X-Git-Url: https://melusine.eu.org/syracuse/G/git/?a=blobdiff_plain;f=luamesh.lua;h=a2c26086189c80146385103cb7c1591a6341827d;hb=299267d3c929e2afe9bd34ec2617b1ccbf79e14d;hp=ad6ec6fcc11d96029fcfb132de9d4ee9cb98ac35;hpb=879d59ce1be390214fb7c0364c44c3fc1acff916;p=delaunay.git diff --git a/luamesh.lua b/luamesh.lua index ad6ec6f..a2c2608 100644 --- a/luamesh.lua +++ b/luamesh.lua @@ -1,3 +1,5 @@ +require "polygon-luamesh" + -- Bowyer and Watson algorithm -- Delaunay meshing function BowyerWatson (listPoints,bbox) @@ -207,6 +209,81 @@ function circoncircle(M, N, P) return Out, rad -- (center [Point], R [float]) end +-- compute the list of the circumcircle of a triangulation +function listCircumCenter(listPoints,triangulation) + 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) + listCircumCircle = listCircumCenter(listPoints, triangulation) + 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 @@ -252,18 +329,216 @@ function rectangleList(a,b,nbrA,nbrB) return listPoints end + +-- trace Voronoi with MP +function traceVoronoiMP(listPoints, triangulation,listVoronoi, points, tri,styleD,styleV) + if(styleD == "dashed") then + sDelaunay = "dashed evenly" + else + sDelaunay = "" + end + if(styleV == "dashed") then + sVoronoi = "dashed evenly" + else + sVoronoi = "" + end + 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 "..sDelaunay.." withcolor \\luameshmpcolorBbox;" + else + output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle "..sDelaunay.." 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 "..sVoronoi.." 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;" + end + end + for i=1,#listCircumC do + output = output .. "drawdot (" .. listCircumC[i].x ..",".. listCircumC[i].y .. ")*u withcolor \\luameshmpcolorVoronoi withpen pencircle scaled 3;" + end + end + + return output +end + + +-- trace Voronoi with TikZ +function traceVoronoiTikZ(listPoints, triangulation,listVoronoi, points, tri,color,colorBbox,colorVoronoi,styleD,styleV) + if(styleD == "dashed") then + sDelaunay = ",dashed" + else + sDelaunay = "" + end + if(styleV == "dashed") then + sVoronoi = ",dashed" + else + sVoronoi = "" + end + listCircumC = listCircumCenter(listPoints,triangulation) + output = "" + for i=1,#listPoints do + output = output .. "\\coordinate (MeshPoints".. i .. ") at (" .. listPoints[i].x .. "," .. listPoints[i].y .. ");" + end + for i=1,#listCircumC do + output = output .. "\\coordinate (CircumPoints".. i .. ") at (" .. listCircumC[i].x .. "," .. listCircumC[i].y .. ");" + 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[color="..colorBbox..sDelaunay.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;" + else + output = output .. "\\draw[color="..color..sDelaunay.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;" + end + end + end + for i=1,#listVoronoi do + PointI = listCircumC[listVoronoi[i][1]] + PointJ = listCircumC[listVoronoi[i][2]] + output = output .. "\\draw[color="..colorVoronoi..sVoronoi.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.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 + for i=1,#listCircumC do + output = output .. "\\draw[color="..colorVoronoi.."] (" .. listCircumC[i].x ..",".. listCircumC[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\CircumPoint_{" .. i .. "}$};" + end + else + 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 {$\\bullet$} ;" + j=j+1 + else + output = output .. "\\draw[color="..color.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} ;" + end + end + for i=1,#listCircumC do + output = output .. "\\draw[color="..colorVoronoi.."] (" .. listCircumC[i].x ..",".. listCircumC[i].y .. ") node {$\\bullet$};" + end + end + return output +end + + + +-- buildVoronoi with MP +function buildVoronoiMPBW(chaine,mode,points,bbox,scale,tri,styleD,styleV) + listPoints = buildList(chaine, mode) + triangulation = BowyerWatson(listPoints,bbox) + listVoronoi = buildVoronoi(listPoints, triangulation) + output = traceVoronoiMP(listPoints,triangulation,listVoronoi,points,tri,styleD,styleV) + output = "\\leavevmode\\begin{mplibcode}beginfig(0);u:="..scale.. ";" .. output .."endfig;\\end{mplibcode}" + tex.sprint(output) +end + + +-- buildVoronoi with TikZ +function buildVoronoiTikZBW(chaine,mode,points,bbox,scale,tri,color,colorBbox,colorVoronoi,styleD,styleV) + listPoints = buildList(chaine, mode) + triangulation = BowyerWatson(listPoints,bbox) + listVoronoi = buildVoronoi(listPoints, triangulation) + output = traceVoronoiTikZ(listPoints,triangulation,listVoronoi,points,tri,color,colorBbox,colorVoronoi,styleD,styleV) + output = "\\noindent\\begin{tikzpicture}[x=" .. scale .. ",y=" .. scale .."]" .. output .."\\end{tikzpicture}" tex.sprint(output) +end + + +-- buildVoronoi with MP +function buildVoronoiMPBWinc(chaine,beginning, ending,mode,points,bbox,scale,tri,styleD,styleV) + listPoints = buildList(chaine, mode) + triangulation = BowyerWatson(listPoints,bbox) + listVoronoi = buildVoronoi(listPoints, triangulation) + output = traceVoronoiMP(listPoints,triangulation,listVoronoi,points,tri,styleD,styleV) + output = "\\leavevmode\\begin{mplibcode}u:="..scale..";"..beginning .. output .. ending .. "\\end{mplibcode}" + tex.sprint(output) +end + + +-- buildVoronoi with TikZ +function buildVoronoiTikZBWinc(chaine,beginning, ending,mode,points,bbox,scale,tri,color,colorBbox,colorVoronoi) + listPoints = buildList(chaine, mode,styleD,styleV) + triangulation = BowyerWatson(listPoints,bbox) + listVoronoi = buildVoronoi(listPoints, triangulation) + output = traceVoronoiTikZ(listPoints,triangulation,listVoronoi,points,tri,color,colorBbox,colorVoronoi,styleD,styleV) + output = "\\noindent\\begin{tikzpicture}[x=" .. scale .. ",y=" .. scale .."]" ..beginning.. output..ending .."\\end{tikzpicture}" + tex.sprint(output) +end + + + -- trace a triangulation with TikZ -function traceMeshTikZ(listPoints, triangulation,points,color) +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]] - output = output .. "\\draw[color="..color.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;" + 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 - output = output .. "\\draw[color=".."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};" + 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 @@ -275,9 +550,8 @@ 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 .. ");" + 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]] @@ -303,12 +577,49 @@ function traceMeshMP(listPoints, triangulation,points) 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) +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 .. ");" + output = output .. "MeshPoints[".. i .. "] = (" .. listPoints[i].x .. "," .. listPoints[i].y .. ")*u;" end if(points=="points") then j=1 @@ -323,36 +634,41 @@ function tracePointsMP(listPoints,points) else for i=1,#listPoints do if(listPoints[i].type == "bbox") then - output = output .. "drawdot (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolorBbox ;" + 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 ;" + output = output .. "drawdot (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u withcolor \\luameshmpcolor withpen pencircle scaled 3;" end end end return output 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}" +-- 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 - tex.sprint(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) + 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 + end + end + return output end -- print points to mesh @@ -374,20 +690,34 @@ function printPointsMPinc(chaine,beginning, ending, mode,points,bbox,scale) listPoints = buildBoundingBox(listPoints) end output = tracePointsMP(listPoints,points) - output = "\\begin{mplibcode}u:="..scale..";"..beginning .. output .. ending .. "\\end{mplibcode}" + 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 --- buildMesh with MP include code -function buildMeshMPBWinc(chaine,beginning, ending,mode,points,bbox,scale) + +-- print points to mesh +function printPointsTikZinc(chaine,beginning, ending, mode,points,bbox,scale,color,colorBbox) listPoints = buildList(chaine, mode) - triangulation = BowyerWatson(listPoints,bbox) - output = traceMeshMP(listPoints, triangulation,points) - output = "\\begin{mplibcode}u:="..scale..";"..beginning .. output .. ending .. "\\end{mplibcode}" + 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) end + -- buildMesh function buildRect(largeur,a,b,nbrA, nbrB) listPoints = rectangleList(a,b,nbrA,nbrB) @@ -417,7 +747,6 @@ function cleanPoly(polygon) i=1 find = false while (i<=#polyCopy and find==false) do - i = i+1 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] @@ -433,27 +762,32 @@ function cleanPoly(polygon) 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} +function TeXaddOnePointTikZ(listPoints,P,step,bbox,color,colorBack, colorNew, colorCircle,colorBbox) output = "" - listPoints = buildList(chaine, "int") -- build the triangulation - triangulation = BowyerWatson(listPoints,"none") + 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]] - output = output .. "\\draw[color="..color.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;" + 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 @@ -471,8 +805,14 @@ function TeXaddOnePointTikZ(chaine,point,step,color,colorBack, colorNew, colorCi output = output .. "\\draw[dashed, color="..colorCircle.."] ("..center.x .. "," .. center.y .. ") circle ("..radius ..");" end -- mark the points + j=1 for i=1,#listPoints do - output = output .. "\\draw[color ="..color.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};" + 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] {$\\NewPoint$};" @@ -488,7 +828,11 @@ function TeXaddOnePointTikZ(chaine,point,step,color,colorBack, colorNew, colorCi 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;" + 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 = "" @@ -498,8 +842,14 @@ function TeXaddOnePointTikZ(chaine,point,step,color,colorBack, colorNew, colorCi end output = output .. "\\draw[color="..colorNew..",fill ="..colorBack..", thick] " .. path .. "cycle;" -- mark the points of the mesh + j=1 for i=1,#listPoints do - output = output .. "\\draw[color="..color.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};" + 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] {$\\NewPoint$};" @@ -515,7 +865,11 @@ function TeXaddOnePointTikZ(chaine,point,step,color,colorBack, colorNew, colorCi 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;" + 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 = "" @@ -531,8 +885,14 @@ function TeXaddOnePointTikZ(chaine,point,step,color,colorBack, colorNew, colorCi 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 - output = output .. "\\draw[color="..color.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};" + 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] {$\\NewPoint$};" @@ -547,7 +907,7 @@ function TeXaddOnePointMPBW(listPoints,P,step,bbox) triangulation = BowyerWatson(listPoints,bbox) badTriangles = buildBadTriangles(P,triangulation) for i=1,#listPoints do - output = output .. "MeshPoints[".. i .. "] = (" .. listPoints[i].x .. "," .. listPoints[i].y .. ");" + output = output .. "MeshPoints[".. i .. "] = (" .. listPoints[i].x .. "," .. listPoints[i].y .. ")*u;" end if(step == "badT") then -- draw all triangle @@ -691,12 +1051,34 @@ function buildListExt(chaine, stop) end -function TeXOnePointTikZ(chaine,point,step,color,colorBack,colorNew,colorCircle,scale) - output = TeXaddOnePointTikZ(chaine,point,step,color,colorBack,colorNew,colorCircle) +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)) + 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,"%((.+),(.+)%)") @@ -724,3 +1106,139 @@ function TeXOnePointMPBWinc(chaine,point,beginning,ending,step,scale,mode,bbox) output = "\\begin{mplibcode}u:="..scale..";"..beginning .. output .. ending .. "\\end{mplibcode}" tex.sprint(output) end + + +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 readGmsh(file) + io.input(file) -- open the file + text=io.read("*all") + local lines = split(text,"\n+") -- all the lines + listPoints={} + 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 + return listPoints, triangulation +end + +function drawGmshMP(file,points,scale) + listPoints,triangulation = readGmsh(file) + output = traceMeshMP(listPoints,triangulation,points) + output = "\\leavevmode\\begin{mplibcode}beginfig(0);u:="..scale.. ";" .. output .."endfig;\\end{mplibcode}" + tex.sprint(output) +end + +function drawGmshMPinc(file,beginning,ending,points,scale) + listPoints,triangulation = readGmsh(file) + output = traceMeshMP(listPoints,triangulation,points) + output = "\\leavevmode\\begin{mplibcode}u:="..scale..";"..beginning .. output .. ending .. "\\end{mplibcode}" + tex.sprint(output) +end + + + +-- +function drawGmshTikZ(file,points,scale,color) + listPoints,triangulation = readGmsh(file) + output = traceMeshTikZ(listPoints, triangulation,points,color,colorBbox) + output = "\\noindent\\begin{tikzpicture}[x=" .. scale .. ",y=" .. scale .."]" .. output .."\\end{tikzpicture}" + tex.sprint(output) +end + +-- +function drawGmshTikZinc(file,beginning, ending,points,scale,color) + listPoints,triangulation = readGmsh(file) + output = traceMeshTikZ(listPoints, triangulation,points,color,colorBbox) + output = "\\noindent\\begin{tikzpicture}[x=" .. scale .. ",y=" .. scale .."]" ..beginning.. output..ending .."\\end{tikzpicture}" + tex.sprint(output) +end + + +-- buildVoronoi with MP +function gmshVoronoiMP(file,points,scale,tri,styleD,styleV) + listPoints,triangulation = readGmsh(file) + listVoronoi = buildVoronoi(listPoints, triangulation) + output = traceVoronoiMP(listPoints,triangulation,listVoronoi,points,tri,styleD,styleV) + output = "\\leavevmode\\begin{mplibcode}beginfig(0);u:="..scale.. ";" .. output .."endfig;\\end{mplibcode}" + tex.sprint(output) +end + + +-- buildVoronoi with TikZ +function gmshVoronoiTikZ(file,points,scale,tri,color,colorVoronoi,styleD,styleV) + listPoints,triangulation = readGmsh(file) + listVoronoi = buildVoronoi(listPoints, triangulation) + output = traceVoronoiTikZ(listPoints,triangulation,listVoronoi,points,tri,color,colorBbox,colorVoronoi,styleD,styleV) + output = "\\noindent\\begin{tikzpicture}[x=" .. scale .. ",y=" .. scale .."]" .. output .."\\end{tikzpicture}" tex.sprint(output) +end + + +-- buildVoronoi with MP +function gmshVoronoiMPinc(file,beginning, ending,points,scale,tri,styleD,styleV) + listPoints,triangulation = readGmsh(file) + listVoronoi = buildVoronoi(listPoints, triangulation) + output = traceVoronoiMP(listPoints,triangulation,listVoronoi,points,tri,styleD,styleV) + output = "\\leavevmode\\begin{mplibcode}u:="..scale..";"..beginning .. output .. ending .. "\\end{mplibcode}" + tex.sprint(output) +end + + +-- buildVoronoi with TikZ +function gmshVoronoiTikZinc(file,beginning, ending,points,scale,tri,color,colorVoronoi,styleD,styleV) + listPoints,triangulation = readGmsh(file) + listVoronoi = buildVoronoi(listPoints, triangulation) + output = traceVoronoiTikZ(listPoints,triangulation,listVoronoi,points,tri,color,colorBbox,colorVoronoi,styleD,styleV) + output = "\\noindent\\begin{tikzpicture}[x=" .. scale .. ",y=" .. scale .."]" ..beginning.. output..ending .."\\end{tikzpicture}" + tex.sprint(output) +end