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geom-spanning-tree.stanza
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geom-spanning-tree.stanza
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defpackage geom/spanning-tree :
import core
import collections
import math
import utils/union-find
import utils/edits
import geom/vec
import geom/line-segment
import geom/delaunay with :
prefix( Edge ) => del-
defn abs (v:Vec2) : Vec2(abs(x(v)), abs(y(v)))
defn map (f:Double -> Double, v:Vec2) : Vec2(f(x(v)), f(y(v)))
public defstruct Edge <: Hashable & Equalable :
a : Int
b : Int
defmethod equal? (e0:Edge, e1:Edge) :
a(e0) == a(e1) and b(e0) == b(e1)
defmethod hash (e:Edge) :
hash(a(e)) + 7 * hash(b(e))
defmethod print (o:OutputStream, e:Edge) :
print(o, "EDGE(%_, %_)" % [a(e), b(e)])
defn length (points:Tuple<Vec2>, e:Edge) -> Double :
magnitude(points[a(e)] - points[b(e)])
public defstruct IntGraph :
id : Int
nbrs : Vector<Int>
defmethod print (o:OutputStream, e:IntGraph) :
print(o, "IntGraph(%_, %_)" % [id(e), nbrs(e)])
defn IntGraph (point:Int) : IntGraph(point, Vector<Int>())
public defstruct SpanningGraph :
points : Tuple<Vec2>
graphs : Tuple<IntGraph>
defn edges (tree:SpanningGraph) -> Seqable<Edge> :
val visited? = HashSet<Int>()
generate<Edge> :
let loop (g:Int = 0) :
add(visited?, g)
for nbr in nbrs(graphs(tree)[g]) do :
if not visited?[nbr] :
yield(Edge(g, nbr))
loop(nbr)
defmethod print (o:OutputStream, e:SpanningGraph) :
print(o, "SpanningGraph(%_, %_)" % [points(e), graphs(e)])
defn length (tree:SpanningGraph) -> Double :
sum(seq(length{points(tree), _}, edges(tree)))
defn all-edges (verts:Tuple<Vertex>) -> Seqable<Edge> :
generate<Edge> :
for i in 0 to length(verts) do :
for j in (i + 1) to length(verts) do :
yield(Edge(i, j))
public defn SpanningGraph (ipoints:Seqable<Vec2>, seed-edges:Tuple<Edge>) -> SpanningGraph :
val points = to-tuple $ ipoints
if length(points) == 0 :
SpanningGraph([], [] as Tuple<IntGraph>)
else :
val verts = to-tuple $ seq(Vertex, points)
val unsorted-edges =
if false and length(points) <= 6 and length(seed-edges) == 0 :
all-edges(verts)
else :
;; println("SPANNING-TREE %_" % [length(points)])
;; val edges = to-tuple $ lazy-qsort(length{points, _}, all-edges(points))
;; val log2n = max(4, ceil-log2(length(points)) - 2)
;; println("LOG2N %_" % [log2n])
val vec2-edges = edges(Subdivision(verts))
;; println("DELAUNAY")
val vert-mapper = to-inttable<Int> $ for (vert in verts, i in 0 to false) seq : id(vert) => i
generate<Edge> :
for e in vec2-edges do :
;; println("e %_ ORG %_ DEST %_" % [e, key?(edge-mapper, org(e)), key?(edge-mapper, dest(e))])
if key?(vert-mapper, id(org(e))) and key?(vert-mapper, id(dest(e))) :
yield(Edge(vert-mapper[id(org(e))], vert-mapper[id(dest(e))]))
val edges = to-tuple $ cat(seed-edges, lazy-qsort(length{points, _}, unsorted-edges))
val graphs = to-tuple $ for i in 0 to length(points) seq : IntGraph(i)
val sets = to-tuple $ for i in 0 to length(points) seq : #UFSet<Int>(i, i, 1)
;; for edge in edges do :
;; println("EDGE %_ LENGTH %_" % [edge, length(points, edge)])
;; for (point in points, i in 0 to false) do :
;; println("%_: %_" % [i, point])
label<False> return :
for edge in edges do :
;; println("CONSIDERING EDGE %_ SETS %_ , %_" % [edge, id(root(sets[a(edge)])), id(root(sets[b(edge)]))])
if root(sets[a(edge)]) != root(sets[b(edge)]) :
add(nbrs(graphs[a(edge)]), b(edge))
add(nbrs(graphs[b(edge)]), a(edge))
merge!(sets[a(edge)], sets[b(edge)])
return(false) when one-set?(sets)
for edge in seed-edges do :
if not contains?(nbrs(graphs[a(edge)]), b(edge)) : add(nbrs(graphs[a(edge)]), b(edge))
if not contains?(nbrs(graphs[b(edge)]), a(edge)) : add(nbrs(graphs[b(edge)]), a(edge))
;; println("DONE")
SpanningGraph(points, graphs)
public defstruct IntTree :
idx : Int
children : Tuple<IntTree>
defmethod print (o:OutputStream, t:IntTree) :
print(o, "IntTree(%_, %_)" % [idx(t), children(t)])
public defstruct SpanningTree :
points : Tuple<Vec2>
tree : IntTree
defmethod print (o:OutputStream, t:SpanningTree) :
print(o, "SpanningTree(%_, %_)" % [points(t), tree(t)])
defn SpanningTree (graph:SpanningGraph) -> SpanningTree :
val visited? = HashSet<Int>()
val tree = let loop (g:Int = 0, d:Int = 0) :
;; for i in 0 to d do: print(" ")
add(visited?, g)
val elts = generate<IntTree> :
for nbr in nbrs(graphs(graph)[g]) do :
yield(loop(nbr, d + 1)) when not visited?[nbr]
IntTree(g, to-tuple $ elts)
SpanningTree(points(graph), tree)
public defn SpanningTree (points:Seqable<Vec2>, seed-edges:Seqable<Edge>) -> SpanningTree :
SpanningTree(SpanningGraph(points, to-tuple $ seed-edges))
public defn SpanningTree (points:Seqable<Vec2>) -> SpanningTree :
SpanningTree(SpanningGraph(points, []))
public defn dump (st:SpanningTree) :
let loop (t:IntTree = tree(st), depth:Int = 0) :
for i in 0 to depth do : print(" ")
println("%_: %_" % [idx(t), points(st)[idx(t)]])
for child in children(t) do :
loop(child, depth + 1)
public defn id-segments (st:SpanningTree) -> Seqable<V2i> :
generate<V2i> :
let loop (t:IntTree = tree(st)) :
for child in children(t) do :
yield(V2i(idx(t), idx(child)))
loop(child)
public defn id-tour (st:SpanningTree) -> Seqable<V2i> :
generate<V2i> :
let loop (t:IntTree = tree(st)) :
for child in children(t) do :
yield(V2i(idx(t), idx(child)))
loop(child)
yield(V2i(idx(child), idx(t)))
public defn segments (st:SpanningTree) -> Seqable<LineSegment2f> :
seq(fn (s) : LineSegment2f(points(st)[s[0]], points(st)[s[1]]), id-segments(st))
;;