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authorKarl Berry <karl@freefriends.org>2019-01-05 22:40:38 +0000
committerKarl Berry <karl@freefriends.org>2019-01-05 22:40:38 +0000
commit22536bb2b5257046d271b1eaa11b4a275d5ec041 (patch)
tree2500eaf5c26b11e00ebd33a64fccfa332cd5a66c /Master/texmf-dist/tex/generic/pgf/graphdrawing/lua/pgf/gd/planar/Embedding.lua
parentcf794f0e2db6857972a9d48d4466a4f03a7057a0 (diff)
pgf (5jan19)
git-svn-id: svn://tug.org/texlive/trunk@49607 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/tex/generic/pgf/graphdrawing/lua/pgf/gd/planar/Embedding.lua')
-rw-r--r--Master/texmf-dist/tex/generic/pgf/graphdrawing/lua/pgf/gd/planar/Embedding.lua787
1 files changed, 787 insertions, 0 deletions
diff --git a/Master/texmf-dist/tex/generic/pgf/graphdrawing/lua/pgf/gd/planar/Embedding.lua b/Master/texmf-dist/tex/generic/pgf/graphdrawing/lua/pgf/gd/planar/Embedding.lua
new file mode 100644
index 00000000000..50fc3672207
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/pgf/graphdrawing/lua/pgf/gd/planar/Embedding.lua
@@ -0,0 +1,787 @@
+local E = {}
+
+require("pgf.gd.planar").Embedding = E
+
+-- includes
+local LinkedList = require("pgf.gd.planar.LinkedList")
+
+E.vertexmetatable = {
+ __tostring = function(v)
+ if v.name then
+ return v.name
+ elseif v.inputvertex then
+ return v.inputvertex.name
+ else
+ return tostring(v)
+ end
+ end
+}
+
+E.halfedgemetatable = {
+ __tostring = function(e)
+ return tostring(e.twin.target)
+ .. " -> "
+ .. tostring(e.target)
+ end
+}
+
+-- create class properties
+E.__index = E
+
+function E.new()
+ local t = {
+ vertices = {},
+ }
+ setmetatable(t, E)
+ return t
+end
+
+function E:add_vertex(name, inputvertex, virtual)
+ virtual = virtual or nil
+ local vertex = {
+ adjmat = {},
+ name = name,
+ inputvertex = inputvertex,
+ virtual = virtual,
+ }
+ setmetatable(vertex, E.vertexmetatable)
+ table.insert(self.vertices, vertex)
+ return vertex
+end
+
+function E:add_edge(v1, v2, after1, after2, virtual)
+ assert(v1.link == nil or v1 == after1.twin.target)
+ assert(v2.link == nil or v2 == after2.twin.target)
+ assert(v1.adjmat[v2] == nil)
+ assert(v2.adjmat[v1] == nil)
+
+ virtual = virtual or nil
+
+ local halfedge1 = {
+ target = v2,
+ virtual = virtual,
+ links = {},
+ }
+ local halfedge2 = {
+ target = v1,
+ virtual = virtual,
+ links = {},
+ }
+ halfedge1.twin = halfedge2
+ halfedge2.twin = halfedge1
+
+ setmetatable(halfedge1, E.halfedgemetatable)
+ setmetatable(halfedge2, E.halfedgemetatable)
+
+ if v1.link == nil then
+ v1.link = halfedge1
+ halfedge1.links[0] = halfedge1
+ halfedge1.links[1] = halfedge1
+ else
+ halfedge1.links[0] = after1.links[0]
+ after1.links[0].links[1] = halfedge1
+ halfedge1.links[1] = after1
+ after1.links[0] = halfedge1
+ end
+
+ if v2.link == nil then
+ v2.link = halfedge2
+ halfedge2.links[0] = halfedge2
+ halfedge2.links[1] = halfedge2
+ else
+ halfedge2.links[0] = after2.links[0]
+ after2.links[0].links[1] = halfedge2
+ halfedge2.links[1] = after2
+ after2.links[0] = halfedge2
+ end
+
+ v1.adjmat[v2] = halfedge1
+ v2.adjmat[v1] = halfedge2
+
+ return halfedge1, halfedge2
+end
+
+function E:remove_virtual()
+ local virtuals = {}
+ for i, v in ipairs(self.vertices) do
+ if v.virtual then
+ table.insert(virtuals, i)
+ else
+ local start = v.link
+ local current = start
+ repeat
+ current = current.links[0]
+ if current.virtual then
+ current.links[0].links[1] = current.links[1]
+ current.links[1].links[0] = current.links[0]
+ v.adjmat[current.target] = nil
+ current.target.adjmat[v] = nil
+ end
+ until current == start
+ end
+ end
+ for i = #virtuals, 1, -1 do
+ self.vertices[virtuals[i]] = self.vertices[#self.vertices]
+ table.remove(self.vertices)
+ end
+end
+
+-- for the use in for-loops
+-- iterates over the adjacency list of a vertex
+-- given a half edge to start and a direction (0 or 1, default 0)
+function E.adjacency_iterator(halfedge, direction)
+ direction = direction or 0
+ local function next_edge(startedge, prevedge)
+ if prevedge == nil then
+ return startedge
+ else
+ local nextedge = prevedge.links[direction]
+ if nextedge ~= startedge then
+ return nextedge
+ else
+ return nil
+ end
+ end
+ end
+ return next_edge, halfedge, nil
+end
+
+function E.face_iterator(halfedge, direction)
+ direction = direction or 0
+ local function next_edge(startedge, prevedge)
+ if prevedge == nil then
+ return startedge
+ else
+ local nextedge = prevedge.twin.links[1 - direction]
+ if nextedge ~= startedge then
+ return nextedge
+ else
+ return nil
+ end
+ end
+ end
+ return next_edge, halfedge, nil
+end
+
+function E:triangulate()
+ local visited = {}
+ for _, vertex in ipairs(self.vertices) do
+ for start in E.adjacency_iterator(vertex.link) do
+ if not visited[start] then
+ local prev = start
+ local beforestart = start.links[0].twin
+ local current = start.twin.links[1]
+ local next = current.twin.links[1]
+ visited[start] = true
+ visited[current] = true
+ visited[next] = true
+ while next ~= beforestart do
+ local halfedge1, halfedge2
+ if vertex ~= current.target
+ and not vertex.adjmat[current.target] then
+ halfedge1, halfedge2 = self:add_edge(
+ vertex, current.target,
+ prev, next,
+ true
+ )
+
+ prev = halfedge1
+ current = next
+ next = next.twin.links[1]
+ elseif not prev.target.adjmat[next.target] then
+ halfedge1, halfedge2 = self:add_edge(
+ prev.target, next.target,
+ current, next.twin.links[1],
+ true
+ )
+
+ current = halfedge1
+ next = halfedge2.links[1]
+ else
+ local helper = next.twin.links[1]
+ halfedge1, halfedge2 = self:add_edge(
+ current.target, helper.target,
+ next, helper.twin.links[1],
+ true
+ )
+
+ next = halfedge1
+ end
+
+ visited[next] = true
+ visited[halfedge1] = true
+ visited[halfedge2] = true
+ end
+ end
+ end
+ end
+end
+
+function E:canonical_order(v1, v2, vn)
+ local n = #self.vertices
+ local order = { v1 }
+ local marks = { [v1] = "ordered", [v2] = 0 }
+ local visited = {}
+ local vk = v1
+ local candidates = LinkedList.new()
+ local listelements = {}
+ for k = 1, n-2 do
+ for halfedge in E.adjacency_iterator(vk.link) do
+ local vertex = halfedge.target
+ if vertex ~= vn then
+ local twin = halfedge.twin
+ visited[twin] = true
+ if marks[vertex] == nil then
+ marks[vertex] = "visited"
+ elseif marks[vertex] ~= "ordered" then
+ local neighbor1 = visited[twin.links[0]]
+ local neighbor2 = visited[twin.links[1]]
+ if marks[vertex] == "visited" then
+ if neighbor1 or neighbor2 then
+ marks[vertex] = 1
+ listelements[vertex] = candidates:addback(vertex)
+ else
+ marks[vertex] = 2
+ end
+ else
+ if neighbor1 == neighbor2 then
+ if neighbor1 and neighbor2 then
+ marks[vertex] = marks[vertex] - 1
+ else
+ marks[vertex] = marks[vertex] + 1
+ end
+ if marks[vertex] == 1 then
+ listelements[vertex]
+ = candidates:addback(vertex)
+ elseif listelements[vertex] then
+ candidates:remove(listelements[vertex])
+ listelements[vertex] = nil
+ end
+ end
+ end
+ end
+ end
+ end
+ vk = candidates:popfirst()
+ order[k+1] = vk
+ marks[vk] = "ordered"
+ end
+ order[n] = vn
+ return order
+end
+
+function E:get_biggest_face()
+ local number = 0
+ local edge
+ local visited = {}
+ for _, vertex in ipairs(self.vertices) do
+ for start in E.adjacency_iterator(vertex.link) do
+ local count = 0
+ if not visited[start] then
+ visited[start] = true
+ local current = start
+ repeat
+ count = count + 1
+ current = current.twin.links[1]
+ until current == start
+ if count > number then
+ number = count
+ edge = start
+ end
+ end
+ end
+ end
+ return edge, number
+end
+
+function E:surround_by_triangle(faceedge, facesize)
+ local divisor = 3
+ if facesize > 3 then
+ divisor = 4
+ end
+ local basenodes = math.floor(facesize / divisor)
+ local extranodes = facesize % divisor
+ local attachnodes = { basenodes, basenodes, basenodes }
+ if facesize > 3 then
+ attachnodes[2] = basenodes * 2
+ end
+ for i = 1,extranodes do
+ attachnodes[i] = attachnodes[i] + 1
+ end
+
+ local v = {
+ self:add_vertex("$v_1$", nil, true),
+ self:add_vertex("$v_n$", nil, true),
+ self:add_vertex("$v_2$", nil, true)
+ }
+ for i = 1,3 do
+ local currentv = v[i]
+ local nextv = v[i % 3 + 1]
+ self:add_edge(currentv, nextv, currentv.link, nextv.link, true)
+ end
+
+ local current = faceedge
+ local next = current.twin.links[1]
+ for i = 1,3 do
+ local vertex = v[i]
+ local otheredge = vertex.adjmat[v[i % 3 + 1]]
+ local previnserted = otheredge.links[1]
+ for count = 1, attachnodes[i] do
+ if not vertex.adjmat[current.target] then
+ previnserted, _ = self:add_edge(vertex, current.target,
+ previnserted, next,
+ true
+ )
+ end
+
+ current = next
+ next = next.twin.links[1]
+ end
+ if not vertex.adjmat[current.target] then
+ previnserted, _ = self:add_edge(
+ vertex, current.target,
+ previnserted, next,
+ true
+ )
+ current = previnserted
+ end
+ end
+ return v[1], v[3], v[2]
+end
+
+function E:improve()
+ local pairdata = {}
+ local inpair = {}
+ for i, v1 in ipairs(self.vertices) do
+ for j = i + 1, #self.vertices do
+ local v2 = self.vertices[j]
+ local pd = self:find_pair_components(v1, v2)
+ if pd then
+ inpair[v1] = true
+ inpair[v2] = true
+ table.insert(pairdata, pd)
+ end
+ end
+ if not inpair[v1] then
+ local pd = self:find_pair_components(v1, nil)
+ if pd then
+ inpair[v1] = true
+ table.insert(pairdata, pd)
+ end
+ end
+ end
+
+ local changed
+ local runs = 1
+ local edgepositions = {}
+ repeat
+ changed = false
+ for i, pd in ipairs(pairdata) do
+ self:improve_separation_pair(pd)
+ end
+ -- check for changes
+ for i, v in ipairs(self.vertices) do
+ local start = v.link
+ local current = start
+ local counter = 1
+ repeat
+ if counter ~= edgepositions[current] then
+ changed = true
+ edgepositions[current] = counter
+ end
+ counter = counter + 1
+ current = current.links[0]
+ until current == start
+ end
+ runs = runs + 1
+ until changed == false or runs > 100
+end
+
+function E:find_pair_components(v1, v2)
+ local visited = {}
+ local companchors = {}
+ local edgecomps = {}
+ local compvertices = {}
+ local islinear = {}
+ local edgeindices = {}
+
+ local pair = { v1, v2 }
+ local start = v1.link
+ local current = start
+ local edgeindex = 1
+ -- start searches from v1
+ repeat
+ edgeindices[current] = edgeindex
+ edgeindex = edgeindex + 1
+ if not edgecomps[current] then
+ local compindex = #companchors + 1
+ local ca, il
+ edgecomps[current] = compindex
+ compvertices[compindex] = {}
+ local target = current.target
+ if target == v2 then
+ edgecomps[current.twin] = compindex
+ ca = 3
+ il = true
+ else
+ ca, il = self:component_dfs(
+ target,
+ pair,
+ visited,
+ edgecomps,
+ compvertices[compindex],
+ compindex
+ )
+ end
+ companchors[compindex] = ca
+ islinear[compindex] = il
+ end
+ current = current.links[0]
+ until current == start
+
+ if v2 then
+ start = v2.link
+ current = start
+ local lastincomp = true
+ local edgeindex = 1
+ -- now find the remaining blocks at v2
+ repeat
+ edgeindices[current] = edgeindex
+ edgeindex = edgeindex + 1
+ if not edgecomps[current] then
+ local compindex = #companchors + 1
+ edgecomps[current] = compindex
+ compvertices[compindex] = {}
+ self:component_dfs(
+ current.target,
+ pair,
+ visited,
+ edgecomps,
+ compvertices[compindex],
+ compindex
+ )
+ companchors[compindex] = 2
+ end
+ current = current.links[0]
+ until current == start
+ end
+
+ -- init compedges, tricomps, twocomps
+ local tricomps = {}
+ local twocomps = {{}, {}}
+ for i, anchors in ipairs(companchors) do
+ if anchors == 3 then
+ table.insert(tricomps, i)
+ else
+ table.insert(twocomps[anchors], i)
+ end
+ end
+
+ local flipimmune = #tricomps == 2
+ and (islinear[tricomps[1]] or islinear[tricomps[2]])
+ if (#tricomps < 2 or flipimmune)
+ and (v2 ~= nil or #twocomps[1] < 2) then
+ return nil
+ end
+
+ -- order tri comps cyclic
+ local function sorter(a, b)
+ return #compvertices[a] < #compvertices[b]
+ end
+
+ table.sort(tricomps, sorter)
+
+ -- determine order of comps
+ local numtricomps = #tricomps
+ local comporder = { {}, {} }
+ local bottom = math.ceil(numtricomps / 2)
+ local top = bottom + 1
+ for i, comp in ipairs(tricomps) do
+ if i % 2 == 1 then
+ comporder[1][bottom] = comp
+ comporder[2][numtricomps - bottom + 1] = comp
+ bottom = bottom - 1
+ else
+ comporder[1][top] = comp
+ comporder[2][numtricomps - top + 1] = comp
+ top = top + 1
+ end
+ end
+
+ local pairdata = {
+ pair = pair,
+ companchors = companchors,
+ edgecomps = edgecomps,
+ edgeindices = edgeindices,
+ compvertices = compvertices,
+ tricomps = tricomps,
+ twocomps = twocomps,
+ comporder = comporder,
+ }
+ return pairdata
+end
+
+function E:component_dfs(v, pair, visited, edgecomps, compvertices, compindex)
+ visited[v] = true
+ local start = v.link
+ local current = start
+ local companchors = 1
+ local numedges = 0
+ local islinear = true
+ table.insert(compvertices, v)
+ repeat
+ numedges = numedges + 1
+ local target = current.target
+ if target == pair[1] or target == pair[2] then
+ edgecomps[current.twin] = compindex
+ if target == pair[2] then
+ companchors = 3
+ end
+ elseif not visited[target] then
+ local ca, il = self:component_dfs(
+ target,
+ pair,
+ visited,
+ edgecomps,
+ compvertices,
+ compindex
+ )
+ if ca == 3 then
+ companchors = 3
+ end
+ islinear = islinear and il
+ end
+ current = current.links[0]
+ until current == start
+ return companchors, islinear and numedges == 2
+end
+
+function E:improve_separation_pair(pairdata)
+ local pair = pairdata.pair
+ local companchors = pairdata.companchors
+ local edgecomps = pairdata.edgecomps
+ local edgeindices = pairdata.edgeindices
+ local compvertices = pairdata.compvertices
+ local tricomps = pairdata.tricomps
+ local twocomps = pairdata.twocomps
+ local comporder = pairdata.comporder
+ local v1 = pair[1]
+ local v2 = pair[2]
+
+ local compedges = {}
+ for i = 1, #companchors do
+ compedges[i] = {{}, {}}
+ end
+
+ local numtricomps = #tricomps
+ local numtwocomps = { #twocomps[1], #twocomps[2] }
+
+ -- find compedges
+ for i = 1, #pair do
+ -- first find an edge that is the first of a triconnected component
+ local start2
+ if v2 then
+ start = pair[i].link
+ current = start
+ local last
+ repeat
+ local comp = edgecomps[current]
+ if companchors[comp] == 3 then
+ if last == nil then
+ last = comp
+ elseif last ~= comp then
+ start2 = current
+ break
+ end
+ end
+ current = current.links[0]
+ until current == start
+ else
+ start2 = pair[i].link
+ end
+ -- now list the edges by components
+ current = start2
+ repeat
+ table.insert(compedges[edgecomps[current]][i], current)
+ current = current.links[0]
+ until current == start2
+ end
+
+ -- count edges on each side of tri comps
+ local edgecount = {}
+ for _, comp in ipairs(tricomps) do
+ edgecount[comp] = {}
+ for i = 1, #pair do
+ local count = 1
+ local current = compedges[comp][i][1]
+ local other = pair[3 - i]
+ while current.target ~= other do
+ count = count + 1
+ current = current.twin.links[0]
+ end
+ edgecount[comp][i] = count
+ end
+ end
+
+ -- determine which comps have to be flipped
+ local flips = {}
+ local numflips = 0
+ local allflipped = true
+ for i, comp in ipairs(comporder[1]) do
+ local side1, side2
+ if i > numtricomps / 2 then
+ side1 = edgecount[comp][1]
+ side2 = edgecount[comp][2]
+ else
+ side1 = edgecount[comp][2]
+ side2 = edgecount[comp][1]
+ end
+ if side1 > side2 then
+ numflips = numflips + 1
+ flips[comp] = true
+ elseif side1 < side2 then
+ allflipped = false
+ end
+ end
+
+ if allflipped then
+ for i, comp in ipairs(tricomps) do
+ flips[comp] = false
+ end
+ else
+ for i, comp in ipairs(tricomps) do
+ if flips[comp] then
+ for _, v in ipairs(compvertices[comp]) do
+ local start = v.link
+ local current = start
+ repeat
+ current.links[0], current.links[1]
+ = current.links[1], current.links[0]
+ current = current.links[1]
+ until current == start
+ end
+ end
+ end
+ end
+
+ -- order edges cyclic per component (one cycle for all tri comps)
+ for i = 1, #pair do
+ if v2 then
+ local co
+ if allflipped then
+ co = comporder[3 - i]
+ else
+ co = comporder[i]
+ end
+
+ local id = co[numtricomps]
+ lastedges = compedges[id][i]
+ if flips[id] then
+ lastedge = lastedges[1]
+ else
+ lastedge = lastedges[#lastedges]
+ end
+
+ -- tri comps
+ for _, id in ipairs(co) do
+ local edges = compedges[id][i]
+ local from
+ local to
+ local step
+ if flips[id] then
+ from = #edges
+ to = 1
+ step = -1
+ else
+ from = 1
+ to = #edges
+ step = 1
+ end
+ for k = from, to, step do
+ local edge = edges[k]
+ lastedge.links[0] = edge
+ edge.links[1] = lastedge
+ lastedge = edge
+ end
+ end
+ end
+
+ -- two comps
+ for _, id in ipairs(twocomps[i]) do
+ lastedges = compedges[id][i]
+ lastedge = lastedges[#lastedges]
+ for _, edge in ipairs(compedges[id][i]) do
+ lastedge.links[0] = edge
+ edge.links[1] = lastedge
+ lastedge = edge
+ end
+ end
+ end
+
+ -- now merge the cycles
+ for i = 1, #pair do
+ local outeredges = {}
+ -- find the biggest face of the tri comps
+ if v2 then
+ local biggestedge
+ local biggestsize
+ local biggestindex
+ local start = compedges[tricomps[1]][i][1]
+ local current = start
+ repeat
+ local size = self:get_face_size(current)
+ if not biggestedge or size > biggestsize
+ or (size == biggestsize
+ and edgeindices[current] > biggestindex) then
+ biggestedge = current
+ biggestsize = size
+ biggestindex = edgeindices[current]
+ end
+ current = current.links[0]
+ until current == start
+ outeredges[1] = biggestedge
+ end
+
+ -- now for every two comp
+ for _, id in ipairs(twocomps[i]) do
+ local biggestedge
+ local biggestsize
+ local biggestindex
+ local start = compedges[id][i][1]
+ local current = start
+ repeat
+ local size = self:get_face_size(current)
+ if not biggestedge or size > biggestsize
+ or (size == biggestsize
+ and edgeindices[current] > biggestindex) then
+ biggestedge = current
+ biggestsize = size
+ biggestindex = edgeindices[current]
+ end
+ current = current.links[0]
+ until current == start
+ table.insert(outeredges, biggestedge)
+ end
+
+ -- now merge all comps at the outer edges
+ local lastedge = outeredges[#outeredges].links[0]
+ for _, edge in ipairs(outeredges) do
+ local nextlastedge = edge.links[0]
+ lastedge.links[1] = edge
+ edge.links[0] = lastedge
+ lastedge = nextlastedge
+ end
+ end
+end
+
+function E:get_face_size(halfedge)
+ local size = 0
+ local current = halfedge
+ repeat
+ size = size + 1
+ current = current.twin.links[1]
+ until current == halfedge
+ return size
+end
+
+return E