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|
-----------------------------------------------------------------------
-- FILE: luamesh-tex.lua
-- DESCRIPTION: functions of luamesh package to produce LaTeX code
-- AUTHOR: Maxime Chupin
-----------------------------------------------------------------------
-- 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)
local listPoints = buildList(chaine, mode)
local triangulation = BowyerWatson(listPoints,bbox)
local 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)
local listPoints = buildList(chaine, mode)
local triangulation = BowyerWatson(listPoints,bbox)
local 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)
local listPoints = buildList(chaine, mode)
local triangulation = BowyerWatson(listPoints,bbox)
local 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)
local listPoints = buildList(chaine, mode,styleD,styleV)
local triangulation = BowyerWatson(listPoints,bbox)
local 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,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
if(points=="dotpoints") 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 {$\\bullet$};"
j=j+1
else
output = output .. "\\draw[color="..color.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$};"
end
end
end
return output
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
end
end
if(points=="dotpoints") then
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
end
return output
end
-- buildMesh with MP
function buildMeshMPBW(chaine,mode,points,bbox,scale)
local listPoints = buildList(chaine, mode)
local 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)
local listPoints = buildList(chaine, mode)
local 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)
local listPoints = buildList(chaine, mode)
local 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)
local listPoints = buildList(chaine, mode)
local 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 .. ")*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
end
end
return output
end
-- print points to mesh
function printPointsMP(chaine,mode,points,bbox,scale)
local 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)
local 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)
local 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)
local 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)
end
-- buildMesh
function buildRect(largeur,a,b,nbrA, nbrB)
local listPoints = rectangleList(a,b,nbrA,nbrB)
local triangulation = BowyerWatson(listPoints,"none")
traceTikZ(listPoints, triangulation,largeur,"none")
end
--
function TeXaddOnePointTikZ(listPoints,P,step,bbox,color,colorBack, colorNew, colorCircle,colorBbox)
output = ""
-- build the triangulation
local triangulation = BowyerWatson(listPoints,bbox)
local badTriangles = buildBadTriangles(P,triangulation,listPoints)
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
local triangulation = {}
local badTriangles = {}
triangulation = BowyerWatson(listPoints,bbox)
badTriangles = buildBadTriangles(P,triangulation,listPoints)
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
function TeXOnePointTikZBW(chaine,point,step,scale,mode,bbox,color,colorBack,colorNew,colorCircle,colorBbox)
local listPoints = {}
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)
local listPoints = {}
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)
local listPoints = {}
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 = TeXaddOnePointMPBW(listPoints,P,step,bbox)
output = "\\leavevmode\\begin{mplibcode}beginfig(0);u:="..scale..";".. output .. "endfig;\\end{mplibcode}"
tex.sprint(output)
end
function TeXOnePointMPBWinc(chaine,point,beginning,ending,step,scale,mode,bbox)
local listPoints = {}
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 = TeXaddOnePointMPBW(listPoints,P,step,bbox)
output = "\\begin{mplibcode}u:="..scale..";"..beginning .. output .. ending .. "\\end{mplibcode}"
tex.sprint(output)
end
function drawGmshMP(file,points,scale)
local 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)
local 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)
local 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)
local 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)
local listPoints,triangulation = readGmsh(file)
local 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)
local listPoints,triangulation = readGmsh(file)
local 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)
local listPoints,triangulation = readGmsh(file)
local 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)
local listPoints,triangulation = readGmsh(file)
local 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
--------------------------------------------------
-- Meshing of a polygon --
--------------------------------------------------
function tracePolygonMP(polygon,points)
output = "";
output = output .. "pair polygon[];"
for i=1,#polygon do
output = output .. "polygon[".. i .. "] = (" .. polygon[i].x .. "," .. polygon[i].y .. ")*u;"
end
output = output .. "draw "
for i=1,#polygon do
output = output .. "(" .. polygon[i].x .. "," .. polygon[i].y .. ")*u -- "
end
output = output .. "cycle withcolor \\luameshmpcolorPoly withpen pencircle scaled 1pt;"
if(points=="points") then
for i=1,#polygon do
output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. polygon[i].x ..",".. polygon[i].y .. ")*u ) withcolor \\luameshmpcolorPoly ;"
end
end
if(points=="dotpoints") then
for i=1,#polygon do
output = output .. "drawdot (" .. polygon[i].x ..",".. polygon[i].y .. ")*u withcolor \\luameshmpcolorPoly withpen pencircle scaled 3;"
end
end
return output
end
function tracePolygonTikZ(polygon,points, colorPoly)
output = "";
for i=1,#polygon do
output = output .. "\\coordinate (polygon".. i .. ") at (" .. polygon[i].x .. "," .. polygon[i].y .. ");"
end
output = output .. "\\draw[color=".. colorPoly .. ", thick]"
for i=1,#polygon do
output = output .. "(" .. polygon[i].x .. "," .. polygon[i].y .. ") -- "
end
output = output .. "cycle;"
if(points=="points") then
for i=1,#polygon do
output = output .. "\\draw[color="..colorPoly.."] (" .. polygon[i].x ..",".. polygon[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};"
end
end
if(points=="dotpoints") then
for i=1,#polygon do
output = output .. "\\draw[color="..colorPoly.."] (" .. polygon[i].x ..",".. polygon[i].y .. ") node {$\\bullet$};"
end
end
return output
end
function drawMeshPolygonMP(chaine,mode,h,step,
points,scale,random)
local polygon = buildList(chaine, mode)
polygon = addPointsPolygon(polygon,h)
local grid = buildGrid(polygon,h,random)
local listPoints = addGridPoints(polygon,grid,h)
if(step=="polygon") then
-- the polygon
output = tracePolygonMP(polygon,points)
end
if(step=="grid") then
-- polygon + grid
output = tracePointsMP(grid,points)
output = output .. tracePolygonMP(polygon,points)
end
if(step=="points") then
-- polygon + only grid points inside the polygon
output = tracePointsMP(listPoints,points)
output = output .. tracePolygonMP(polygon,points)
end
if(step=="mesh") then
-- polygon + mesh
triangulation = BowyerWatson(listPoints,"none") -- no bbox
output = traceMeshMP(listPoints,triangulation,points)
output = output .. tracePolygonMP(polygon,points)
end
output = "\\leavevmode\\begin{mplibcode}beginfig(0);u:="..scale.. ";" .. output .."endfig;\\end{mplibcode}"
tex.sprint(output)
end
function drawMeshPolygonTikZ(chaine,mode,h,step,
points,scale,color,colorPoly,random)
local polygon = buildList(chaine, mode)
polygon = addPointsPolygon(polygon,h)
local grid = buildGrid(polygon,h,random)
local listPoints = addGridPoints(polygon,grid,h)
if(step=="polygon") then
-- the polygon
output = tracePolygonTikZ(polygon,points,colorPoly)
end
if(step=="grid") then
-- polygon + grid
output = tracePointsTikZ(grid,points,color,"none") -- none for colorBbox
output = output .. tracePolygonTikZ(polygon,points,colorPoly)
end
if(step=="points") then
-- polygon + only grid points inside the polygon
output = tracePointsTikZ(listPoints,points,color,"none")
output = output .. tracePolygonTikZ(polygon,points,colorPoly)
end
if(step=="mesh") then
-- polygon + mesh
triangulation = BowyerWatson(listPoints,"none") -- no bbox
output = traceMeshTikZ(listPoints,triangulation,points,color,"none")
output = output .. tracePolygonTikZ(polygon,points,colorPoly)
end
output = "\\noindent\\begin{tikzpicture}[x=" .. scale .. ",y=" .. scale .."]" .. output .."\\end{tikzpicture}"
tex.sprint(output)
end
function drawMeshPolygonMPinc(chaine,beginning,ending,mode,h,step,
points,scale,random)
local polygon = buildList(chaine, mode)
polygon = addPointsPolygon(polygon,h)
local grid = buildGrid(polygon,h,random)
local listPoints = addGridPoints(polygon,grid,h)
if(step=="polygon") then
-- the polygon
output = tracePolygonMP(polygon,points)
end
if(step=="grid") then
-- polygon + grid
output = tracePointsMP(grid,points)
output = output .. tracePolygonMP(polygon,points)
end
if(step=="points") then
-- polygon + only grid points inside the polygon
output = tracePointsMP(listPoints,points)
output = output .. tracePolygonMP(polygon,points)
end
if(step=="mesh") then
-- polygon + mesh
triangulation = BowyerWatson(listPoints,"none") -- no bbox
output = traceMeshMP(listPoints,triangulation,points)
output = output .. tracePolygonMP(polygon,points)
end
output = "\\begin{mplibcode}u:="..scale..";"..beginning .. output .. ending .. "\\end{mplibcode}"
tex.sprint(output)
end
function drawMeshPolygonTikZinc(chaine,beginning,ending,mode,h,step,
points,scale,color,colorPoly,random)
local polygon = buildList(chaine, mode)
polygon = addPointsPolygon(polygon,h)
local grid = buildGrid(polygon,h,random)
local listPoints = addGridPoints(polygon,grid,h)
if(step=="polygon") then
-- the polygon
output = tracePolygonTikZ(polygon,points,colorPoly)
end
if(step=="grid") then
-- polygon + grid
output = tracePointsTikZ(grid,points,color,"none") -- none for colorBbox
output = output .. tracePolygonTikZ(polygon,points,colorPoly)
end
if(step=="points") then
-- polygon + only grid points inside the polygon
output = tracePointsTikZ(listPoints,points,color,"none")
output = output .. tracePolygonTikZ(polygon,points,colorPoly)
end
if(step=="mesh") then
-- polygon + mesh
triangulation = BowyerWatson(listPoints,"none") -- no bbox
output = traceMeshTikZ(listPoints,triangulation,points,color,"none")
output = output .. tracePolygonTikZ(polygon,points,colorPoly)
end
output = "\\noindent\\begin{tikzpicture}[x="..scale..",y="..scale.."]".. beginning..output ..ending.. "\\end{tikzpicture}"
tex.sprint(output)
end
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