Mercurial > gemma
view pkg/octree/triangulation.go @ 4606:dfe9cde6a20c geoserver_sql_views
Reflect database model changes for SQL views in backend
In principle, we could use many datasources with different database
schemas, but this would imply changing GeoServer initialization,
service filtering, endpoints and eventually more. Since we do not need
it, just hard-code the schema name as a constant.
author | Tom Gottfried <tom@intevation.de> |
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date | Thu, 05 Sep 2019 12:23:31 +0200 |
parents | ec86a7155377 |
children |
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// Copyright (C) 2018 Michael Fogleman // // Permission is hereby granted, free of charge, to any person obtaining // a copy of this software and associated documentation files (the "Software"), // to deal in the Software without restriction, including without limitation // the rights to use, copy, modify, merge, publish, distribute, sublicense, // and/or sell copies of the Software, and to permit persons to whom the // Software is furnished to do so, subject to the following conditions: // // The above copyright notice and this permission notice shall be included // in all copies or substantial portions of the Software. // // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS // OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL // THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, // OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. package octree import ( "fmt" "log" "math" "gonum.org/v1/gonum/stat" ) type Triangulation struct { Points []Vertex ConvexHull []Vertex Triangles []int32 Halfedges []int32 } // Triangulate returns a Delaunay triangulation of the provided points. func Triangulate(points []Vertex) (*Triangulation, error) { t := newTriangulator(points) err := t.triangulate() return &Triangulation{points, t.convexHull(), t.triangles, t.halfedges}, err } func (t *Triangulation) EstimateTooLong() float64 { num := len(t.Triangles) / 3 lengths := make([]float64, 0, num) points := t.Points tris: for i := 0; i < num; i++ { idx := i * 3 var max float64 vs := t.Triangles[idx : idx+3] for j, vj := range vs { if t.Halfedges[idx+j] < 0 { continue tris } k := (j + 1) % 3 if l := points[vj].Distance2D(points[vs[k]]); l > max { max = l } } lengths = append(lengths, max) } std := stat.StdDev(lengths, nil) return 3.5 * std } func (t *Triangulation) ConcaveHull(tooLong float64) (LineStringZ, map[int32]struct{}) { if tooLong <= 0 { tooLong = t.EstimateTooLong() } tooLong *= tooLong var candidates []int32 points := t.Points for i, num := 0, len(t.Triangles)/3; i < num; i++ { idx := i * 3 var max float64 vs := t.Triangles[idx : idx+3] for j, vj := range vs { k := (j + 1) % 3 if l := points[vj].SquaredDistance2D(points[vs[k]]); l > max { max = l } } if max > tooLong { candidates = append(candidates, int32(i)) } } removed := map[int32]struct{}{} isBorder := func(n int32) bool { n *= 3 for i := int32(0); i < 3; i++ { e := n + i o := t.Halfedges[e] if o < 0 { return true } if _, found := removed[o/3]; found { return true } } return false } var newCandidates []int32 log.Printf("info: candidates: %d\n", len(candidates)) for len(candidates) > 0 { oldRemoved := len(removed) for _, i := range candidates { if isBorder(i) { removed[i] = struct{}{} } else { newCandidates = append(newCandidates, i) } } if oldRemoved == len(removed) { break } candidates = newCandidates newCandidates = newCandidates[:0] } log.Printf("info: candidates left: %d\n", len(candidates)) log.Printf("info: triangles: %d\n", len(t.Triangles)/3) log.Printf("info: triangles to remove: %d\n", len(removed)) type edge struct { a, b int32 prev, next *edge } isClosed := func(e *edge) bool { for curr := e.next; curr != nil; curr = curr.next { if curr == e { return true } } return false } open := map[int32]*edge{} var rings []*edge for i, num := int32(0), int32(len(t.Triangles)/3); i < num; i++ { if _, found := removed[i]; found { continue } n := i * 3 for j := int32(0); j < 3; j++ { e := n + j f := t.Halfedges[e] if f >= 0 { if _, found := removed[f/3]; !found { continue } } a := t.Triangles[e] b := t.Triangles[n+(j+1)%3] curr := &edge{a: a, b: b} if old := open[a]; old != nil { delete(open, a) if old.a == a { old.prev = curr curr.next = old } else { old.next = curr curr.prev = old } if isClosed(old) { rings = append(rings, old) } } else { open[a] = curr } if old := open[b]; old != nil { delete(open, b) if old.b == b { old.next = curr curr.prev = old } else { old.prev = curr curr.next = old } if isClosed(old) { rings = append(rings, old) } } else { open[b] = curr } } } if len(open) > 0 { log.Printf("warn: open vertices left: %d\n", len(open)) } if len(rings) == 0 { log.Println("warn: no ring found") return nil, removed } curr := rings[0] polygon := LineStringZ{ points[curr.a], points[curr.b], } for curr = curr.next; curr != rings[0]; curr = curr.next { polygon = append(polygon, points[curr.b]) } polygon = append(polygon, t.Points[rings[0].a]) log.Printf("length of boundary: %d\n", len(polygon)) return polygon, removed } func (t *Triangulation) TriangleSlices() [][]int32 { sl := make([][]int32, len(t.Triangles)/3) var j int for i := range sl { sl[i] = t.Triangles[j : j+3] j += 3 } return sl } func (t *Triangulation) Tin() *Tin { min := Vertex{math.MaxFloat64, math.MaxFloat64, math.MaxFloat64} max := Vertex{-math.MaxFloat64, -math.MaxFloat64, -math.MaxFloat64} vertices := t.Points for _, v := range vertices { min.Minimize(v) max.Maximize(v) } return &Tin{ Vertices: vertices, Triangles: t.TriangleSlices(), Min: min, Max: max, } } func (t *Triangulation) area() float64 { var result float64 points := t.Points ts := t.Triangles for i := 0; i < len(ts); i += 3 { p0 := points[ts[i+0]] p1 := points[ts[i+1]] p2 := points[ts[i+2]] result += area(p0, p1, p2) } return result / 2 } // Validate performs several sanity checks on the Triangulation to check for // potential errors. Returns nil if no issues were found. You normally // shouldn't need to call this function but it can be useful for debugging. func (t *Triangulation) Validate() error { // verify halfedges for i1, i2 := range t.Halfedges { if i1 != -1 && t.Halfedges[i1] != i2 { return fmt.Errorf("invalid halfedge connection") } if i2 != -1 && t.Halfedges[i2] != int32(i1) { return fmt.Errorf("invalid halfedge connection") } } // verify convex hull area vs sum of triangle areas hull1 := t.ConvexHull hull2 := ConvexHull(t.Points) area1 := polygonArea(hull1) area2 := polygonArea(hull2) area3 := t.area() if math.Abs(area1-area2) > 1e-9 || math.Abs(area1-area3) > 1e-9 { return fmt.Errorf("hull areas disagree: %f, %f, %f", area1, area2, area3) } // verify convex hull perimeter perimeter1 := polygonPerimeter(hull1) perimeter2 := polygonPerimeter(hull2) if math.Abs(perimeter1-perimeter2) > 1e-9 { return fmt.Errorf("hull perimeters disagree: %f, %f", perimeter1, perimeter2) } return nil }