Mercurial > gemma
annotate pkg/mesh/triangulator.go @ 5333:6c0f40676984 extented-report
Run xlsx templating in a read-only transaction.
author | Sascha L. Teichmann <sascha.teichmann@intevation.de> |
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date | Tue, 01 Jun 2021 00:37:03 +0200 |
parents | f4abfd0ee8ad |
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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 mesh |
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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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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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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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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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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.
Sascha L. Teichmann <sascha.teichmann@intevation.de>
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183 for k := 0; k < n; k++ { |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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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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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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200 key := tri.hashKey(p) |
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Incorporated fogleman's fast Delaunay triangulation adjuted to our vertex model.
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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.
Sascha L. Teichmann <sascha.teichmann@intevation.de>
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 } |