
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85 | else if (PA(i,d) > hi_bnd) hi_bnd = PA(i,d); |
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86 | } |
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87 | bnds.lo[d] = lo_bnd; |
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88 | bnds.hi[d] = hi_bnd; |
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89 | } |
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90 | } |
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91 | |
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92 | void annEnclCube( // compute smallest enclosing cube |
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93 | ANNpointArray pa, // point array |
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94 | ANNidxArray pidx, // point indices |
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95 | int n, // number of points |
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96 | int dim, // dimension |
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97 | ANNorthRect &bnds) // bounding cube (returned) |
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98 | { |
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99 | int d; |
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100 | // compute smallest enclosing rect |
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101 | annEnclRect(pa, pidx, n, dim, bnds); |
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102 | |
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103 | ANNcoord max_len = 0; // max length of any side |
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104 | for (d = 0; d < dim; d++) { // determine max side length |
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105 | ANNcoord len = bnds.hi[d] - bnds.lo[d]; |
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106 | if (len > max_len) { // update max_len if longest |
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107 | max_len = len; |
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108 | } |
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109 | } |
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110 | for (d = 0; d < dim; d++) { // grow sides to match max |
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111 | ANNcoord len = bnds.hi[d] - bnds.lo[d]; |
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112 | ANNcoord half_diff = (max_len - len) / 2; |
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113 | bnds.lo[d] -= half_diff; |
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114 | bnds.hi[d] += half_diff; |
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115 | } |
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116 | } |
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117 | |
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118 | //---------------------------------------------------------------------- |
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119 | // annBoxDistance - utility routine which computes distance from point to |
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120 | // box (Note: most distances to boxes are computed using incremental |
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121 | // distance updates, not this function.) |
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122 | //---------------------------------------------------------------------- |
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123 | |
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124 | ANNdist annBoxDistance( // compute distance from point to box |
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125 | const ANNpoint q, // the point |
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126 | const ANNpoint lo, // low point of box |
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127 | const ANNpoint hi, // high point of box |
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128 | int dim) // dimension of space |
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129 | { |
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130 | register ANNdist dist = 0.0; // sum of squared distances |
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131 | register ANNdist t; |
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132 | |
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133 | for (register int d = 0; d < dim; d++) { |
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134 | if (q[d] < lo[d]) { // q is left of box |
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135 | t = ANNdist(lo[d]) - ANNdist(q[d]); |
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136 | dist = ANN_SUM(dist, ANN_POW(t)); |
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137 | } |
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138 | else if (q[d] > hi[d]) { // q is right of box |
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139 | t = ANNdist(q[d]) - ANNdist(hi[d]); |
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140 | dist = ANN_SUM(dist, ANN_POW(t)); |
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141 | } |
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142 | } |
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143 | ANN_FLOP(4*dim) // increment floating op count |
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144 | |
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145 | return dist; |
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146 | } |
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147 | |
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148 | //---------------------------------------------------------------------- |
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149 | // annSpread - find spread along given dimension |
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150 | // annMinMax - find min and max coordinates along given dimension |
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151 | // annMaxSpread - find dimension of max spread |
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152 | //---------------------------------------------------------------------- |
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153 | |
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154 | ANNcoord annSpread( // compute point spread along dimension |
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155 | ANNpointArray pa, // point array |
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156 | ANNidxArray pidx, // point indices |
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157 | int n, // number of points |
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158 | int d) // dimension to check |
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159 | { |
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160 | ANNcoord min = PA(0,d); // compute max and min coords |
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161 | ANNcoord max = PA(0,d); |
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162 | for (int i = 1; i < n; i++) { |
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163 | ANNcoord c = PA(i,d); |
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164 | if (c < min) min = c; |
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165 | else if (c > max) max = c; |
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166 | } |
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167 | return (max - min); // total spread is difference |
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168 | } |
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169 | |
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170 | void annMinMax( // compute min and max coordinates along dim |
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171 | ANNpointArray pa, // point array |
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172 | ANNidxArray pidx, // point indices |
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173 | int n, // number of points |
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174 | int d, // dimension to check |
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175 | ANNcoord &min, // minimum value (returned) |
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176 | ANNcoord &max) // maximum value (returned) |
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177 | { |
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178 | min = PA(0,d); // compute max and min coords |
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179 | max = PA(0,d); |
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180 | for (int i = 1; i < n; i++) { |
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181 | ANNcoord c = PA(i,d); |
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182 | if (c < min) min = c; |
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183 | else if (c > max) max = c; |
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184 | } |
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185 | } |
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186 | |
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187 | int annMaxSpread( // compute dimension of max spread |
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188 | ANNpointArray pa, // point array |
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189 | ANNidxArray pidx, // point indices |
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190 | int n, // number of points |
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191 | int dim) // dimension of space |
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192 | { |
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193 | int max_dim = 0; // dimension of max spread |
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194 | ANNcoord max_spr = 0; // amount of max spread |
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195 | |
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196 | if (n == 0) return max_dim; // no points, who cares? |
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197 | |
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198 | for (int d = 0; d < dim; d++) { // compute spread along each dim |
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199 | ANNcoord spr = annSpread(pa, pidx, n, d); |
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200 | if (spr > max_spr) { // bigger than current max |
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201 | max_spr = spr; |
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202 | max_dim = d; |
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203 | } |
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204 | } |
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205 | return max_dim; |
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206 | } |
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207 | |
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208 | //---------------------------------------------------------------------- |
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209 | // annMedianSplit - split point array about its median |
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210 | // Splits a subarray of points pa[0..n] about an element of given |
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211 | // rank (median: n_lo = n/2) with respect to dimension d. It places |
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212 | // the element of rank n_lo-1 correctly (because our splitting rule |
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213 | // takes the mean of these two). On exit, the array is permuted so |
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214 | // that: |
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215 | // |
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216 | // pa[0..n_lo-2][d] <= pa[n_lo-1][d] <= pa[n_lo][d] <= pa[n_lo+1..n-1][d]. |
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217 | // |
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218 | // The mean of pa[n_lo-1][d] and pa[n_lo][d] is returned as the |
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219 | // splitting value. |
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220 | // |
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221 | // All indexing is done indirectly through the index array pidx. |
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222 | // |
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223 | // This function uses the well known selection algorithm due to |
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224 | // C.A.R. Hoare. |
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225 | //---------------------------------------------------------------------- |
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226 | |
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227 | // swap two points in pa array |
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228 | #define PASWAP(a,b) { int tmp = pidx[a]; pidx[a] = pidx[b]; pidx[b] = tmp; } |
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229 | |
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230 | void annMedianSplit( |
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231 | ANNpointArray pa, // points to split |
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232 | ANNidxArray pidx, // point indices |
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233 | int n, // number of points |
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234 | int d, // dimension along which to split |
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235 | ANNcoord &cv, // cutting value |
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236 | int n_lo) // split into n_lo and n-n_lo |
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237 | { |
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238 | int l = 0; // left end of current subarray |
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239 | int r = n-1; // right end of current subarray |
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240 | while (l < r) { |
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241 | register int i = (r+l)/2; // select middle as pivot |
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242 | register int k; |
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243 | |
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244 | if (PA(i,d) > PA(r,d)) // make sure last > pivot |
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245 | PASWAP(i,r) |
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246 | PASWAP(l,i); // move pivot to first position |
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247 | |
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248 | ANNcoord c = PA(l,d); // pivot value |
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249 | i = l; |
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250 | k = r; |
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251 | for(;;) { // pivot about c |
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252 | while (PA(++i,d) < c) ; |
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253 | while (PA(--k,d) > c) ; |
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254 | if (i < k) PASWAP(i,k) else break; |
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255 | } |
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256 | PASWAP(l,k); // pivot winds up in location k |
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257 | |
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258 | if (k > n_lo) r = k-1; // recurse on proper subarray |
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259 | else if (k < n_lo) l = k+1; |
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260 | else break; // got the median exactly |
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261 | } |
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262 | if (n_lo > 0) { // search for next smaller item |
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263 | ANNcoord c = PA(0,d); // candidate for max |
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264 | int k = 0; // candidate's index |
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265 | for (int i = 1; i < n_lo; i++) { |
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266 | if (PA(i,d) > c) { |
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267 | c = PA(i,d); |
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268 | k = i; |
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269 | } |
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270 | } |
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271 | PASWAP(n_lo-1, k); // max among pa[0..n_lo-1] to pa[n_lo-1] |
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272 | } |
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273 | // cut value is midpoint value |
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274 | cv = (PA(n_lo-1,d) + PA(n_lo,d))/2.0; |
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275 | } |
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276 | |
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277 | //---------------------------------------------------------------------- |
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278 | // annPlaneSplit - split point array about a cutting plane |
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279 | // Split the points in an array about a given plane along a |
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280 | // given cutting dimension. On exit, br1 and br2 are set so |
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281 | // that: |
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282 | // |
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283 | // pa[ 0 ..br1-1] < cv |
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284 | // pa[br1..br2-1] == cv |
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285 | // pa[br2.. n -1] > cv |
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286 | // |
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287 | // All indexing is done indirectly through the index array pidx. |
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288 | // |
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289 | //---------------------------------------------------------------------- |
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290 | |
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291 | void annPlaneSplit( // split points by a plane |
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292 | ANNpointArray pa, // points to split |
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293 | ANNidxArray pidx, // point indices |
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294 | int n, // number of points |
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295 | int d, // dimension along which to split |
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296 | ANNcoord cv, // cutting value |
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297 | int &br1, // first break (values < cv) |
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298 | int &br2) // second break (values == cv) |
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299 | { |
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300 | int l = 0; |
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301 | int r = n-1; |
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302 | for(;;) { // partition pa[0..n-1] about cv |
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303 | while (l < n && PA(l,d) < cv) l++; |
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304 | while (r >= 0 && PA(r,d) >= cv) r--; |
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305 | if (l > r) break; |
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306 | PASWAP(l,r); |
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307 | l++; r--; |
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308 | } |
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309 | br1 = l; // now: pa[0..br1-1] < cv <= pa[br1..n-1] |
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310 | r = n-1; |
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311 | for(;;) { // partition pa[br1..n-1] about cv |
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312 | while (l < n && PA(l,d) <= cv) l++; |
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313 | while (r >= br1 && PA(r,d) > cv) r--; |
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314 | if (l > r) break; |
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315 | PASWAP(l,r); |
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316 | l++; r--; |
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317 | } |
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318 | br2 = l; // now: pa[br1..br2-1] == cv < pa[br2..n-1] |
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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 | // annBoxSplit - split point array about a orthogonal rectangle |
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324 | // Split the points in an array about a given orthogonal |
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325 | // rectangle. On exit, n_in is set to the number of points |
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326 | // that are inside (or on the boundary of) the rectangle. |
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327 | // |
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328 | // All indexing is done indirectly through the index array pidx. |
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329 | // |
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330 | //---------------------------------------------------------------------- |
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331 | |
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332 | void annBoxSplit( // split points by a box |
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333 | ANNpointArray pa, // points to split |
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334 | ANNidxArray pidx, // point indices |
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335 | int n, // number of points |
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336 | int dim, // dimension of space |
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337 | ANNorthRect &box, // the box |
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338 | int &n_in) // number of points inside (returned) |
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339 | { |
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340 | int l = 0; |
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341 | int r = n-1; |
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342 | for(;;) { // partition pa[0..n-1] about box |
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343 | while (l < n && box.inside(dim, PP(l))) l++; |
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344 | while (r >= 0 && !box.inside(dim, PP(r))) r--; |
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345 | if (l > r) break; |
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346 | PASWAP(l,r); |
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347 | l++; r--; |
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348 | } |
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349 | n_in = l; // now: pa[0..n_in-1] inside and rest outside |
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350 | } |
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351 | |
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352 | //---------------------------------------------------------------------- |
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353 | // annSplitBalance - compute balance factor for a given plane split |
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354 | // Balance factor is defined as the number of points lying |
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355 | // below the splitting value minus n/2 (median). Thus, a |
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356 | // median split has balance 0, left of this is negative and |
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357 | // right of this is positive. (The points are unchanged.) |
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358 | //---------------------------------------------------------------------- |
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359 | |
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360 | int annSplitBalance( // determine balance factor of a split |
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361 | ANNpointArray pa, // points to split |
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362 | ANNidxArray pidx, // point indices |
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363 | int n, // number of points |
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364 | int d, // dimension along which to split |
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365 | ANNcoord cv) // cutting value |
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366 | { |
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367 | int n_lo = 0; |
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368 | for(int i = 0; i < n; i++) { // count number less than cv |
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369 | if (PA(i,d) < cv) n_lo++; |
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370 | } |
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371 | return n_lo - n/2; |
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372 | } |
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373 | |
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374 | //---------------------------------------------------------------------- |
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375 | // annBox2Bnds - convert bounding box to list of bounds |
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376 | // Given two boxes, an inner box enclosed within a bounding |
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377 | // box, this routine determines all the sides for which the |
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378 | // inner box is strictly contained with the bounding box, |
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379 | // and adds an appropriate entry to a list of bounds. Then |
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380 | // we allocate storage for the final list of bounds, and return |
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381 | // the resulting list and its size. |
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382 | //---------------------------------------------------------------------- |
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383 | |
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384 | void annBox2Bnds( // convert inner box to bounds |
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385 | const ANNorthRect &inner_box, // inner box |
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386 | const ANNorthRect &bnd_box, // enclosing box |
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387 | int dim, // dimension of space |
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388 | int &n_bnds, // number of bounds (returned) |
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389 | ANNorthHSArray &bnds) // bounds array (returned) |
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390 | { |
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391 | int i; |
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392 | n_bnds = 0; // count number of bounds |
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393 | for (i = 0; i < dim; i++) { |
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394 | if (inner_box.lo[i] > bnd_box.lo[i]) // low bound is inside |
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395 | n_bnds++; |
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396 | if (inner_box.hi[i] < bnd_box.hi[i]) // high bound is inside |
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397 | n_bnds++; |
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398 | } |
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399 | |
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400 | bnds = new ANNorthHalfSpace[n_bnds]; // allocate appropriate size |
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401 | |
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402 | int j = 0; |
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403 | for (i = 0; i < dim; i++) { // fill the array |
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404 | if (inner_box.lo[i] > bnd_box.lo[i]) { |
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405 | bnds[j].cd = i; |
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406 | bnds[j].cv = inner_box.lo[i]; |
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407 | bnds[j].sd = +1; |
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408 | j++; |
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409 | } |
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410 | if (inner_box.hi[i] < bnd_box.hi[i]) { |
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411 | bnds[j].cd = i; |
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412 | bnds[j].cv = inner_box.hi[i]; |
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413 | bnds[j].sd = -1; |
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414 | j++; |
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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 | // annBnds2Box - convert list of bounds to bounding box |
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421 | // Given an enclosing box and a list of bounds, this routine |
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422 | // computes the corresponding inner box. It is assumed that |
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423 | // the box points have been allocated already. |
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424 | //---------------------------------------------------------------------- |
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425 | |
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426 | void annBnds2Box( |
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427 | const ANNorthRect &bnd_box, // enclosing box |
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428 | int dim, // dimension of space |
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429 | int n_bnds, // number of bounds |
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430 | ANNorthHSArray bnds, // bounds array |
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431 | ANNorthRect &inner_box) // inner box (returned) |
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432 | { |
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433 | annAssignRect(dim, inner_box, bnd_box); // copy bounding box to inner |
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434 | |
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435 | for (int i = 0; i < n_bnds; i++) { |
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436 | bnds[i].project(inner_box.lo); // project each endpoint |
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437 | bnds[i].project(inner_box.hi); |
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438 | } |
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439 | } |
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