+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
-- 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
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
-- compute the list of the circumcircle of a triangulation
function listCircumCenter(listPoints,triangulation)
- list = {}
+ local list = {}
for j=1,#triangulation do
A = listPoints[triangulation[j][1]]
B = listPoints[triangulation[j][2]]
-- build the edges of the Voronoi diagram with a given triangulation
function buildVoronoi(listPoints, triangulation)
- listCircumCircle = listCircumCenter(listPoints, triangulation)
- listVoronoi = {}
+ local listCircumCircle = listCircumCenter(listPoints, triangulation)
+ local listVoronoi = {}
for i=1,#listCircumCircle do
listN = findNeighbour(triangulation[i],i,triangulation)
for j=1,#listN do
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 Voronoi with MP
-function traceVoronoiMP(listPoints, triangulation,listVoronoi, points, tri)
- listCircumC = listCircumCenter(listPoints,triangulation)
- output = "";
- output = output .. " pair MeshPoints[];"
- for i=1,#listPoints do
- output = output .. "MeshPoints[".. i .. "] = (" .. listPoints[i].x .. "," .. listPoints[i].y .. ")*u;"
- end
- output = output .. " pair CircumCenters[];"
- for i=1,#listCircumC do
- output = output .. "CircumCenters[".. i .. "] = (" .. listCircumC[i].x .. "," .. listCircumC[i].y .. ")*u;"
- end
- if(tri=="show") then
- for i=1,#triangulation do
- PointI = listPoints[triangulation[i][1]]
- PointJ = listPoints[triangulation[i][2]]
- PointK = listPoints[triangulation[i][3]]
- if(triangulation[i].type == "bbox") then
- output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolorBbox;"
- else
- output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolor;"
- end
- end
- end
- for i=1,#listVoronoi do
- PointI = listCircumC[listVoronoi[i][1]]
- PointJ = listCircumC[listVoronoi[i][2]]
- output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u withcolor \\luameshmpcolorVoronoi;"
- end
- if(points=="points") then
- j=1
- for i=1,#listPoints do
- if(listPoints[i].type == "bbox") then
- output = output .. "dotlabel.llft (btex $\\MeshPoint^{*}_{"..j.."}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolorBbox ;"
- j=j+1
- else
- output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolor ;"
- end
- end
- for i=1,#listCircumC do
- output = output .. "dotlabel.llft (btex $\\CircumPoint_{" .. i .. "}$ etex, (" .. listCircumC[i].x ..",".. listCircumC[i].y .. ")*u ) withcolor \\luameshmpcolorVoronoi ;"
- end
- else
- j=1
- for i=1,#listPoints do
- if(listPoints[i].type == "bbox") then
- output = output .. "drawdot (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u withcolor \\luameshmpcolorBbox withpen pencircle scaled 3;"
- j=j+1
- else
- output = output .. "drawdot (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u withcolor \\luameshmpcolor withpen pencircle scaled 3;"
+-- 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
- end
- for i=1,#listCircumC do
- output = output .. "drawdot (" .. listCircumC[i].x ..",".. listCircumC[i].y .. ")*u withcolor \\luameshmpcolorVoronoi withpen pencircle scaled 3;"
+ k=k+n
end
end
-
- return output
-end
-
-
-
--- buildVoronoi with MP
-function buildVoronoiMPBW(chaine,mode,points,bbox,scale,tri)
- listPoints = buildList(chaine, mode)
- triangulation = BowyerWatson(listPoints,bbox)
- listVoronoi = buildVoronoi(listPoints, triangulation)
- output = traceVoronoiMP(listPoints,triangulation,listVoronoi,points,tri)
- output = "\\leavevmode\\begin{mplibcode}beginfig(0);u:="..scale.. ";" .. output .."endfig;\\end{mplibcode}"
- tex.sprint(output)
+ return newPolygon
end
+-- function to build a gridpoints from the bounding box
+-- with a prescribed
+function buildGrid(listPoints,h)
+ -- listPoints : list of the points of the polygon, ordered
+ -- h : parameter for the grid
+ xmin, xmax, ymin, ymax = BoundingBox(listPoints)
-
--- trace a triangulation with TikZ
-function traceMeshTikZ(listPoints, triangulation,points,color,colorBbox)
- output = ""
- for i=1,#listPoints do
- output = output .. "\\coordinate (MeshPoints".. i .. ") at (" .. 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]]
- if(triangulation[i].type == "bbox") then
- output = output .. "\\draw[color="..colorBbox.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
- else
- output = output .. "\\draw[color="..color.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
- end
- end
- if(points=="points") then
- j=1
- for i=1,#listPoints do
- if(listPoints[i].type == "bbox") then
- output = output .. "\\draw[color="..colorBbox.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint^*_{" .. j .. "}$};"
- j=j+1
- else
- output = output .. "\\draw[color="..color.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};"
- end
- end
- end
- return output
+ local grid = rectangleList(xmin,xmax,ymin,ymax,h)
+ return grid
end
-
--- trace a triangulation with MP
-function traceMeshMP(listPoints, triangulation,points)
- output = "";
- output = output .. " pair MeshPoints[];"
- for i=1,#listPoints do
- output = output .. "MeshPoints[".. i .. "] = (" .. listPoints[i].x .. "," .. listPoints[i].y .. ")*u;"
- end
-
- for i=1,#triangulation do
- PointI = listPoints[triangulation[i][1]]
- PointJ = listPoints[triangulation[i][2]]
- PointK = listPoints[triangulation[i][3]]
- if(triangulation[i].type == "bbox") then
- output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolorBbox;"
- else
- output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolor;"
- end
- end
- if(points=="points") then
- j=1
- for i=1,#listPoints do
- if(listPoints[i].type == "bbox") then
- output = output .. "dotlabel.llft (btex $\\MeshPoint^{*}_{"..j.."}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolorBbox ;"
- j=j+1
- else
- output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolor ;"
- end
+-- function to build the list of points in the rectangle
+function rectangleList(xmin,xmax,ymin,ymax,h)
+ 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
+ listPoints[k] = {x = xmin+(i-1)*h, y=ymin+(j-1)*h}
+ k=k+1
end
end
- return output
-end
-
-
--- buildMesh with MP
-function buildMeshMPBW(chaine,mode,points,bbox,scale)
- listPoints = buildList(chaine, mode)
- triangulation = BowyerWatson(listPoints,bbox)
- output = traceMeshMP(listPoints, triangulation,points)
- output = "\\leavevmode\\begin{mplibcode}beginfig(0);u:="..scale.. ";" .. output .."endfig;\\end{mplibcode}"
- tex.sprint(output)
-end
-
--- buildMesh with MP include code
-function buildMeshMPBWinc(chaine,beginning, ending,mode,points,bbox,scale)
- listPoints = buildList(chaine, mode)
- triangulation = BowyerWatson(listPoints,bbox)
- output = traceMeshMP(listPoints, triangulation,points)
- output = "\\leavevmode\\begin{mplibcode}u:="..scale..";"..beginning .. output .. ending .. "\\end{mplibcode}"
- tex.sprint(output)
-end
-
--- buildMesh with TikZ
-function buildMeshTikZBW(chaine,mode,points,bbox,scale,color,colorBbox)
- listPoints = buildList(chaine, mode)
- triangulation = BowyerWatson(listPoints,bbox)
- output = traceMeshTikZ(listPoints, triangulation,points,color,colorBbox)
- output = "\\noindent\\begin{tikzpicture}[x=" .. scale .. ",y=" .. scale .."]" .. output .."\\end{tikzpicture}"
- tex.sprint(output)
-end
-
--- buildMesh with TikZ
-function buildMeshTikZBWinc(chaine,beginning, ending,mode,points,bbox,scale,color,colorBbox)
- listPoints = buildList(chaine, mode)
- triangulation = BowyerWatson(listPoints,bbox)
- output = traceMeshTikZ(listPoints, triangulation,points,color,colorBbox)
- output = "\\noindent\\begin{tikzpicture}[x=" .. scale .. ",y=" .. scale .."]" ..beginning.. output..ending .."\\end{tikzpicture}"
- tex.sprint(output)
+ return listPoints
end
--- print points of the mesh
-function tracePointsMP(listPoints,points)
- output = "";
- output = output .. " pair MeshPoints[];"
- for i=1,#listPoints do
- output = output .. "MeshPoints[".. i .. "] = (" .. listPoints[i].x .. "," .. listPoints[i].y .. ")*u;"
- end
- if(points=="points") then
- j=1
- for i=1,#listPoints do
- if(listPoints[i].type == "bbox") then
- output = output .. "dotlabel.llft (btex $\\MeshPoint^{*}_{" .. j .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolorBbox ;"
- j=j+1
- else
- output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolor ;"
- end
- end
- else
- for i=1,#listPoints do
- if(listPoints[i].type == "bbox") then
- output = output .. "drawdot (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u withcolor \\luameshmpcolorBbox withpen pencircle scaled 3;"
- else
- output = output .. "drawdot (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u withcolor \\luameshmpcolor withpen pencircle scaled 3;"
- end
- end
- end
- return output
-end
-
--- print points of the mesh
-function tracePointsTikZ(listPoints,points,color,colorBbox)
- output = "";
- for i=1,#listPoints do
- output = output .. "\\coordinate (MeshPoints".. i .. ") at (" .. listPoints[i].x .. "," .. listPoints[i].y .. ");"
- end
- if(points=="points") then
- j=1
- for i=1,#listPoints do
- if(listPoints[i].type == "bbox") then
- output = output .. "\\draw[color="..colorBbox.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint^*_{" .. j .. "}$};"
- j = j+1
- else
- output = output .. "\\draw[color="..color.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};"
- end
- end
- else
- for i=1,#listPoints do
- if(listPoints[i].type == "bbox") then
- output = output .. "\\draw[color="..colorBbox.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} ;"
- else
- output = output .. "\\draw[color="..color.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} ;"
- end
+-- 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
- return output
-end
-
--- print points to mesh
-function printPointsMP(chaine,mode,points,bbox,scale)
- listPoints = buildList(chaine, mode)
- if(bbox == "bbox" ) then
- listPoints = buildBoundingBox(listPoints)
- end
- output = tracePointsMP(listPoints,points)
- output = "\\leavevmode\\begin{mplibcode}beginfig(0);u:="..scale.. ";" .. output .."endfig;\\end{mplibcode}"
- tex.sprint(output)
-end
-
-
--- print points to mesh
-function printPointsMPinc(chaine,beginning, ending, mode,points,bbox,scale)
- listPoints = buildList(chaine, mode)
- if(bbox == "bbox" ) then
- listPoints = buildBoundingBox(listPoints)
- end
- output = tracePointsMP(listPoints,points)
- output = "\\leavevmode\\begin{mplibcode}u:="..scale..";"..beginning .. output .. ending .. "\\end{mplibcode}"
- tex.sprint(output)
-end
-
--- print points to mesh
-function printPointsTikZ(chaine,mode,points,bbox,scale,color,colorBbox)
- listPoints = buildList(chaine, mode)
- if(bbox == "bbox" ) then
- listPoints = buildBoundingBox(listPoints)
- end
- output = tracePointsTikZ(listPoints,points,color,colorBbox)
- output = "\\noindent\\begin{tikzpicture}[x=" .. scale .. ",y=" .. scale .."]" .. output .."\\end{tikzpicture}"
- tex.sprint(output)
-end
-
-
--- print points to mesh
-function printPointsTikZinc(chaine,beginning, ending, mode,points,bbox,scale,color,colorBbox)
- listPoints = buildList(chaine, mode)
- if(bbox == "bbox" ) then
- listPoints = buildBoundingBox(listPoints)
- end
- output = tracePointsTikZ(listPoints,points,color,colorBbox)
- output = "\\noindent\\begin{tikzpicture}[x=" .. scale .. ",y=" .. scale .."]" ..beginning.. output..ending .."\\end{tikzpicture}"
- 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
-
-local function shallowCopy(original)
- local copy = {}
- for key, value in pairs(original) do
- copy[key] = value
- end
- return copy
-end
-- function give a real polygon without repeting points
function cleanPoly(polygon)
- polyNew = {}
- polyCopy = shallowCopy(polygon)
+ local polyNew = {}
+ local polyCopy = shallowCopy(polygon)
e1 = polyCopy[1][1]
e2 = polyCopy[1][2]
table.insert(polyNew, e1)
return polyNew
end
---
-function TeXaddOnePointTikZ(listPoints,P,step,bbox,color,colorBack, colorNew, colorCircle,colorBbox)
- output = ""
- -- build the triangulation
- triangulation = BowyerWatson(listPoints,bbox)
- badTriangles = buildBadTriangles(P,triangulation)
- for i=1,#listPoints do
- output = output .. "\\coordinate (MeshPoints".. i .. ") at (" .. 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]]
- if(triangulation[i].type == "bbox") then
- output = output .. "\\draw[color="..colorBbox.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
- else
- output = output .. "\\draw[color="..color.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
- end
- 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
- j=1
- for i=1,#listPoints do
- if(listPoints[i].type == "bbox") then
- output = output .. "\\draw[color="..colorBbox.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint^*_{" .. j .. "}$};"
- j = j+1
- else
- output = output .. "\\draw[color="..color.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};"
- end
- 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]]
- if(triangulation[i].type == "bbox") then
- output = output .. "\\draw[color="..colorBbox.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
- else
- output = output .. "\\draw[color="..color.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
- end
- 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
- j=1
- for i=1,#listPoints do
- if(listPoints[i].type == "bbox") then
- output = output .. "\\draw[color="..colorBbox.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint^*_{" .. j .. "}$};"
- j=j+1
- else
- output = output .. "\\draw[color="..color.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};"
- end
- 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]]
- if(triangulation[i].type == "bbox") then
- output = output .. "\\draw[color="..colorBbox.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
- else
- output = output .. "\\draw[color="..color.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
- end
- 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
- j=1
- for i=1,#listPoints do
- if(listPoints[i].type == "bbox") then
- output = output .. "\\draw[color="..colorBbox.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint^*_{" .. j .. "}$};"
- j=j+1
- else
- output = output .. "\\draw[color="..color.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};"
- end
- 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 TeXaddOnePointMPBW(listPoints,P,step,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 .. ")*u;"
- 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]]
- if(triangulation[i].type == "bbox") then
- output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolorBbox;"
- else
- output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolor;"
- end
- 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 \\luameshmpcolor;"
- output = output .. "fill (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolorBack;"
- 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 \\luameshmpcolorCircle;"
- end
- -- mark the points
- j=1
- for i=1,#listPoints do
- if(listPoints[i].type == "bbox") then
- output = output .. "dotlabel.llft (btex $\\MeshPoint^{*}_{" .. j .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolorBbox ;"
- j=j+1
- else
- output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolor ;"
- end
- end
- -- mark the point to add
- output = output .. "dotlabel.llft (btex $\\NewPoint$ etex,(" .. P.x ..",".. P.y .. ")*u) withcolor \\luameshmpcolorNew;"
- 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]]
- if(triangulation[i].type == "bbox") then
- output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolorBbox;"
- else
- output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolor;"
- end
- 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 \\luameshmpcolorBack;"
- output = output .. "draw " .. path .. "cycle withcolor \\luameshmpcolorNew withpen pencircle scaled 1pt;"
- -- mark the points of the mesh
- j=1
- for i=1,#listPoints do
- if(listPoints[i].type == "bbox") then
- output = output .. "dotlabel.llft (btex $\\MeshPoint^{*}_{" .. j .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolorBbox ;"
- j=j+1
- else
- output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolor ;"
- end
- end
- -- mark the adding point
- output = output .. "dotlabel.llft (btex $\\NewPoint$ etex,(" .. P.x ..",".. P.y .. ")*u) withcolor \\luameshmpcolorNew ;"
- 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]]
- if(triangulation[i].type == "bbox") then
- output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolorBbox;"
- else
- output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolor;"
- end
- 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 \\luameshmpcolorBack;"
- -- 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 \\luameshmpcolorNew withpen pencircle scaled 1pt;"
- output = output .. "draw".."(".. listPoints[polygon[i][1]].x .. "," .. listPoints[polygon[i][1]].y .. ")*u -- (" .. P.x .. "," .. P.y ..")*u withcolor \\luameshmpcolorNew withpen pencircle scaled 1pt;"
- output = output .. "draw".."(".. listPoints[polygon[i][2]].x .. "," .. listPoints[polygon[i][2]].y .. ")*u -- (" .. P.x .. "," .. P.y ..")*u withcolor \\luameshmpcolorNew withpen pencircle scaled 1pt;"
- end
- -- mark points
- j=1
- for i=1,#listPoints do
- if(listPoints[i].type == "bbox") then
- output = output .. "dotlabel.llft (btex $\\MeshPoint^{*}_{" .. j .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolorBbox ;"
- j=j+1
- else
- output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolor ;"
- end
- end
- -- mark the added point
- output = output .. "dotlabel.llft (btex $\\NewPoint$ etex,(" .. P.x ..",".. P.y .. ")*u) withcolor \\luameshmpcolorNew ;"
- 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 TeXOnePointTikZBW(chaine,point,step,scale,mode,bbox,color,colorBack,colorNew,colorCircle,colorBbox)
- 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 = TeXaddOnePointTikZ(listPoints,P,step,bbox,color,colorBack,colorNew,colorCircle,colorBbox)
- output = "\\noindent\\begin{tikzpicture}[x="..scale..",y="..scale.."]".. output .. "\\end{tikzpicture}"
- tex.sprint(output)
-end
-
-function TeXOnePointTikZBWinc(chaine,point,beginning, ending,step,scale,mode,bbox,color,colorBack,colorNew,colorCircle,colorBbox)
- 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))
+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
- output = TeXaddOnePointTikZ(listPoints,P,step,bbox,color,colorBack,colorNew,colorCircle,colorBbox)
- output = "\\noindent\\begin{tikzpicture}[x="..scale..",y="..scale.."]".. beginning..output ..ending.. "\\end{tikzpicture}"
- tex.sprint(output)
-end
-
-function TeXOnePointMPBW(chaine,point,step,scale,mode,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))
+ if last_end <= #pString then
+ cap = pString:sub(last_end)
+ table.insert(Table, cap)
end
- output = TeXaddOnePointMPBW(listPoints,P,step,bbox)
- output = "\\leavevmode\\begin{mplibcode}beginfig(0);u:="..scale..";".. output .. "endfig;\\end{mplibcode}"
- tex.sprint(output)
+ return Table
end
-function TeXOnePointMPBWinc(chaine,point,beginning,ending,step,scale,mode,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))
+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
- output = TeXaddOnePointMPBW(listPoints,P,step,bbox)
- output = "\\begin{mplibcode}u:="..scale..";"..beginning .. output .. ending .. "\\end{mplibcode}"
- tex.sprint(output)
+ return listPoints, triangulation
end