+require "luamesh-polygon"
+require "luamesh-tex"
+
+local function shallowCopy(original)
+ local copy = {}
+ for key, value in pairs(original) do
+ copy[key] = value
+ end
+ return copy
+end
+
-- Bowyer and Watson algorithm
-- Delaunay meshing
function BowyerWatson (listPoints,bbox)
local triangulation = {}
- local lgth = #listPoints
+ lgth = #listPoints
-- add four points to listPoints to have a bounding box
listPoints = buildBoundingBox(listPoints)
-- the first triangle
- triangulation[1] = {lgth+1, lgth+2, lgth+3}
+ triangulation[1] = {lgth+1, lgth+2, lgth+3,type="bbox"}
-- the second triangle
- triangulation[2] = {lgth+1, lgth+3, lgth+4}
+ triangulation[2] = {lgth+1, lgth+3, lgth+4,type="bbox"}
-- add points one by one
for i=1,lgth do
-- find the triangles which the circumcircle contained the point to add
- badTriangles = buildBadTriangles(listPoints[i],triangulation)
+ badTriangles = buildBadTriangles(listPoints[i],triangulation,listPoints)
-- build the polygon of the cavity containing the point to add
polygon = buildCavity(badTriangles, triangulation)
-- remove the bad triangles
end
-- build the new triangles and add them to triangulation
for j=1,#polygon do
- table.insert(triangulation,{polygon[j][1],polygon[j][2],i})
+ if((polygon[j][1]>lgth) or (polygon[j][2]>lgth) or (i>lgth)) then
+ table.insert(triangulation,{polygon[j][1],polygon[j][2],i,type="bbox"})
+ else
+ table.insert(triangulation,{polygon[j][1],polygon[j][2],i,type="in"})
+ end
end
end -- end adding points of the listPoints
-- remove bounding box
ymin = ymin - eps
ymax = ymax + eps
-- add points of the bounding box in last positions
- table.insert(listPoints,{x=xmin,y=ymin})
- table.insert(listPoints,{x=xmin,y=ymax})
- table.insert(listPoints,{x=xmax,y=ymax})
- table.insert(listPoints,{x=xmax,y=ymin})
+ table.insert(listPoints,{x=xmin,y=ymin,type="bbox"})
+ table.insert(listPoints,{x=xmin,y=ymax,type="bbox"})
+ table.insert(listPoints,{x=xmax,y=ymax,type="bbox"})
+ table.insert(listPoints,{x=xmax,y=ymin,type="bbox"})
return listPoints
end
+function BoundingBox(listPoints)
+ -- listPoints : list of points
+ -- epsV : parameter for the distance of the bounding box
+ local xmin, xmax, ymin, ymax, eps
+ xmin = 1000
+ ymin = 1000
+ xmax = -1000
+ ymax = -1000
+ for i=1,#listPoints do
+ if (listPoints[i].x < xmin) then
+ xmin = listPoints[i].x
+ end
+ if (listPoints[i].x > xmax) then
+ xmax = listPoints[i].x
+ end
+ if (listPoints[i].y < ymin) then
+ ymin = listPoints[i].y
+ end
+ if (listPoints[i].y > ymax) then
+ ymax = listPoints[i].y
+ end
+ end
+ eps = math.max(math.abs(xmax-xmin),math.abs(ymax-ymin))*0.15
+ xmin = xmin - eps
+ xmax = xmax + eps
+ ymin = ymin - eps
+ ymax = ymax + eps
+ return xmin, xmax, ymin, ymax
+end
+
function removeBoundingBox(triangulation,lgth)
-- build the four bounding box edge
point1 = lgth+1
point3 = lgth+3
point4 = lgth+4
-- for all triangle
- newTriangulation = {}
+ local newTriangulation = {}
for i=1,#triangulation do
boolE1 = pointInTriangle(point1,triangulation[i])
boolE2 = pointInTriangle(point2,triangulation[i])
end
-function buildBadTriangles(point, triangulation)
- badTriangles = {}
+function buildBadTriangles(point, triangulation,listPoints)
+ local badTriangles = {}
for j=1,#triangulation do -- for all triangles
A = listPoints[triangulation[j][1]]
B = listPoints[triangulation[j][2]]
-- construction of the cavity composed by the bad triangles around the point to add
function buildCavity(badTriangles, triangulation)
- polygon = {}
+ local polygon = {}
for j=1,#badTriangles do -- for all bad triangles
ind = badTriangles[j]
for k=1,3 do -- for all edges
return Out, rad -- (center [Point], R [float])
end
+-- compute the list of the circumcircle of a triangulation
+function listCircumCenter(listPoints,triangulation)
+ local list = {}
+ for j=1,#triangulation do
+ A = listPoints[triangulation[j][1]]
+ B = listPoints[triangulation[j][2]]
+ C = listPoints[triangulation[j][3]]
+ center, radius = circoncircle(A,B,C)
+ table.insert(list,{x=center.x,y=center.y,r=radius})
+ end
+ return list
+end
+
+-- find the three neighbour triangles of T
+function findNeighbour(T,i,triangulation)
+ -- T : triangle
+ -- i : index of T in triangualation
+ -- triangulation
+
+ list = {}
+ -- define the three edge
+ e1 = {T[1],T[2]}
+ e2 = {T[2],T[3]}
+ e3 = {T[3],T[1]}
+ for j=1,#triangulation do
+ if j~= i then
+ if(edgeInTriangle(e1,triangulation[j])) then
+ table.insert(list,j)
+ end
+ if(edgeInTriangle(e2,triangulation[j])) then
+ table.insert(list,j)
+ end
+ if(edgeInTriangle(e3,triangulation[j])) then
+ table.insert(list,j)
+ end
+ end
+ end
+ return list
+end
+
+-- test if edge are the same (reverse)
+function equalEdge(e1,e2)
+ if(((e1[1] == e2[1]) and (e1[2] == e2[2])) or ((e1[1] == e2[2]) and (e1[2] == e2[1]))) then
+ return true
+ else
+ return false
+ end
+end
+
+-- test if the edge belongs to the list
+function edgeInList(e,listE)
+ output = false
+ for i=1,#listE do
+ if(equalEdge(e,listE[i])) then
+ output = true
+ end
+ end
+ return output
+end
+
+-- build the edges of the Voronoi diagram with a given triangulation
+function buildVoronoi(listPoints, triangulation)
+ local listCircumCircle = listCircumCenter(listPoints, triangulation)
+ local listVoronoi = {}
+ for i=1,#listCircumCircle do
+ listN = findNeighbour(triangulation[i],i,triangulation)
+ for j=1,#listN do
+ edge = {i,listN[j]}
+ if( not edgeInList(edge, listVoronoi)) then
+ table.insert(listVoronoi, edge)
+ end
+ end
+ end
+ return listVoronoi
+end
--------------------------- TeX
-- build the list of points
function buildList(chaine, mode)
-- if mode = int : the list is given in the chaine string (x1,y1);(x2,y2);...;(xn,yn)
-- if mode = ext : the list is given in a file line by line with space separation
- listPoints = {}
+ local listPoints = {}
if mode == "int" then
local points = string.explode(chaine, ";")
local lgth=#points
end
---
-function rectangleList(a,b,nbrA,nbrB)
- stepA = a/nbrA
- stepB = b/nbrB
- listPoints = {}
- k=1
- for i=1,(nbrA+1) do
- for j=1,(nbrB+1) do
- listPoints[k] = {x = (i-1)*stepA, y=(j-1)*stepB}
- k=k+1
- end
- end
- return listPoints
-end
-
--- trace a triangulation with TikZ
-function traceMeshTikZ(listPoints, triangulation,points,color)
- output = ""
- for i=1,#triangulation do
- PointI = listPoints[triangulation[i][1]]
- PointJ = listPoints[triangulation[i][2]]
- PointK = listPoints[triangulation[i][3]]
- output = output .. "\\draw[color="..color.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
- end
- if(points=="points") then
- for i=1,#listPoints do
- output = output .. "\\draw[color=".."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};"
+-- function to add points on a polygon to respect
+-- the size of unit mesh
+function addPointsPolygon(polygon,h)
+ local newPolygon = shallowCopy(polygon)
+ k=0 -- to follow in the newPolygon
+ for i=1,#polygon do
+ k = k+1
+ ip = (i)%(#polygon)+1
+ dist = math.sqrt(math.pow(polygon[i].x-polygon[ip].x,2) + math.pow(polygon[i].y-polygon[ip].y,2))
+ -- if the distance between two ponits of the polygon is greater than 1.5*h
+ if(dist>=2*h) then
+ n = math.floor(dist/h)
+ step = dist/(n+1)
+ for j=1,n do
+ a = {x=polygon[i].x+j*step*(polygon[ip].x-polygon[i].x)/dist,y=polygon[i].y+j*step*(polygon[ip].y-polygon[i].y)/dist}
+ table.insert(newPolygon,k+j,a)
+ end
+ k=k+n
end
end
- return output
+ return newPolygon
end
+-- function to build a gridpoints from the bounding box
+-- with a prescribed
+function buildGrid(listPoints,h,random)
+ -- listPoints : list of the points of the polygon, ordered
+ -- h : parameter for the grid
+ xmin, xmax, ymin, ymax = BoundingBox(listPoints)
--- trace a triangulation with MP
-function traceMeshMP(listPoints, triangulation,points,color)
- output = "";
- output = output .. " pair MeshPoints[];"
- for i=1,#listPoints do
- output = output .. "MeshPoints[".. i .. "] = (" .. listPoints[i].x .. "," .. listPoints[i].y .. ");"
- end
-
- for i=1,#triangulation do
- PointI = listPoints[triangulation[i][1]]
- PointJ = listPoints[triangulation[i][2]]
- PointK = listPoints[triangulation[i][3]]
- output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\mpcolor{"..color.. "};"
- end
- if(points=="points") then
- for i=1,#listPoints do
- output = output .. "dotlabel.llft( btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u) withcolor \\mpcolor{"..color.. "};"
- end
- end
- return output
+ local grid = rectangleList(xmin,xmax,ymin,ymax,h,random)
+ return grid
end
-
-
--- buildMesh with TikZ
-function buildMeshTikZ(chaine,mode,points,bbox,full,scale,color)
- listPoints = buildList(chaine, mode)
- triangulation = BowyerWatson(listPoints,bbox)
- output = traceMeshTikZ(listPoints, triangulation,points,color)
- if(full=="full") then
- output = "\\noindent\\begin{tikzpicture}[x=" .. scale .. ",y=" .. scale .."]" .. output .."\\end{tikzpicture}"
+-- function to build the list of points in the rectangle
+function rectangleList(xmin,xmax,ymin,ymax,h,random)
+ -- for the random
+ math.randomseed( os.time() )
+ nbrX = math.floor(math.abs(xmax-xmin)/h)
+ nbrY = math.floor(math.abs(ymax-ymin)/h)
+ local listPoints = {}
+ k=1
+ for i=1,(nbrX+1) do
+ for j=1,(nbrY+1) do
+ rd = math.random()
+ if(random=="perturb") then
+ fact = 0.3*h
+ --print(fact)
+ else
+ fact = 0.0
+ end
+ listPoints[k] = {x = xmin+(i-1)*h+rd*fact, y=ymin+(j-1)*h+rd*fact}
+ k=k+1
+ end
end
- tex.sprint(output)
+ return listPoints
end
--- buildMesh with MP
-function buildMeshMP(chaine,mode,points,bbox,full,scale,color)
- listPoints = buildList(chaine, mode)
- triangulation = BowyerWatson(listPoints,bbox)
- output = traceMeshMP(listPoints, triangulation,points,color)
- if(full=="full") then
- output = "\\leavevmode\\begin{mplibcode}beginfig(0);u:="..scale.. ";" .. output .."endfig;\\end{mplibcode}"
- else
- output = "u:="..scale.. ";".. output
+-- function to add points from a grid to the interior of a polygon
+function addGridPoints(polygon, grid,h)
+ local listPoints = shallowCopy(polygon)
+ k = #polygon
+ for i=1, #grid do
+ --print(grid[i].x,grid[i].y)
+ --print(isInside(polygon,grid[i]))
+ if(isInside(polygon,grid[i],h)) then
+ k=k+1
+ listPoints[k] = grid[i]
+ end
end
- tex.sprint(output)
+ return listPoints
end
--- buildMesh
-function buildRect(largeur,a,b,nbrA, nbrB)
- listPoints = rectangleList(a,b,nbrA,nbrB)
- triangulation = BowyerWatson(listPoints,"none")
- traceTikZ(listPoints, triangulation,largeur,"none")
-end
-- function give a real polygon without repeting points
function cleanPoly(polygon)
- polyNew = {}
- e1 = polygon[1][1]
- e2 = polygon[1][2]
+ local polyNew = {}
+ local polyCopy = shallowCopy(polygon)
+ e1 = polyCopy[1][1]
+ e2 = polyCopy[1][2]
table.insert(polyNew, e1)
table.insert(polyNew, e2)
+ table.remove(polyCopy,1)
j = 2
- for i=2,#polygon do
- bool1 = (polygon[i][1] == polyNew[j])
- bool2 = (polygon[i][2] == polyNew[j])
- if(bool1 or bool2) then -- the edge has a common point with polyNew[j]
- if(not bool1) then
- table.insert(polyNew, polygon[i][1])
- j = j+1
- elseif(not bool2) then
- table.insert(polyNew, polygon[i][2])
- j = j+1
+ while #polyCopy>1 do
+ i=1
+ find = false
+ while (i<=#polyCopy and find==false) do
+ bool1 = (polyCopy[i][1] == polyNew[j])
+ bool2 = (polyCopy[i][2] == polyNew[j])
+ if(bool1 or bool2) then -- the edge has a common point with polyNew[j]
+ if(not bool1) then
+ table.insert(polyNew, polyCopy[i][1])
+ find = true
+ table.remove(polyCopy,i)
+ j = j+1
+ elseif(not bool2) then
+ table.insert(polyNew, polyCopy[i][2])
+ find = true
+ table.remove(polyCopy,i)
+ j = j+1
+ end
end
+ i=i+1
end
end
return polyNew
end
---
-function TeXaddOnePointTikZ(chaine,point,step,color,colorBack, colorNew, colorCircle)
- Sx,Sy=string.match(point,"%((.+),(.+)%)")
- P = {x=Sx, y=Sy}
- output = ""
- listPoints = buildList(chaine, "int")
- -- build the triangulation
- triangulation = BowyerWatson(listPoints,"none")
- badTriangles = buildBadTriangles(P,triangulation)
- if(step == "badT") then
- -- draw all triangle
- for i=1,#triangulation do
- PointI = listPoints[triangulation[i][1]]
- PointJ = listPoints[triangulation[i][2]]
- PointK = listPoints[triangulation[i][3]]
- output = output .. "\\draw[color="..color.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
- end
- -- draw and fill the bad triangle
- for i=1,#badTriangles do
- PointI = listPoints[triangulation[badTriangles[i]][1]]
- PointJ = listPoints[triangulation[badTriangles[i]][2]]
- PointK = listPoints[triangulation[badTriangles[i]][3]]
- output = output .. "\\draw[fill="..colorBack.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
- end
- -- draw the circoncircle
- for i=1,#badTriangles do
- PointI = listPoints[triangulation[badTriangles[i]][1]]
- PointJ = listPoints[triangulation[badTriangles[i]][2]]
- PointK = listPoints[triangulation[badTriangles[i]][3]]
- center, radius = circoncircle(PointI, PointJ, PointK)
- output = output .. "\\draw[dashed, color="..colorCircle.."] ("..center.x .. "," .. center.y .. ") circle ("..radius ..");"
- end
- -- mark the points
- for i=1,#listPoints do
- output = output .. "\\draw[color ="..color.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};"
- end
- -- mark the point to add
- output = output .. "\\draw[color="..colorNew.."] (" .. P.x ..",".. P.y .. ") node {$\\bullet$} node[anchor=north east] {$\\NewPoint$};"
- elseif(step == "cavity") then
- polygon = buildCavity(badTriangles, triangulation)
- polyNew = cleanPoly(polygon)
- -- remove the bad triangles
- for j=1,#badTriangles do
- table.remove(triangulation,badTriangles[j]-(j-1))
- end
- -- draw the triangles
- for i=1,#triangulation do
- PointI = listPoints[triangulation[i][1]]
- PointJ = listPoints[triangulation[i][2]]
- PointK = listPoints[triangulation[i][3]]
- output = output .. "\\draw[color="..color.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
- end
- -- fill and draw the cavity
- path = ""
- for i=1,#polyNew do
- PointI = listPoints[polyNew[i]]
- path = path .. "(".. PointI.x ..",".. PointI.y ..")--"
- end
- output = output .. "\\draw[color="..colorNew..",fill ="..colorBack..", thick] " .. path .. "cycle;"
- -- mark the points of the mesh
- for i=1,#listPoints do
- output = output .. "\\draw[color="..color.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};"
- end
- -- mark the adding point
- output = output .. "\\draw[color="..colorNew.."] (" .. P.x ..",".. P.y .. ") node {$\\bullet$} node[anchor=north east] {$\\NewPoint$};"
- elseif(step == "newT") then
- polygon = buildCavity(badTriangles, triangulation)
- polyNew = cleanPoly(polygon)
- -- remove the bad triangles
- for j=1,#badTriangles do
- table.remove(triangulation,badTriangles[j]-(j-1))
- end
- -- draw the triangle of the triangulation
- for i=1,#triangulation do
- PointI = listPoints[triangulation[i][1]]
- PointJ = listPoints[triangulation[i][2]]
- PointK = listPoints[triangulation[i][3]]
- output = output .. "\\draw[color ="..color.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
- end
- -- fill and draw the cavity
- path = ""
- for i=1,#polyNew do
- PointI = listPoints[polyNew[i]]
- path = path .. "(".. PointI.x ..",".. PointI.y ..")--"
- end
- output = output .. "\\draw[color="..colorNew..",fill ="..colorBack..", thick] " .. path .. "cycle;"
- -- draw the new triangles composed by the edges of the polygon and the added point
- for i=1,#polygon do
- output = output .. "\\draw[color=TeXCluaMeshNewTikZ, thick]".."(".. listPoints[polygon[i][1]].x .. "," .. listPoints[polygon[i][1]].y .. ") -- (" .. listPoints[polygon[i][2]].x .. "," .. listPoints[polygon[i][2]].y ..");"
- output = output .. "\\draw[color="..colorNew..", thick]".."(".. listPoints[polygon[i][1]].x .. "," .. listPoints[polygon[i][1]].y .. ") -- (" .. P.x .. "," .. P.y ..");"
- output = output .. "\\draw[color="..colorNew..", thick]".."(".. listPoints[polygon[i][2]].x .. "," .. listPoints[polygon[i][2]].y .. ") -- (" .. P.x .. "," .. P.y ..");"
- end
- -- mark points
- for i=1,#listPoints do
- output = output .. "\\draw[color="..color.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};"
- end
- -- mark the added point
- output = output .. "\\draw[color="..colorNew.."] (" .. P.x ..",".. P.y .. ") node {$\\bullet$} node[anchor=north east] {$\\NewPoint$};"
- end
- return output
-end
-
-function TeXaddOnePointMP(listPoints,P,step,color,colorBack, colorNew, colorCircle,bbox)
- output = "";
- output = output .. "pair MeshPoints[];"
- -- build the triangulation
- triangulation = BowyerWatson(listPoints,bbox)
- badTriangles = buildBadTriangles(P,triangulation)
- for i=1,#listPoints do
- output = output .. "MeshPoints[".. i .. "] = (" .. listPoints[i].x .. "," .. listPoints[i].y .. ");"
- end
- if(step == "badT") then
- -- draw all triangle
- for i=1,#triangulation do
- PointI = listPoints[triangulation[i][1]]
- PointJ = listPoints[triangulation[i][2]]
- PointK = listPoints[triangulation[i][3]]
- output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\mpcolorcolor;"
- end
- -- draw and fill the bad triangle
- for i=1,#badTriangles do
- PointI = listPoints[triangulation[badTriangles[i]][1]]
- PointJ = listPoints[triangulation[badTriangles[i]][2]]
- PointK = listPoints[triangulation[badTriangles[i]][3]]
- output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\mpcolorcolor;"
- output = output .. "fill (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\mpcolorcolorBack;"
- end
- -- draw the circoncircle
- for i=1,#badTriangles do
- PointI = listPoints[triangulation[badTriangles[i]][1]]
- PointJ = listPoints[triangulation[badTriangles[i]][2]]
- PointK = listPoints[triangulation[badTriangles[i]][3]]
- center, radius = circoncircle(PointI, PointJ, PointK)
- output = output .. "draw fullcircle scaled ("..radius .."*2u) shifted ("..center.x .. "*u," .. center.y .. "*u) dashed evenly withcolor \\mpcolorcolorCircle;"
- end
- -- mark the points
- for i=1,#listPoints do
- output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\mpcolorcolor;"
- end
- -- mark the point to add
- output = output .. "dotlabel.llft (btex $\\NewPoint$ etex,(" .. P.x ..",".. P.y .. ")*u) withcolor \\mpcolorcolorNew;"
- elseif(step == "cavity") then
- polygon = buildCavity(badTriangles, triangulation)
- polyNew = cleanPoly(polygon)
- -- remove the bad triangles
- for j=1,#badTriangles do
- table.remove(triangulation,badTriangles[j]-(j-1))
- end
- -- draw the triangles
- for i=1,#triangulation do
- PointI = listPoints[triangulation[i][1]]
- PointJ = listPoints[triangulation[i][2]]
- PointK = listPoints[triangulation[i][3]]
- output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\mpcolorcolor;"
- end
- -- fill and draw the cavity
- path = ""
- for i=1,#polyNew do
- PointI = listPoints[polyNew[i]]
- path = path .. "(".. PointI.x ..",".. PointI.y ..")*u--"
- end
- output = output .. "fill " .. path .. "cycle withcolor \\mpcolorcolorBack;"
- output = output .. "draw " .. path .. "cycle withcolor \\mpcolorcolorNew withpen pencircle scaled 1pt;"
- -- mark the points of the mesh
- for i=1,#listPoints do
- output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\mpcolorcolor ;"
- end
- -- mark the adding point
- output = output .. "dotlabel.llft (btex $\\NewPoint$ etex,(" .. P.x ..",".. P.y .. ")*u) withcolor \\mpcolorcolorNew ;"
- elseif(step == "newT") then
- polygon = buildCavity(badTriangles, triangulation)
- polyNew = cleanPoly(polygon)
- -- remove the bad triangles
- for j=1,#badTriangles do
- table.remove(triangulation,badTriangles[j]-(j-1))
- end
- -- draw the triangle of the triangulation
- for i=1,#triangulation do
- PointI = listPoints[triangulation[i][1]]
- PointJ = listPoints[triangulation[i][2]]
- PointK = listPoints[triangulation[i][3]]
- output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\mpcolorcolor ;"
- end
- -- fill the cavity
- path = ""
- for i=1,#polyNew do
- PointI = listPoints[polyNew[i]]
- path = path .. "(".. PointI.x ..",".. PointI.y ..")*u--"
- end
- output = output .. "fill " .. path .. "cycle withcolor \\mpcolorcolorBack;"
- -- draw the new triangles composed by the edges of the polygon and the added point
- for i=1,#polygon do
- output = output .. "draw".."(".. listPoints[polygon[i][1]].x .. "," .. listPoints[polygon[i][1]].y .. ")*u -- (" .. listPoints[polygon[i][2]].x .. "," .. listPoints[polygon[i][2]].y ..")*u withcolor \\mpcolorcolorNew withpen pencircle scaled 1pt;"
- output = output .. "draw".."(".. listPoints[polygon[i][1]].x .. "," .. listPoints[polygon[i][1]].y .. ")*u -- (" .. P.x .. "," .. P.y ..")*u withcolor \\mpcolorcolorNew withpen pencircle scaled 1pt;"
- output = output .. "draw".."(".. listPoints[polygon[i][2]].x .. "," .. listPoints[polygon[i][2]].y .. ")*u -- (" .. P.x .. "," .. P.y ..")*u withcolor \\mpcolorcolorNew withpen pencircle scaled 1pt;"
- end
- -- mark points
- for i=1,#listPoints do
- output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\mpcolorcolor ;"
- end
- -- mark the added point
- output = output .. "dotlabel.llft (btex $\\NewPoint$ etex,(" .. P.x ..",".. P.y .. ")*u) withcolor \\mpcolorcolorNew ;"
- end
- return output
-end
-- build the list of points extern and stop at nbr
function buildListExt(chaine, stop)
- listPoints = {}
+ local listPoints = {}
io.input(chaine) -- open the file
text=io.read("*all")
lines=string.explode(text,"\n+") -- all the lines
return point, listPoints
end
-
-function TeXOnePointTikZ(chaine,point,step,color,colorBack,colorNew,colorCircle,scale)
- output = TeXaddOnePointTikZ(chaine,point,step,color,colorBack,colorNew,colorCircle)
- output = "\\noindent\\begin{tikzpicture}[x="..scale..",y="..scale.."]".. output .. "\\end{tikzpicture}"
- tex.sprint(output)
+function split(pString, pPattern)
+ local Table = {} -- NOTE: use {n = 0} in Lua-5.0
+ local fpat = "(.-)" .. pPattern
+ local last_end = 1
+ local s, e, cap = pString:find(fpat, 1)
+ while s do
+ if s ~= 1 or cap ~= "" then
+ table.insert(Table,cap)
+ end
+ last_end = e+1
+ s, e, cap = pString:find(fpat, last_end)
+ end
+ if last_end <= #pString then
+ cap = pString:sub(last_end)
+ table.insert(Table, cap)
+ end
+ return Table
end
-function TeXOnePointMP(chaine,point,step,color,colorBack,colorNew,colorCircle,scale,mode,picture,bbox)
- if(mode=="int") then
- Sx,Sy=string.match(point,"%((.+),(.+)%)")
- P = {x=Sx, y=Sy}
- listPoints = buildList(chaine, mode)
- else
- -- point is a number
- P, listPoints = buildListExt(chaine,tonumber(point))
- end
- output = TeXaddOnePointMP(listPoints,P,step,color,colorBack,colorNew,colorCircle,bbox)
- if(picture=="full") then
- output = "\\leavevmode\\begin{mplibcode}beginfig(0);u:="..scale..";".. output .. "endfig;\\end{mplibcode}"
- else
- output = "u:="..scale..";".. output
+function readGmsh(file)
+ io.input(file) -- open the file
+ text=io.read("*all")
+ local lines = split(text,"\n+") -- all the lines
+ local listPoints={}
+ local triangulation ={}
+ boolNodes = false
+ Jnodes = 0
+ boolElements = false
+ Jelements = 0
+ J=0
+ for i=1,#lines-J do
+ if(lines[i+J] == "$EndNodes") then
+ boolNodes = false
+ -- go to the next line
+ end
+ if(boolNodes) then -- we are in the Nodes environment
+ xy=split(lines[i+J]," +")
+ table.insert(listPoints,{x=tonumber(xy[2]),y=tonumber(xy[3])})
+ end
+ if(lines[i+J] == "$Nodes") then
+ boolNodes = true
+ -- go to the next line
+ J=J+1
+ end
+ if(lines[i+J] == "$EndElements") then
+ boolElements = false
+ -- go to the next line
+ end
+ if(boolElements) then -- we are in the Nodes environment
+ xy=split(lines[i+J]," +")
+ if(tonumber(xy[2]) == 2) then -- if the element is a triangle
+ nbrTags = xy[3]+1
+ table.insert(triangulation,{tonumber(xy[2+nbrTags+1]),tonumber(xy[2+nbrTags+2]),tonumber(xy[2+nbrTags+3])})
+ end
+ end
+ if(lines[i+J] == "$Elements") then
+ boolElements = true
+ -- go to the next line
+ J=J+1
+ end
end
- tex.sprint(output)
+ return listPoints, triangulation
end
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