Mercurial > gemma
annotate pkg/mesh/polygon.go @ 5477:a3d46cee9f69
merge
author | Thomas Junk <thomas.junk@intevation.de> |
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date | Tue, 17 Aug 2021 16:52:15 +0200 |
parents | 866eae1bd888 |
children | 5f47eeea988d |
rev | line source |
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1 // This is Free Software under GNU Affero General Public License v >= 3.0 |
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2 // without warranty, see README.md and license for details. |
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3 // |
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4 // SPDX-License-Identifier: AGPL-3.0-or-later |
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5 // License-Filename: LICENSES/AGPL-3.0.txt |
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6 // |
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7 // Copyright (C) 2018 by via donau |
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8 // – Österreichische Wasserstraßen-Gesellschaft mbH |
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9 // Software engineering by Intevation GmbH |
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10 // |
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11 // Author(s): |
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12 // * Sascha L. Teichmann <sascha.teichmann@intevation.de> |
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13 |
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14 package mesh |
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15 |
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16 import ( |
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17 "bytes" |
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18 "encoding/binary" |
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19 "fmt" |
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20 "log" |
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21 "math" |
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22 |
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23 "github.com/tidwall/rtree" |
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24 |
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25 "gemma.intevation.de/gemma/pkg/wkb" |
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26 ) |
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27 |
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28 type ( |
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29 ring []float64 |
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30 |
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31 Polygon struct { |
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32 rings []ring |
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33 indices []*rtree.RTree |
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34 } |
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35 |
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36 IntersectionType byte |
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37 |
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38 lineSegment []float64 |
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39 ) |
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40 |
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41 const ( |
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42 IntersectionInside IntersectionType = iota |
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43 IntersectionOutSide |
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44 IntersectionOverlaps |
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45 ) |
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46 |
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47 func (ls lineSegment) Rect() ([2]float64, [2]float64) { |
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48 |
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49 var min, max [2]float64 |
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50 |
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51 if ls[0] < ls[2] { |
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52 min[0] = ls[0] |
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53 max[0] = ls[2] |
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54 } else { |
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55 min[0] = ls[2] |
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56 max[0] = ls[0] |
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57 } |
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58 |
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59 if ls[1] < ls[3] { |
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60 min[1] = ls[1] |
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61 max[1] = ls[3] |
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62 } else { |
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63 min[1] = ls[3] |
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64 max[1] = ls[1] |
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65 } |
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66 |
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67 return min, max |
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68 } |
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69 |
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70 func (p *Polygon) Indexify() { |
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71 indices := make([]*rtree.RTree, len(p.rings)) |
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72 |
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73 for i := range indices { |
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74 index := new(rtree.RTree) |
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75 indices[i] = index |
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76 |
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77 rng := p.rings[i] |
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78 |
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79 for i := 0; i < len(rng); i += 2 { |
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80 var ls lineSegment |
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81 if i+4 <= len(rng) { |
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82 ls = lineSegment(rng[i : i+4]) |
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83 } else { |
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84 ls = []float64{rng[i], rng[i+1], rng[0], rng[1]} |
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85 } |
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86 min, max := ls.Rect() |
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87 index.Insert(min, max, ls) |
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88 } |
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89 } |
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90 |
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91 p.indices = indices |
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92 } |
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93 |
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94 func (ls lineSegment) intersects(a Box2D) bool { |
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95 p1x := ls[0] |
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96 p1y := ls[1] |
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97 p2x := ls[2] |
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98 p2y := ls[3] |
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99 |
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100 left := a.X1 |
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101 right := a.X2 |
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102 top := a.Y1 |
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103 bottom := a.Y2 |
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104 |
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105 // The direction of the ray |
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106 dx := p2x - p1x |
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107 dy := p2y - p1y |
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108 |
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109 min, max := 0.0, 1.0 |
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110 |
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111 var t0, t1 float64 |
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112 |
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113 // Left and right sides. |
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114 // - If the line is parallel to the y axis. |
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115 if dx == 0 { |
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116 if p1x < left || p1x > right { |
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117 return false |
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118 } |
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119 } else { |
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120 // - Make sure t0 holds the smaller value by checking the direction of the line. |
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121 if dx > 0 { |
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122 t0 = (left - p1x) / dx |
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123 t1 = (right - p1x) / dx |
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124 } else { |
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125 t1 = (left - p1x) / dx |
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126 t0 = (right - p1x) / dx |
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127 } |
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128 |
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129 if t0 > min { |
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130 min = t0 |
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131 } |
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132 if t1 < max { |
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133 max = t1 |
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134 } |
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135 if min > max || max < 0 { |
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136 return false |
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137 } |
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138 } |
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139 |
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140 // The top and bottom side. |
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141 // - If the line is parallel to the x axis. |
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142 if dy == 0 { |
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143 if p1y < top || p1y > bottom { |
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144 return false |
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145 } |
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146 } else { |
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147 // - Make sure t0 holds the smaller value by checking the direction of the line. |
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148 if dy > 0 { |
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149 t0 = (top - p1y) / dy |
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150 t1 = (bottom - p1y) / dy |
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151 } else { |
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152 t1 = (top - p1y) / dy |
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153 t0 = (bottom - p1y) / dy |
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154 } |
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155 |
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156 if t0 > min { |
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157 min = t0 |
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158 } |
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159 if t1 < max { |
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160 max = t1 |
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161 } |
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162 if min > max || max < 0 { |
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163 return false |
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164 } |
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165 } |
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166 |
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167 // The point of intersection |
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168 // ix = p1x + dx*min |
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169 // iy = p1y + dy*min |
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170 return true |
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171 } |
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172 |
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173 func (ls lineSegment) intersectsLineSegment(o lineSegment) bool { |
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174 |
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175 p0 := ls[:2] |
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176 p1 := ls[2:4] |
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177 p2 := o[:2] |
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178 p3 := o[2:4] |
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179 |
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180 s10x := p1[0] - p0[0] |
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181 s10y := p1[1] - p0[1] |
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182 s32x := p3[0] - p2[0] |
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183 s32y := p3[1] - p2[1] |
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184 |
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185 den := s10x*s32y - s32x*s10y |
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186 |
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187 if den == 0 { |
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188 return false |
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189 } |
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190 |
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191 denPos := den > 0 |
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192 |
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193 s02x := p0[0] - p2[0] |
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194 s02y := p0[1] - p2[1] |
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195 |
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196 sNum := s10x*s02y - s10y*s02x |
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197 if sNum < 0 == denPos { |
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198 return false |
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199 } |
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200 |
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201 tNum := s32x*s02y - s32y*s02x |
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202 if tNum < 0 == denPos { |
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203 return false |
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204 } |
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205 |
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206 if sNum > den == denPos || tNum > den == denPos { |
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207 return false |
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208 } |
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209 |
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210 // t := tNum / den |
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211 // intersection at( p0[0] + (t * s10x), p0[1] + (t * s10y) ) |
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212 return true |
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213 } |
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214 |
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215 func (p *Polygon) IntersectionBox2D(box Box2D) IntersectionType { |
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216 |
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217 if len(p.rings) == 0 { |
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218 return IntersectionOutSide |
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219 } |
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220 |
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221 min, max := box.Rect() |
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222 |
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223 for _, index := range p.indices { |
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224 var intersects bool |
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225 index.Search(min, max, func(_, _ [2]float64, item interface{}) bool { |
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226 if item.(lineSegment).intersects(box) { |
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227 intersects = true |
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228 return false |
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229 } |
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230 return true |
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231 }) |
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232 if intersects { |
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233 return IntersectionOverlaps |
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234 } |
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235 } |
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236 |
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237 // No intersection -> check inside or outside |
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238 // if an abritrary point is inside or not. |
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239 |
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240 // Check holes first: inside a hole means outside. |
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241 if len(p.rings) > 1 { |
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242 for _, hole := range p.rings[1:] { |
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243 if contains(hole, box.X1, box.Y1) { |
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244 return IntersectionOutSide |
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245 } |
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246 } |
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247 } |
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248 |
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249 // Check shell |
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250 if contains(p.rings[0], box.X1, box.Y1) { |
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251 return IntersectionInside |
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252 } |
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253 return IntersectionOutSide |
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254 } |
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255 |
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256 func (p *Polygon) IntersectionWithTriangle(t *Triangle) IntersectionType { |
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257 box := t.BBox() |
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258 min, max := box.Rect() |
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259 for _, index := range p.indices { |
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260 var intersects bool |
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261 index.Search(min, max, func(_, _ [2]float64, item interface{}) bool { |
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262 ls := item.(lineSegment) |
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263 other := make(lineSegment, 4) |
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264 for i := range t { |
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265 other[0] = t[i].X |
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266 other[1] = t[i].Y |
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267 other[2] = t[(i+1)%len(t)].X |
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268 other[3] = t[(i+1)%len(t)].Y |
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269 if ls.intersectsLineSegment(other) { |
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270 intersects = true |
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271 return false |
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272 } |
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273 } |
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274 return true |
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275 }) |
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276 if intersects { |
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277 return IntersectionOverlaps |
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278 } |
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279 } |
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280 // No intersection -> check inside or outside |
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281 // if an abritrary point is inside or not. |
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282 pX, pY := t[0].X, t[0].Y |
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283 |
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284 // Check holes first: inside a hole means outside. |
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285 if len(p.rings) > 1 { |
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286 for _, hole := range p.rings[1:] { |
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287 if contains(hole, pX, pY) { |
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288 return IntersectionOutSide |
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289 } |
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290 } |
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291 } |
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292 |
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293 // Check shell |
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294 if contains(p.rings[0], pX, pY) { |
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295 return IntersectionInside |
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296 } |
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297 return IntersectionOutSide |
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298 } |
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299 |
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300 func (rng ring) length() int { |
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301 return len(rng) / 2 |
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302 } |
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303 |
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304 func (rng ring) point(i int) (float64, float64) { |
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305 i *= 2 |
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306 return rng[i], rng[i+1] |
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307 } |
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308 |
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309 type segments interface { |
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310 length() int |
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311 point(int) (float64, float64) |
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312 } |
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313 |
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314 func contains(s segments, pX, pY float64) bool { |
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315 |
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316 n := s.length() |
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317 if n < 3 { |
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318 return false |
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319 } |
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320 |
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321 sX, sY := s.point(0) |
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322 eX, eY := s.point(n - 1) |
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323 |
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324 const eps = 0.0000001 |
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325 |
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326 if math.Abs(sX-eX) > eps || math.Abs(sY-eY) > eps { |
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327 // It's not closed! |
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328 return false |
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329 } |
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330 |
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331 var inside bool |
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332 |
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333 for i := 1; i < n; i++ { |
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334 eX, eY := s.point(i) |
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335 if intersectsWithRaycast(pX, pY, sX, sY, eX, eY) { |
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336 inside = !inside |
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337 } |
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338 sX, sY = eX, eY |
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339 } |
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340 |
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341 return inside |
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342 } |
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343 |
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344 // Using the raycast algorithm, this returns whether or not the passed in point |
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345 // Intersects with the edge drawn by the passed in start and end points. |
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346 // Original implementation: http://rosettacode.org/wiki/Ray-casting_algorithm#Go |
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347 func intersectsWithRaycast(pX, pY, sX, sY, eX, eY float64) bool { |
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348 |
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349 // Always ensure that the the first point |
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350 // has a y coordinate that is less than the second point |
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351 if sY > eY { |
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352 // Switch the points if otherwise. |
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353 sX, sY, eX, eY = eX, eY, sX, sY |
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354 } |
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355 |
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356 // Move the point's y coordinate |
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357 // outside of the bounds of the testing region |
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358 // so we can start drawing a ray |
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359 for pY == sY || pY == eY { |
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360 pY = math.Nextafter(pY, math.Inf(1)) |
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361 } |
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362 |
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363 // If we are outside of the polygon, indicate so. |
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364 if pY < sY || pY > eY { |
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365 return false |
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366 } |
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367 |
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368 if sX > eX { |
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369 if pX > sX { |
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370 return false |
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371 } |
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372 if pX < eX { |
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373 return true |
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374 } |
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375 } else { |
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376 if pX > eX { |
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377 return false |
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378 } |
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379 if pX < sX { |
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380 return true |
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381 } |
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382 } |
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383 |
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384 raySlope := (pY - sY) / (pX - sX) |
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385 diagSlope := (eY - sY) / (eX - sX) |
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386 |
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387 return raySlope >= diagSlope |
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388 } |
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389 |
3658
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390 func (p *Polygon) NumVertices(ring int) int { |
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391 if ring < 0 || ring >= len(p.rings) { |
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392 return 0 |
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393 } |
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394 return len(p.rings[ring]) / 2 |
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395 } |
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396 |
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397 func (p *Polygon) Vertices(ring int, fn func(float64, float64)) { |
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398 if ring < 0 || ring >= len(p.rings) { |
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399 return |
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400 } |
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401 rng := p.rings[ring] |
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402 for i := 0; i < len(rng); i += 2 { |
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403 fn(rng[i+0], rng[i+1]) |
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404 } |
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405 } |
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406 |
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407 func (p *Polygon) AsWKB() []byte { |
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408 |
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409 size := 1 + 4 + 4 |
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410 for _, r := range p.rings { |
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411 size += 4 + len(r)*8 |
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412 } |
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413 |
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414 buf := bytes.NewBuffer(make([]byte, 0, size)) |
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415 |
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416 binary.Write(buf, binary.LittleEndian, wkb.NDR) |
01ce3ba9b0d0
Fixed generating of random points.
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417 binary.Write(buf, binary.LittleEndian, wkb.Polygon) |
01ce3ba9b0d0
Fixed generating of random points.
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parents:
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418 binary.Write(buf, binary.LittleEndian, uint32(len(p.rings))) |
01ce3ba9b0d0
Fixed generating of random points.
Sascha L. Teichmann <sascha.teichmann@intevation.de>
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419 |
01ce3ba9b0d0
Fixed generating of random points.
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parents:
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420 for _, r := range p.rings { |
01ce3ba9b0d0
Fixed generating of random points.
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421 binary.Write(buf, binary.LittleEndian, uint32(len(r)/2)) |
01ce3ba9b0d0
Fixed generating of random points.
Sascha L. Teichmann <sascha.teichmann@intevation.de>
parents:
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422 for i := 0; i < len(r); i += 2 { |
01ce3ba9b0d0
Fixed generating of random points.
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423 binary.Write(buf, binary.LittleEndian, math.Float64bits(r[i+0])) |
01ce3ba9b0d0
Fixed generating of random points.
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parents:
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424 binary.Write(buf, binary.LittleEndian, math.Float64bits(r[i+1])) |
01ce3ba9b0d0
Fixed generating of random points.
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parents:
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425 } |
01ce3ba9b0d0
Fixed generating of random points.
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426 } |
01ce3ba9b0d0
Fixed generating of random points.
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427 |
01ce3ba9b0d0
Fixed generating of random points.
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428 return buf.Bytes() |
01ce3ba9b0d0
Fixed generating of random points.
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429 } |
01ce3ba9b0d0
Fixed generating of random points.
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430 |
2489
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Added a WKB reader for clipping polygon.
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431 func (p *Polygon) FromWKB(data []byte) error { |
4f292ff74d9e
Added a WKB reader for clipping polygon.
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432 |
4f292ff74d9e
Added a WKB reader for clipping polygon.
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433 r := bytes.NewReader(data) |
4f292ff74d9e
Added a WKB reader for clipping polygon.
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434 |
4f292ff74d9e
Added a WKB reader for clipping polygon.
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435 endian, err := r.ReadByte() |
4f292ff74d9e
Added a WKB reader for clipping polygon.
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436 |
4f292ff74d9e
Added a WKB reader for clipping polygon.
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437 var order binary.ByteOrder |
4f292ff74d9e
Added a WKB reader for clipping polygon.
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438 |
4f292ff74d9e
Added a WKB reader for clipping polygon.
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parents:
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439 switch { |
4f292ff74d9e
Added a WKB reader for clipping polygon.
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440 case err != nil: |
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Added a WKB reader for clipping polygon.
Sascha L. Teichmann <teichmann@intevation.de>
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441 return err |
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Added a WKB reader for clipping polygon.
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parents:
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442 case endian == wkb.NDR: |
4f292ff74d9e
Added a WKB reader for clipping polygon.
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443 order = binary.LittleEndian |
4f292ff74d9e
Added a WKB reader for clipping polygon.
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444 case endian == wkb.XDR: |
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Added a WKB reader for clipping polygon.
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445 order = binary.BigEndian |
4f292ff74d9e
Added a WKB reader for clipping polygon.
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446 default: |
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Added a WKB reader for clipping polygon.
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447 return fmt.Errorf("unknown byte order %x", endian) |
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Added a WKB reader for clipping polygon.
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448 } |
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Added a WKB reader for clipping polygon.
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449 |
4f292ff74d9e
Added a WKB reader for clipping polygon.
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450 var geomType uint32 |
4f292ff74d9e
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451 err = binary.Read(r, order, &geomType) |
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Added a WKB reader for clipping polygon.
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452 |
4f292ff74d9e
Added a WKB reader for clipping polygon.
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453 switch { |
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Added a WKB reader for clipping polygon.
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454 case err != nil: |
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Added a WKB reader for clipping polygon.
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455 return err |
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Added a WKB reader for clipping polygon.
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456 case geomType != wkb.Polygon: |
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Added a WKB reader for clipping polygon.
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457 return fmt.Errorf("unknown geometry type %x", geomType) |
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Added a WKB reader for clipping polygon.
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458 } |
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Added a WKB reader for clipping polygon.
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459 |
4f292ff74d9e
Added a WKB reader for clipping polygon.
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460 var numRings uint32 |
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461 if err = binary.Read(r, order, &numRings); err != nil { |
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Added a WKB reader for clipping polygon.
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462 return err |
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Added a WKB reader for clipping polygon.
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463 } |
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Added a WKB reader for clipping polygon.
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464 |
2490
c9164ff98871
Started with point in polygon check.
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465 rngs := make([]ring, numRings) |
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466 |
2498
843f39b9327e
Handle hole more precisely.
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467 log.Printf("info: Number of rings: %d\n", len(rngs)) |
843f39b9327e
Handle hole more precisely.
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468 |
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469 for rng := uint32(0); rng < numRings; rng++ { |
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470 var numVertices uint32 |
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471 if err = binary.Read(r, order, &numVertices); err != nil { |
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Added a WKB reader for clipping polygon.
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472 return err |
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Added a WKB reader for clipping polygon.
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473 } |
4f292ff74d9e
Added a WKB reader for clipping polygon.
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|
474 |
2498
843f39b9327e
Handle hole more precisely.
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parents:
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475 log.Printf("info: Number of vertices in ring %d: %d\n", rng, numVertices) |
843f39b9327e
Handle hole more precisely.
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parents:
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476 |
2490
c9164ff98871
Started with point in polygon check.
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477 numVertices *= 2 |
c9164ff98871
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478 vertices := make([]float64, numVertices) |
2489
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Added a WKB reader for clipping polygon.
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479 |
2490
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Started with point in polygon check.
Sascha L. Teichmann <sascha.teichmann@intevation.de>
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480 for v := uint32(0); v < numVertices; v += 2 { |
2489
4f292ff74d9e
Added a WKB reader for clipping polygon.
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|
481 var lat, lon uint64 |
4f292ff74d9e
Added a WKB reader for clipping polygon.
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|
482 if err = binary.Read(r, order, &lat); err != nil { |
4f292ff74d9e
Added a WKB reader for clipping polygon.
Sascha L. Teichmann <teichmann@intevation.de>
parents:
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|
483 return err |
4f292ff74d9e
Added a WKB reader for clipping polygon.
Sascha L. Teichmann <teichmann@intevation.de>
parents:
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|
484 } |
4f292ff74d9e
Added a WKB reader for clipping polygon.
Sascha L. Teichmann <teichmann@intevation.de>
parents:
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|
485 if err = binary.Read(r, order, &lon); err != nil { |
4f292ff74d9e
Added a WKB reader for clipping polygon.
Sascha L. Teichmann <teichmann@intevation.de>
parents:
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|
486 return err |
4f292ff74d9e
Added a WKB reader for clipping polygon.
Sascha L. Teichmann <teichmann@intevation.de>
parents:
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diff
changeset
|
487 } |
2490
c9164ff98871
Started with point in polygon check.
Sascha L. Teichmann <sascha.teichmann@intevation.de>
parents:
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|
488 vertices[v] = math.Float64frombits(lat) |
c9164ff98871
Started with point in polygon check.
Sascha L. Teichmann <sascha.teichmann@intevation.de>
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|
489 vertices[v+1] = math.Float64frombits(lon) |
2489
4f292ff74d9e
Added a WKB reader for clipping polygon.
Sascha L. Teichmann <teichmann@intevation.de>
parents:
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|
490 } |
4f292ff74d9e
Added a WKB reader for clipping polygon.
Sascha L. Teichmann <teichmann@intevation.de>
parents:
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diff
changeset
|
491 |
2490
c9164ff98871
Started with point in polygon check.
Sascha L. Teichmann <sascha.teichmann@intevation.de>
parents:
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diff
changeset
|
492 rngs[rng] = vertices |
2489
4f292ff74d9e
Added a WKB reader for clipping polygon.
Sascha L. Teichmann <teichmann@intevation.de>
parents:
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diff
changeset
|
493 } |
4f292ff74d9e
Added a WKB reader for clipping polygon.
Sascha L. Teichmann <teichmann@intevation.de>
parents:
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diff
changeset
|
494 |
2490
c9164ff98871
Started with point in polygon check.
Sascha L. Teichmann <sascha.teichmann@intevation.de>
parents:
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changeset
|
495 p.rings = rngs |
2489
4f292ff74d9e
Added a WKB reader for clipping polygon.
Sascha L. Teichmann <teichmann@intevation.de>
parents:
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changeset
|
496 |
4f292ff74d9e
Added a WKB reader for clipping polygon.
Sascha L. Teichmann <teichmann@intevation.de>
parents:
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changeset
|
497 return nil |
4f292ff74d9e
Added a WKB reader for clipping polygon.
Sascha L. Teichmann <teichmann@intevation.de>
parents:
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changeset
|
498 } |
3650
01ce3ba9b0d0
Fixed generating of random points.
Sascha L. Teichmann <sascha.teichmann@intevation.de>
parents:
2587
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changeset
|
499 |
01ce3ba9b0d0
Fixed generating of random points.
Sascha L. Teichmann <sascha.teichmann@intevation.de>
parents:
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|
500 func (p *Polygon) FromLineStringZ(ls LineStringZ) { |
01ce3ba9b0d0
Fixed generating of random points.
Sascha L. Teichmann <sascha.teichmann@intevation.de>
parents:
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|
501 r := make([]float64, 2*len(ls)) |
01ce3ba9b0d0
Fixed generating of random points.
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|
502 var pos int |
01ce3ba9b0d0
Fixed generating of random points.
Sascha L. Teichmann <sascha.teichmann@intevation.de>
parents:
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|
503 for i := range ls { |
01ce3ba9b0d0
Fixed generating of random points.
Sascha L. Teichmann <sascha.teichmann@intevation.de>
parents:
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changeset
|
504 r[pos+0] = ls[i].X |
01ce3ba9b0d0
Fixed generating of random points.
Sascha L. Teichmann <sascha.teichmann@intevation.de>
parents:
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changeset
|
505 r[pos+1] = ls[i].Y |
01ce3ba9b0d0
Fixed generating of random points.
Sascha L. Teichmann <sascha.teichmann@intevation.de>
parents:
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changeset
|
506 pos += 2 |
01ce3ba9b0d0
Fixed generating of random points.
Sascha L. Teichmann <sascha.teichmann@intevation.de>
parents:
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diff
changeset
|
507 } |
01ce3ba9b0d0
Fixed generating of random points.
Sascha L. Teichmann <sascha.teichmann@intevation.de>
parents:
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changeset
|
508 p.rings = []ring{r} |
01ce3ba9b0d0
Fixed generating of random points.
Sascha L. Teichmann <sascha.teichmann@intevation.de>
parents:
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changeset
|
509 } |