X-Git-Url: https://melusine.eu.org/syracuse/G/git/?a=blobdiff_plain;f=luamesh.lua;h=af3da3109fb9cf72d1d8e2a14f5f433dad74b9d0;hb=81576bf772cf5a397a9a380eb6f30b97270710c5;hp=c8ffc51bcd1191173754c0d8e06784d9c75e83a6;hpb=f86b1ec82bbbba1a96989bb5d6f5b78e261659a1;p=delaunay.git diff --git a/luamesh.lua b/luamesh.lua index c8ffc51..af3da31 100644 --- a/luamesh.lua +++ b/luamesh.lua @@ -207,6 +207,81 @@ 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 @@ -252,9 +327,157 @@ function rectangleList(a,b,nbrA,nbrB) 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;" + 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) + 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.."] (".. 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 + end + for i=1,#listVoronoi do + PointI = listCircumC[listVoronoi[i][1]] + PointJ = listCircumC[listVoronoi[i][2]] + output = output .. "\\draw[color="..colorVoronoi.."] (".. 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 + 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 + 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) + 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) +end + + +-- buildVoronoi with TikZ +function buildVoronoiTikZBW(chaine,mode,points,bbox,scale,tri,color,colorBbox,colorVoronoi) + listPoints = buildList(chaine, mode) + triangulation = BowyerWatson(listPoints,bbox) + listVoronoi = buildVoronoi(listPoints, triangulation) + output = traceVoronoiTikZ(listPoints,triangulation,listVoronoi,points,tri,color,colorBbox,colorVoronoi) + output = "\\noindent\\begin{tikzpicture}[x=" .. scale .. ",y=" .. scale .."]" .. output .."\\end{tikzpicture}" tex.sprint(output) +end + + + -- 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]] @@ -266,9 +489,11 @@ function traceMeshTikZ(listPoints, triangulation,points,color,colorBbox) 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] {$\\MeshPoint_{" .. i .. "}$};" + 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 @@ -283,7 +508,7 @@ 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 @@ -353,7 +578,7 @@ 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 @@ -380,10 +605,15 @@ 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] {$\\MeshPoint_{" .. i .. "}$};" + 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 @@ -419,7 +649,7 @@ 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 @@ -498,11 +728,14 @@ function cleanPoly(polygon) end -- -function TeXaddOnePointTikZ(chaine,point,step,color,colorBack, colorNew, colorCircle,colorBbox) +function TeXaddOnePointTikZ(listPoints,P,step,bbox,color,colorBack, colorNew, colorCircle,colorBbox) output = "" -- 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 @@ -531,9 +764,11 @@ 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 if(listPoints[i].type == "bbox") then - output = output .. "\\draw[color="..colorBbox.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};" + 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 @@ -566,9 +801,11 @@ 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 if(listPoints[i].type == "bbox") then - output = output .. "\\draw[color="..colorBbox.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};" + 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 @@ -607,9 +844,11 @@ 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 if(listPoints[i].type == "bbox") then - output = output .. "\\draw[color="..colorBbox.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};" + 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 @@ -627,7 +866,7 @@ 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 @@ -780,7 +1019,7 @@ function TeXOnePointTikZBW(chaine,point,step,scale,mode,bbox,color,colorBack,col -- point is a number P, listPoints = buildListExt(chaine,tonumber(point)) end - output = TeXaddOnePointTikZ(chaine,point,step,color,colorBack,colorNew,colorCircle,colorBbox) + 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 @@ -794,7 +1033,7 @@ function TeXOnePointTikZBWinc(chaine,point,beginning, ending,step,scale,mode,bbo -- point is a number P, listPoints = buildListExt(chaine,tonumber(point)) end - output = TeXaddOnePointTikZ(chaine,point,step,color,colorBack,colorNew,colorCircle,colorBbox) + 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