Mercurial > gemma
annotate pkg/octree/triangulator.go @ 4488:bff6c5c1db4f
client: pdf-gen: improve adding bottleneck info to pdf
* Check if the bottleneck is in the current view to add its info to the exported pdf and the pdf filename, this avoid wrong filename and wrong info in pdf in case view has been changed to another location.
* Set the bottleneck to print after moving to it in map.
author | Fadi Abbud <fadi.abbud@intevation.de> |
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date | Fri, 27 Sep 2019 11:15:02 +0200 |
parents | d12c2f4d3483 |
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rev | line source |
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1 // Copyright (C) 2018 Michael Fogleman |
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2 // |
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3 // Permission is hereby granted, free of charge, to any person obtaining |
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4 // a copy of this software and associated documentation files (the "Software"), |
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5 // to deal in the Software without restriction, including without limitation |
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6 // the rights to use, copy, modify, merge, publish, distribute, sublicense, |
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7 // and/or sell copies of the Software, and to permit persons to whom the |
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8 // Software is furnished to do so, subject to the following conditions: |
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9 // |
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10 // The above copyright notice and this permission notice shall be included |
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11 // in all copies or substantial portions of the Software. |
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12 // |
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13 // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS |
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14 // OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
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15 // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL |
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16 // THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
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17 // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, |
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18 // OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. |
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19 |
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20 package octree |
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21 |
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22 import ( |
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23 "errors" |
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24 "math" |
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25 "sort" |
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26 ) |
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27 |
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28 type triangulator struct { |
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29 points []Vertex |
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30 squaredDistances []float64 |
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31 ids []int32 |
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32 center Vertex |
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33 triangles []int32 |
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34 halfedges []int32 |
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35 trianglesLen int |
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36 hull *node |
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37 hash []*node |
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38 } |
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39 |
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40 func newTriangulator(points []Vertex) *triangulator { |
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41 return &triangulator{points: points} |
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42 } |
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43 |
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44 // sorting a triangulator sorts the `ids` such that the referenced points |
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45 // are in order by their distance to `center` |
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46 func (tri *triangulator) Len() int { |
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47 return len(tri.points) |
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48 } |
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49 |
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50 func (tri *triangulator) Swap(i, j int) { |
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51 tri.ids[i], tri.ids[j] = tri.ids[j], tri.ids[i] |
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52 } |
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53 |
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54 func (tri *triangulator) Less(i, j int) bool { |
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55 d1 := tri.squaredDistances[tri.ids[i]] |
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56 d2 := tri.squaredDistances[tri.ids[j]] |
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57 if d1 != d2 { |
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58 return d1 < d2 |
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59 } |
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60 p1 := tri.points[tri.ids[i]] |
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61 p2 := tri.points[tri.ids[j]] |
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62 if p1.X != p2.X { |
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63 return p1.X < p2.X |
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64 } |
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65 return p1.Y < p2.Y |
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66 } |
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67 |
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68 func (tri *triangulator) triangulate() error { |
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69 points := tri.points |
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70 |
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71 n := len(points) |
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72 if n == 0 { |
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73 return nil |
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74 } |
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75 |
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76 tri.ids = make([]int32, n) |
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77 |
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78 // compute bounds |
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79 x0 := points[0].X |
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80 y0 := points[0].Y |
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81 x1 := points[0].X |
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82 y1 := points[0].Y |
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83 for i, p := range points { |
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84 if p.X < x0 { |
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85 x0 = p.X |
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86 } |
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87 if p.X > x1 { |
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88 x1 = p.X |
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89 } |
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90 if p.Y < y0 { |
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91 y0 = p.Y |
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92 } |
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93 if p.Y > y1 { |
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94 y1 = p.Y |
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95 } |
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96 tri.ids[i] = int32(i) |
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97 } |
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98 |
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99 var i0, i1, i2 int32 |
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100 |
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101 // pick a seed point close to midpoint |
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102 m := Vertex{X: (x0 + x1) / 2, Y: (y0 + y1) / 2} |
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103 minDist := infinity |
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104 for i, p := range points { |
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105 d := p.SquaredDistance2D(m) |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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106 if d < minDist { |
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107 i0 = int32(i) |
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108 minDist = d |
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109 } |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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110 } |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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111 |
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112 // find point closest to seed point |
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113 minDist = infinity |
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114 for i, p := range points { |
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115 if int32(i) == i0 { |
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116 continue |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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117 } |
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118 d := p.SquaredDistance2D(points[i0]) |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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119 if d > 0 && d < minDist { |
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120 i1 = int32(i) |
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121 minDist = d |
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122 } |
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123 } |
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124 |
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125 // find the third point which forms the smallest circumcircle |
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126 minRadius := infinity |
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127 for i, p := range points { |
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128 if int32(i) == i0 || int32(i) == i1 { |
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129 continue |
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130 } |
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131 r := circumradius(points[i0], points[i1], p) |
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132 if r < minRadius { |
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133 i2 = int32(i) |
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134 minRadius = r |
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135 } |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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136 } |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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137 if minRadius == infinity { |
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Made 'golint' more happy with the octree package.
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138 return errors.New("no delaunay triangulation exists for this input") |
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139 } |
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140 |
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141 // swap the order of the seed points for counter-clockwise orientation |
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142 if area(points[i0], points[i1], points[i2]) < 0 { |
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143 i1, i2 = i2, i1 |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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144 } |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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145 |
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146 tri.center = circumcenter(points[i0], points[i1], points[i2]) |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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147 |
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148 // sort the points by distance from the seed triangle circumcenter |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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149 tri.squaredDistances = make([]float64, n) |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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150 for i, p := range points { |
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151 tri.squaredDistances[i] = p.SquaredDistance2D(tri.center) |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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152 } |
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153 sort.Sort(tri) |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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154 |
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155 // initialize a hash table for storing edges of the advancing convex hull |
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156 hashSize := int(math.Ceil(math.Sqrt(float64(n)))) |
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157 tri.hash = make([]*node, hashSize) |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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158 |
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159 // initialize a circular doubly-linked list that will hold an advancing convex hull |
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160 nodes := make([]node, n) |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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161 |
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162 e := newNode(nodes, i0, nil) |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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163 e.t = 0 |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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164 tri.hashEdge(e) |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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165 |
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166 e = newNode(nodes, i1, e) |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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167 e.t = 1 |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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parents:
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168 tri.hashEdge(e) |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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169 |
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170 e = newNode(nodes, i2, e) |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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171 e.t = 2 |
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172 tri.hashEdge(e) |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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173 |
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174 tri.hull = e |
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175 |
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176 maxTriangles := 2*n - 5 |
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177 tri.triangles = make([]int32, maxTriangles*3) |
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178 tri.halfedges = make([]int32, maxTriangles*3) |
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179 |
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180 tri.addTriangle(i0, i1, i2, -1, -1, -1) |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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181 |
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182 pp := Vertex{X: infinity, Y: infinity} |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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183 for k := 0; k < n; k++ { |
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184 i := tri.ids[k] |
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185 p := points[i] |
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186 |
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187 // skip nearly-duplicate points |
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188 if p.SquaredDistance2D(pp) < eps { |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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189 continue |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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parents:
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190 } |
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191 pp = p |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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192 |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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193 // skip seed triangle points |
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194 if i == int32(i0) || i == int32(i1) || i == int32(i2) { |
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195 continue |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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196 } |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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197 |
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198 // find a visible edge on the convex hull using edge hash |
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199 var start *node |
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parents:
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200 key := tri.hashKey(p) |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
Sascha L. Teichmann <sascha.teichmann@intevation.de>
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201 for j := 0; j < len(tri.hash); j++ { |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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202 start = tri.hash[key] |
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203 if start != nil && start.i >= 0 { |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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parents:
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204 break |
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205 } |
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206 key++ |
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207 if key >= len(tri.hash) { |
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208 key = 0 |
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209 } |
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210 } |
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211 start = start.prev |
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212 |
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213 e := start |
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214 for area(p, points[e.i], points[e.next.i]) >= 0 { |
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215 e = e.next |
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216 if e == start { |
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217 e = nil |
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218 break |
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219 } |
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220 } |
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221 if e == nil { |
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222 // likely a near-duplicate point; skip it |
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223 continue |
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224 } |
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225 walkBack := e == start |
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226 |
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227 // add the first triangle from the point |
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228 t := tri.addTriangle(e.i, i, e.next.i, -1, -1, e.t) |
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229 e.t = t // keep track of boundary triangles on the hull |
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230 e = newNode(nodes, i, e) |
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231 |
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232 // recursively flip triangles from the point until they satisfy the Delaunay condition |
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233 e.t = tri.legalize(t + 2) |
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234 |
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235 // walk forward through the hull, adding more triangles and flipping recursively |
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236 q := e.next |
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237 for area(p, points[q.i], points[q.next.i]) < 0 { |
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238 t = tri.addTriangle(q.i, i, q.next.i, q.prev.t, -1, q.t) |
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239 q.prev.t = tri.legalize(t + 2) |
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240 tri.hull = q.remove() |
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241 q = q.next |
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242 } |
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243 |
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244 if walkBack { |
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245 // walk backward from the other side, adding more triangles and flipping |
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246 q := e.prev |
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247 for area(p, points[q.prev.i], points[q.i]) < 0 { |
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248 t = tri.addTriangle(q.prev.i, i, q.i, -1, q.t, q.prev.t) |
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249 tri.legalize(t + 2) |
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250 q.prev.t = t |
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251 tri.hull = q.remove() |
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252 q = q.prev |
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253 } |
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254 } |
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255 |
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256 // save the two new edges in the hash table |
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257 tri.hashEdge(e) |
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258 tri.hashEdge(e.prev) |
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259 } |
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260 |
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261 tri.triangles = tri.triangles[:tri.trianglesLen] |
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262 tri.halfedges = tri.halfedges[:tri.trianglesLen] |
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263 |
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264 return nil |
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265 } |
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266 |
4151
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267 func (tri *triangulator) hashKey(point Vertex) int { |
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268 d := point.Sub2D(tri.center) |
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269 return int(pseudoAngle(d.X, d.Y) * float64(len(tri.hash))) |
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270 } |
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271 |
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272 func (tri *triangulator) hashEdge(e *node) { |
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Made 'golint' more happy with the octree package.
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273 tri.hash[tri.hashKey(tri.points[e.i])] = e |
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274 } |
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275 |
4151
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Made 'golint' more happy with the octree package.
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276 func (tri *triangulator) addTriangle(i0, i1, i2, a, b, c int32) int32 { |
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277 i := int32(tri.trianglesLen) |
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Made 'golint' more happy with the octree package.
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278 tri.triangles[i] = i0 |
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279 tri.triangles[i+1] = i1 |
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280 tri.triangles[i+2] = i2 |
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Made 'golint' more happy with the octree package.
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281 tri.link(i, a) |
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282 tri.link(i+1, b) |
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283 tri.link(i+2, c) |
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284 tri.trianglesLen += 3 |
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285 return i |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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parents:
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|
286 } |
620038ade708
Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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parents:
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287 |
4151
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288 func (tri *triangulator) link(a, b int32) { |
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289 tri.halfedges[a] = b |
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290 if b >= 0 { |
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291 tri.halfedges[b] = a |
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|
292 } |
620038ade708
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293 } |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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294 |
4151
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295 func (tri *triangulator) legalize(a int32) int32 { |
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296 // if the pair of triangles doesn't satisfy the Delaunay condition |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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parents:
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297 // (p1 is inside the circumcircle of [p0, pl, pr]), flip them, |
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298 // then do the same check/flip recursively for the new pair of triangles |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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parents:
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299 // |
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parents:
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300 // pl pl |
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parents:
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301 // /||\ / \ |
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302 // al/ || \bl al/ \a |
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Sascha L. Teichmann <sascha.teichmann@intevation.de>
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303 // / || \ / \ |
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304 // / a||b \ flip /___ar___\ |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
Sascha L. Teichmann <sascha.teichmann@intevation.de>
parents:
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305 // p0\ || /p1 => p0\---bl---/p1 |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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306 // \ || / \ / |
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307 // ar\ || /br b\ /br |
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308 // \||/ \ / |
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309 // pr pr |
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310 |
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311 b := tri.halfedges[a] |
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312 |
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313 a0 := a - a%3 |
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314 b0 := b - b%3 |
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315 |
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316 al := a0 + (a+1)%3 |
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317 ar := a0 + (a+2)%3 |
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318 bl := b0 + (b+2)%3 |
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319 |
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320 if b < 0 { |
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321 return ar |
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322 } |
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323 |
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324 p0 := tri.triangles[ar] |
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325 pr := tri.triangles[a] |
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326 pl := tri.triangles[al] |
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327 p1 := tri.triangles[bl] |
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328 |
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329 illegal := inCircle(tri.points[p0], tri.points[pr], tri.points[pl], tri.points[p1]) |
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330 |
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331 if illegal { |
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332 tri.triangles[a] = p1 |
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333 tri.triangles[b] = p0 |
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334 |
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335 // edge swapped on the other side of the hull (rare) |
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336 // fix the halfedge reference |
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337 if tri.halfedges[bl] == -1 { |
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338 e := tri.hull |
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339 for { |
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340 if e.t == bl { |
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341 e.t = a |
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342 break |
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343 } |
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344 e = e.next |
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345 if e == tri.hull { |
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346 break |
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347 } |
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348 } |
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349 } |
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350 |
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351 tri.link(a, tri.halfedges[bl]) |
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352 tri.link(b, tri.halfedges[ar]) |
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353 tri.link(ar, bl) |
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354 |
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355 br := b0 + (b+1)%3 |
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356 |
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357 tri.legalize(a) |
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358 return tri.legalize(br) |
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359 } |
620038ade708
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360 |
620038ade708
Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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361 return ar |
620038ade708
Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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parents:
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362 } |
620038ade708
Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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363 |
4151
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364 func (tri *triangulator) convexHull() []Vertex { |
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365 var result []Vertex |
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366 e := tri.hull |
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367 for e != nil { |
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368 result = append(result, tri.points[e.i]) |
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369 e = e.prev |
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370 if e == tri.hull { |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
Sascha L. Teichmann <sascha.teichmann@intevation.de>
parents:
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|
371 break |
620038ade708
Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
Sascha L. Teichmann <sascha.teichmann@intevation.de>
parents:
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|
372 } |
620038ade708
Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
Sascha L. Teichmann <sascha.teichmann@intevation.de>
parents:
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373 } |
620038ade708
Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
Sascha L. Teichmann <sascha.teichmann@intevation.de>
parents:
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374 return result |
620038ade708
Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
Sascha L. Teichmann <sascha.teichmann@intevation.de>
parents:
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|
375 } |