--- /dev/null
+-- Bowyer and Watson algorithm
+-- Delaunay meshing
+function BowyerWatson (listPoints,bbox)
+ local triangulation = {}
+ local lgth = #listPoints
+ -- add four points to listPoints to have a bounding box
+ listPoints = buildBoundingBox(listPoints)
+ -- the first triangle
+ triangulation[1] = {lgth+1, lgth+2, lgth+3}
+ -- the second triangle
+ triangulation[2] = {lgth+1, lgth+3, lgth+4}
+ -- 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)
+ -- build the polygon of the cavity containing the point to add
+ polygon = buildCavity(badTriangles, triangulation)
+ -- remove the bad triangles
+ for j=1,#badTriangles do
+ table.remove(triangulation,badTriangles[j]-(j-1))
+ end
+ -- build the new triangles and add them to triangulation
+ for j=1,#polygon do
+ table.insert(triangulation,{polygon[j][1],polygon[j][2],i})
+ end
+ end -- end adding points of the listPoints
+ -- remove bounding box
+ if(bbox ~= "bbox") then
+ triangulation = removeBoundingBox(triangulation,lgth)
+ table.remove(listPoints,lgth+1)
+ table.remove(listPoints,lgth+1)
+ table.remove(listPoints,lgth+1)
+ table.remove(listPoints,lgth+1)
+ end
+ return triangulation
+end
+
+
+function buildBoundingBox(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
+ -- add points of the bounding box in last positions
+ table.insert(listPoints,{x=xmin,y=ymin})
+ table.insert(listPoints,{x=xmin,y=ymax})
+ table.insert(listPoints,{x=xmax,y=ymax})
+ table.insert(listPoints,{x=xmax,y=ymin})
+ return listPoints
+end
+
+function removeBoundingBox(triangulation,lgth)
+ -- build the four bounding box edge
+ point1 = lgth+1
+ point2 = lgth+2
+ point3 = lgth+3
+ point4 = lgth+4
+ -- for all triangle
+ newTriangulation = {}
+ for i=1,#triangulation do
+ boolE1 = pointInTriangle(point1,triangulation[i])
+ boolE2 = pointInTriangle(point2,triangulation[i])
+ boolE3 = pointInTriangle(point3,triangulation[i])
+ boolE4 = pointInTriangle(point4,triangulation[i])
+ if((not boolE1) and (not boolE2) and (not boolE3) and (not boolE4)) then
+ table.insert(newTriangulation,triangulation[i])
+ end
+ end
+ return newTriangulation
+end
+
+
+function buildBadTriangles(point, triangulation)
+ badTriangles = {}
+ for j=1,#triangulation do -- for all triangles
+ A = listPoints[triangulation[j][1]]
+ B = listPoints[triangulation[j][2]]
+ C = listPoints[triangulation[j][3]]
+ center, radius = circoncircle(A,B,C)
+ CP = Vector(center,point)
+ if(VectorNorm(CP)<radius) then -- the point belongs to the circoncirle
+ table.insert(badTriangles,j)
+ end
+ end
+ return badTriangles
+end
+
+-- construction of the cavity composed by the bad triangles around the point to add
+function buildCavity(badTriangles, triangulation)
+ polygon = {}
+ for j=1,#badTriangles do -- for all bad triangles
+ ind = badTriangles[j]
+ for k=1,3 do -- for all edges
+ edge = {triangulation[ind][k],triangulation[ind][k%3+1]}
+ edgeBord = false
+ for l = 1,#badTriangles do -- for all badtriangles
+ badInd = badTriangles[l]
+ if(badInd ~= ind) then -- if not the current one
+ edgeBord = edgeBord or edgeInTriangle(edge,triangulation[badInd])
+ end
+ end --
+ -- if the edge does not belong to another bad triangle
+ if(edgeBord == false) then
+ -- insert the edge to the cavity
+ table.insert(polygon,edge)
+ end
+ end --
+ end --
+ return polygon
+end
+
+function edgeInTriangle(e,t)
+ in1 = false
+ in2 = false
+ for i=1,3 do
+ if e[1] == t[i] then
+ in1 = true
+ end
+ if e[2] == t[i] then
+ in2 = true
+ end
+ end
+ out = (in1 and in2)
+ return out
+end
+
+function pointInTriangle(e,t)
+ in1 = false
+ for i=1,3 do
+ if e == t[i] then
+ in1 = true
+ end
+ end
+ return in1
+end
+
+
+function Vector(A,B)
+ local out = {x = B.x - A.x, y = B.y - A.y}
+ return out
+end
+
+function VectorNorm(NP)
+ return math.sqrt(NP.x*NP.x +NP.y*NP.y)
+end
+
+-- circoncircle
+function circoncircle(M, N, P)
+ -- Compute center and radius of the circoncircle of the triangle M N P
+
+ -- return : (center [Point],radius [float])
+
+ local MN = Vector(M,N)
+ local NP = Vector(N,P)
+ local PM = Vector(P,M)
+ m = VectorNorm(NP) -- |NP|
+ n = VectorNorm(PM) -- |PM|
+ p = VectorNorm(MN) -- |MN|
+
+ d = (m + n + p) * (-m + n + p) * (m - n + p) * (m + n - p)
+ if d > 0 then
+ rad = m * n * p / math.sqrt(d)
+ else
+ rad = 0
+ end
+ d = -2 * (M.x * NP.y + N.x * PM.y + P.x * MN.y)
+ O = {x=0, y=0}
+ OM = Vector(O, M)
+ ON = Vector(O, N)
+ OP = Vector(O, P)
+ om2 = math.pow(VectorNorm(OM),2) -- |OM|**2
+ on2 = math.pow(VectorNorm(ON),2) -- |ON|**2
+ op2 = math.pow(VectorNorm(OP),2) -- |OP|**2
+ x0 = -(om2 * NP.y + on2 * PM.y + op2 * MN.y) / d
+ y0 = (om2 * NP.x + on2 * PM.x + op2 * MN.x) / d
+ if d == 0 then
+ Out = {nil, nil}
+ else
+ Out = {x=x0, y=y0}
+ end
+ return Out, rad -- (center [Point], R [float])
+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 = {}
+ if mode == "int" then
+ local points = string.explode(chaine, ";")
+ local lgth=#points
+ for i=1,lgth do
+ Sx,Sy=string.match(points[i],"%((.+),(.+)%)")
+ listPoints[i]={x=tonumber(Sx),y=tonumber(Sy)}
+ end
+ elseif mode == "ext" then
+ io.input(chaine) -- open the file
+ text=io.read("*all")
+ lines=string.explode(text,"\n+") -- all the lines
+ tablePoints={}
+ for i=1,#lines do
+ xy=string.explode(lines[i]," +")
+ listPoints[i]={x=tonumber(xy[1]),y=tonumber(xy[2])}
+ end
+ else
+ print("Non existing mode")
+ end
+ return listPoints
+end
+
+
+--
+function rectangleList(a,b,nbrA,nbrB)
+ stepA = a/nbrA
+ stepB = b/nbrB
+ listPoints = {}
+ k=1
+ for i=1,(nbrA+1) do
+ for j=1,(nbrB+1) do
+ listPoints[k] = {x = (i-1)*stepA, y=(j-1)*stepB}
+ k=k+1
+ end
+ end
+ return listPoints
+end
+
+-- trace a triangulation with TikZ
+function traceMeshTikZ(listPoints, triangulation,points,color)
+ output = ""
+ for i=1,#triangulation do
+ PointI = listPoints[triangulation[i][1]]
+ PointJ = listPoints[triangulation[i][2]]
+ PointK = listPoints[triangulation[i][3]]
+ output = output .. "\\draw[color="..color.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
+ end
+ if(points=="points") then
+ for i=1,#listPoints do
+ output = output .. "\\draw[color=".."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};"
+ end
+ end
+ return output
+end
+
+
+-- trace a triangulation with MP
+function traceMeshMP(listPoints, triangulation,points,color)
+ output = "";
+ output = output .. " pair MeshPoints[];"
+ for i=1,#listPoints do
+ output = output .. "MeshPoints[".. i .. "] = (" .. listPoints[i].x .. "," .. listPoints[i].y .. ");"
+ end
+
+ for i=1,#triangulation do
+ PointI = listPoints[triangulation[i][1]]
+ PointJ = listPoints[triangulation[i][2]]
+ PointK = listPoints[triangulation[i][3]]
+ output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\mpcolor{"..color.. "};"
+ end
+ if(points=="points") then
+ for i=1,#listPoints do
+ output = output .. "dotlabel.llft( btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u) withcolor \\mpcolor{"..color.. "};"
+ end
+ end
+ return output
+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}"
+ end
+ tex.sprint(output)
+end
+
+
+-- buildMesh with MP
+function buildMeshMP(chaine,mode,points,bbox,full,scale,color)
+ listPoints = buildList(chaine, mode)
+ triangulation = BowyerWatson(listPoints,bbox)
+ output = traceMeshMP(listPoints, triangulation,points,color)
+ if(full=="full") then
+ output = "\\leavevmode\\begin{mplibcode}beginfig(0);u:="..scale.. ";" .. output .."endfig;\\end{mplibcode}"
+ else
+ output = "u:="..scale.. ";".. output
+ end
+ tex.sprint(output)
+end
+
+-- buildMesh
+function buildRect(largeur,a,b,nbrA, nbrB)
+ listPoints = rectangleList(a,b,nbrA,nbrB)
+ triangulation = BowyerWatson(listPoints,"none")
+ traceTikZ(listPoints, triangulation,largeur,"none")
+end
+
+
+-- function give a real polygon without repeting points
+function cleanPoly(polygon)
+ polyNew = {}
+ e1 = polygon[1][1]
+ e2 = polygon[1][2]
+ table.insert(polyNew, e1)
+ table.insert(polyNew, e2)
+ j = 2
+ for i=2,#polygon do
+ bool1 = (polygon[i][1] == polyNew[j])
+ bool2 = (polygon[i][2] == polyNew[j])
+ if(bool1 or bool2) then -- the edge has a common point with polyNew[j]
+ if(not bool1) then
+ table.insert(polyNew, polygon[i][1])
+ j = j+1
+ elseif(not bool2) then
+ table.insert(polyNew, polygon[i][2])
+ j = j+1
+ end
+ end
+ end
+ return polyNew
+end
+
+--
+function TeXaddOnePointTikZ(chaine,point,step,color,colorBack, colorNew, colorCircle)
+ Sx,Sy=string.match(point,"%((.+),(.+)%)")
+ P = {x=Sx, y=Sy}
+ output = ""
+ listPoints = buildList(chaine, "int")
+ -- build the triangulation
+ triangulation = BowyerWatson(listPoints,"none")
+ badTriangles = buildBadTriangles(P,triangulation)
+ if(step == "badT") then
+ -- draw all triangle
+ for i=1,#triangulation do
+ PointI = listPoints[triangulation[i][1]]
+ PointJ = listPoints[triangulation[i][2]]
+ PointK = listPoints[triangulation[i][3]]
+ output = output .. "\\draw[color="..color.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
+ end
+ -- draw and fill the bad triangle
+ for i=1,#badTriangles do
+ PointI = listPoints[triangulation[badTriangles[i]][1]]
+ PointJ = listPoints[triangulation[badTriangles[i]][2]]
+ PointK = listPoints[triangulation[badTriangles[i]][3]]
+ output = output .. "\\draw[fill="..colorBack.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
+ end
+ -- draw the circoncircle
+ for i=1,#badTriangles do
+ PointI = listPoints[triangulation[badTriangles[i]][1]]
+ PointJ = listPoints[triangulation[badTriangles[i]][2]]
+ PointK = listPoints[triangulation[badTriangles[i]][3]]
+ center, radius = circoncircle(PointI, PointJ, PointK)
+ output = output .. "\\draw[dashed, color="..colorCircle.."] ("..center.x .. "," .. center.y .. ") circle ("..radius ..");"
+ end
+ -- mark the points
+ for i=1,#listPoints do
+ output = output .. "\\draw[color ="..color.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};"
+ end
+ -- mark the point to add
+ output = output .. "\\draw[color="..colorNew.."] (" .. P.x ..",".. P.y .. ") node {$\\bullet$} node[anchor=north east] {$\\NewPoint$};"
+ elseif(step == "cavity") then
+ polygon = buildCavity(badTriangles, triangulation)
+ polyNew = cleanPoly(polygon)
+ -- remove the bad triangles
+ for j=1,#badTriangles do
+ table.remove(triangulation,badTriangles[j]-(j-1))
+ end
+ -- draw the triangles
+ for i=1,#triangulation do
+ PointI = listPoints[triangulation[i][1]]
+ PointJ = listPoints[triangulation[i][2]]
+ PointK = listPoints[triangulation[i][3]]
+ output = output .. "\\draw[color="..color.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
+ end
+ -- fill and draw the cavity
+ path = ""
+ for i=1,#polyNew do
+ PointI = listPoints[polyNew[i]]
+ path = path .. "(".. PointI.x ..",".. PointI.y ..")--"
+ end
+ output = output .. "\\draw[color="..colorNew..",fill ="..colorBack..", thick] " .. path .. "cycle;"
+ -- mark the points of the mesh
+ for i=1,#listPoints do
+ output = output .. "\\draw[color="..color.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};"
+ end
+ -- mark the adding point
+ output = output .. "\\draw[color="..colorNew.."] (" .. P.x ..",".. P.y .. ") node {$\\bullet$} node[anchor=north east] {$\\NewPoint$};"
+ elseif(step == "newT") then
+ polygon = buildCavity(badTriangles, triangulation)
+ polyNew = cleanPoly(polygon)
+ -- remove the bad triangles
+ for j=1,#badTriangles do
+ table.remove(triangulation,badTriangles[j]-(j-1))
+ end
+ -- draw the triangle of the triangulation
+ for i=1,#triangulation do
+ PointI = listPoints[triangulation[i][1]]
+ PointJ = listPoints[triangulation[i][2]]
+ PointK = listPoints[triangulation[i][3]]
+ output = output .. "\\draw[color ="..color.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
+ end
+ -- fill and draw the cavity
+ path = ""
+ for i=1,#polyNew do
+ PointI = listPoints[polyNew[i]]
+ path = path .. "(".. PointI.x ..",".. PointI.y ..")--"
+ end
+ output = output .. "\\draw[color="..colorNew..",fill ="..colorBack..", thick] " .. path .. "cycle;"
+ -- draw the new triangles composed by the edges of the polygon and the added point
+ for i=1,#polygon do
+ output = output .. "\\draw[color=TeXCluaMeshNewTikZ, thick]".."(".. listPoints[polygon[i][1]].x .. "," .. listPoints[polygon[i][1]].y .. ") -- (" .. listPoints[polygon[i][2]].x .. "," .. listPoints[polygon[i][2]].y ..");"
+ output = output .. "\\draw[color="..colorNew..", thick]".."(".. listPoints[polygon[i][1]].x .. "," .. listPoints[polygon[i][1]].y .. ") -- (" .. P.x .. "," .. P.y ..");"
+ output = output .. "\\draw[color="..colorNew..", thick]".."(".. listPoints[polygon[i][2]].x .. "," .. listPoints[polygon[i][2]].y .. ") -- (" .. P.x .. "," .. P.y ..");"
+ end
+ -- mark points
+ for i=1,#listPoints do
+ output = output .. "\\draw[color="..color.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};"
+ end
+ -- mark the added point
+ output = output .. "\\draw[color="..colorNew.."] (" .. P.x ..",".. P.y .. ") node {$\\bullet$} node[anchor=north east] {$\\NewPoint$};"
+ end
+ return output
+end
+
+function TeXaddOnePointMP(listPoints,P,step,color,colorBack, colorNew, colorCircle)
+ output = "";
+ output = output .. "pair MeshPoints[];"
+ -- build the triangulation
+ triangulation = BowyerWatson(listPoints,"none")
+ badTriangles = buildBadTriangles(P,triangulation)
+ for i=1,#listPoints do
+ output = output .. "MeshPoints[".. i .. "] = (" .. listPoints[i].x .. "," .. listPoints[i].y .. ");"
+ end
+ if(step == "badT") then
+ -- draw all triangle
+ for i=1,#triangulation do
+ PointI = listPoints[triangulation[i][1]]
+ PointJ = listPoints[triangulation[i][2]]
+ PointK = listPoints[triangulation[i][3]]
+ output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\mpcolor{" .. color .."};"
+ 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 \\mpcolor{" .. color .."};"
+ output = output .. "fill (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\mpcolor{" .. colorBack .."};"
+ 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 \\mpcolor{" .. colorCircle .."};"
+ end
+ -- mark the points
+ for i=1,#listPoints do
+ output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\mpcolor{" .. color .."};"
+ end
+ -- mark the point to add
+ output = output .. "dotlabel.llft (btex $\\NewPoint$ etex,(" .. P.x ..",".. P.y .. ")*u) withcolor \\mpcolor{" .. colorNew .."};"
+ elseif(step == "cavity") then
+ polygon = buildCavity(badTriangles, triangulation)
+ polyNew = cleanPoly(polygon)
+ -- remove the bad triangles
+ for j=1,#badTriangles do
+ table.remove(triangulation,badTriangles[j]-(j-1))
+ end
+ -- draw the triangles
+ for i=1,#triangulation do
+ PointI = listPoints[triangulation[i][1]]
+ PointJ = listPoints[triangulation[i][2]]
+ PointK = listPoints[triangulation[i][3]]
+ output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\mpcolor{" .. color .."};"
+ 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 \\mpcolor{" .. colorBack .."};"
+ output = output .. "draw " .. path .. "cycle withcolor \\mpcolor{" .. colorNew .."} withpen pencircle scaled 1pt;"
+ -- mark the points of the mesh
+ for i=1,#listPoints do
+ output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\mpcolor{" .. color .."};"
+ end
+ -- mark the adding point
+ output = output .. "dotlabel.llft (btex $\\NewPoint$ etex,(" .. P.x ..",".. P.y .. ")*u) withcolor \\mpcolor{" .. colorNew .."};"
+ elseif(step == "newT") then
+ polygon = buildCavity(badTriangles, triangulation)
+ polyNew = cleanPoly(polygon)
+ -- remove the bad triangles
+ for j=1,#badTriangles do
+ table.remove(triangulation,badTriangles[j]-(j-1))
+ end
+ -- draw the triangle of the triangulation
+ for i=1,#triangulation do
+ PointI = listPoints[triangulation[i][1]]
+ PointJ = listPoints[triangulation[i][2]]
+ PointK = listPoints[triangulation[i][3]]
+ output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\mpcolor{" .. color .."};"
+ 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 \\mpcolor{" .. colorBack .."};"
+ -- 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 \\mpcolor{" .. colorNew .."} withpen pencircle scaled 1pt;"
+ output = output .. "draw".."(".. listPoints[polygon[i][1]].x .. "," .. listPoints[polygon[i][1]].y .. ")*u -- (" .. P.x .. "," .. P.y ..")*u withcolor \\mpcolor{" .. colorNew .."} withpen pencircle scaled 1pt;"
+ output = output .. "draw".."(".. listPoints[polygon[i][2]].x .. "," .. listPoints[polygon[i][2]].y .. ")*u -- (" .. P.x .. "," .. P.y ..")*u withcolor \\mpcolor{" .. colorNew .."} withpen pencircle scaled 1pt;"
+ end
+ -- mark points
+ for i=1,#listPoints do
+ output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\mpcolor{" .. color .."};"
+ end
+ -- mark the added point
+ output = output .. "dotlabel.llft (btex $\\NewPoint$ etex,(" .. P.x ..",".. P.y .. ")*u) withcolor \\mpcolor{ " .. colorNew .."};"
+ end
+ return output
+end
+
+
+-- build the list of points extern and stop at nbr
+function buildListExt(chaine, stop)
+ listPoints = {}
+ io.input(chaine) -- open the file
+ text=io.read("*all")
+ lines=string.explode(text,"\n+") -- all the lines
+ for i=1,tonumber(stop) do
+ xy=string.explode(lines[i]," +")
+ table.insert(listPoints,{x=tonumber(xy[1]),y=tonumber(xy[2])})
+ end
+ xy=string.explode(lines[stop+1]," +")
+ point={x=tonumber(xy[1]),y=tonumber(xy[2])}
+ return point, listPoints
+end
+
+
+function TeXFullOnePointTikZ(chaine,point,step,color,colorBack,colorNew,colorCircle,scale)
+ output = TeXaddOnePointTikZ(chaine,point,step,color,colorBack,colorNew,colorCircle)
+ output = "\\noindent\\begin{tikzpicture}[x="..scale..",y="..scale.."]".. output .. "\\end{tikzpicture}"
+ tex.sprint(output)
+end
+
+function TeXFullOnePointMP(chaine,point,step,color,colorBack,colorNew,colorCircle,scale,mode)
+ if(mode=="int") then
+ Sx,Sy=string.match(point,"%((.+),(.+)%)")
+ P = {x=Sx, y=Sy}
+ listPoints = buildList(chaine, mode)
+ else
+ -- point is a number
+ P, listPoints = buildListExt(chaine,tonumber(point))
+ end
+ output = TeXaddOnePointMP(listPoints,P,step,color,colorBack,colorNew,colorCircle)
+ output = "\\leavevmode\\begin{mplibcode}beginfig(0);u:="..scale..";".. output .. "endfig;\\end{mplibcode}"
+ tex.sprint(output)
+end
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Projets / delaunay.git / commitdiff
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