-- add four points to listPoints to have a bounding box
listPoints = buildBoundingBox(listPoints)
-- the first triangle
- triangulation[1] = {lgth+1, lgth+2, lgth+3}
+ triangulation[1] = {lgth+1, lgth+2, lgth+3,type="bbox"}
-- the second triangle
- triangulation[2] = {lgth+1, lgth+3, lgth+4}
+ triangulation[2] = {lgth+1, lgth+3, lgth+4,type="bbox"}
-- add points one by one
for i=1,lgth do
-- find the triangles which the circumcircle contained the point to add
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})
+ if((polygon[j][1]>lgth) or (polygon[j][2]>lgth) or (i>lgth)) then
+ table.insert(triangulation,{polygon[j][1],polygon[j][2],i,type="bbox"})
+ else
+ table.insert(triangulation,{polygon[j][1],polygon[j][2],i,type="in"})
+ end
end
end -- end adding points of the listPoints
-- remove bounding box
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})
+ table.insert(listPoints,{x=xmin,y=ymin,type="bbox"})
+ table.insert(listPoints,{x=xmin,y=ymax,type="bbox"})
+ table.insert(listPoints,{x=xmax,y=ymax,type="bbox"})
+ table.insert(listPoints,{x=xmax,y=ymin,type="bbox"})
return listPoints
end
-- trace a triangulation with MP
-function traceMeshMP(listPoints, triangulation,points,color)
+function traceMeshMP(listPoints, triangulation,points)
output = "";
output = output .. " pair MeshPoints[];"
for i=1,#listPoints 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.. "};"
+ 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
- output = output .. "dotlabel.llft( btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u) withcolor \\mpcolor{"..color.. "};"
+ 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
+ return 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 .. ");"
+ 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 ;"
+ else
+ output = output .. "drawdot (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolor ;"
+ end
end
end
return output
-- buildMesh with MP
-function buildMeshMPBW(chaine,mode,points,bbox,full,scale,color)
+function buildMeshMPBW(chaine,mode,points,bbox,scale)
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
+ output = traceMeshMP(listPoints, triangulation,points)
+ output = "\\leavevmode\\begin{mplibcode}beginfig(0);u:="..scale.. ";" .. output .."endfig;\\end{mplibcode}"
+ tex.sprint(output)
+end
+
+-- print points to mesh
+function printPointsMP(chaine,mode,points,bbox,scale)
+ listPoints = buildList(chaine, mode)
+ if(bbox == "bbox" ) then
+ listPoints = buildBoundingBox(listPoints)
+ end
+ output = tracePointsMP(listPoints,points)
+ output = "\\leavevmode\\begin{mplibcode}beginfig(0);u:="..scale.. ";" .. output .."endfig;\\end{mplibcode}"
+ tex.sprint(output)
+end
+
+
+-- print points to mesh
+function printPointsMPinc(chaine,beginning, ending, mode,points,bbox,scale)
+ listPoints = buildList(chaine, mode)
+ if(bbox == "bbox" ) then
+ listPoints = buildBoundingBox(listPoints)
end
+ output = tracePointsMP(listPoints,points)
+ output = "\\begin{mplibcode}u:="..scale..";"..beginning .. output .. ending .. "\\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 = "\\begin{mplibcode}u:="..scale..";"..beginning .. output .. ending .. "\\end{mplibcode}"
tex.sprint(output)
end
traceTikZ(listPoints, triangulation,largeur,"none")
end
+local function shallowCopy(original)
+ local copy = {}
+ for key, value in pairs(original) do
+ copy[key] = value
+ end
+ return copy
+end
-- function give a real polygon without repeting points
function cleanPoly(polygon)
polyNew = {}
- e1 = polygon[1][1]
- e2 = polygon[1][2]
+ polyCopy = shallowCopy(polygon)
+ e1 = polyCopy[1][1]
+ e2 = polyCopy[1][2]
table.insert(polyNew, e1)
table.insert(polyNew, e2)
+ table.remove(polyCopy,1)
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
+ while #polyCopy>1 do
+ 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]
+ if(not bool1) then
+ table.insert(polyNew, polyCopy[i][1])
+ find = true
+ table.remove(polyCopy,i)
+ j = j+1
+ elseif(not bool2) then
+ table.insert(polyNew, polyCopy[i][2])
+ find = true
+ table.remove(polyCopy,i)
+ j = j+1
+ end
end
end
end
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 \\luameshmpcolor;"
+ 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
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
- output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolor;"
+ 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;"
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 \\luameshmpcolor;"
+ 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 = ""
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
- output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolor ;"
+ 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 ;"
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 \\luameshmpcolor ;"
+ 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 = ""
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
- output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolor ;"
+ 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 ;"
tex.sprint(output)
end
-function TeXOnePointMPBW(chaine,point,step,scale,mode,picture,bbox)
+function TeXOnePointMPBW(chaine,point,step,scale,mode,bbox)
if(mode=="int") then
Sx,Sy=string.match(point,"%((.+),(.+)%)")
P = {x=Sx, y=Sy}
tex.sprint(output)
end
-function TeXOnePointMPBWinc(chaine,point,beginning,ending,step,scale,mode,picture,bbox)
+function TeXOnePointMPBWinc(chaine,point,beginning,ending,step,scale,mode,bbox)
if(mode=="int") then
Sx,Sy=string.match(point,"%((.+),(.+)%)")
P = {x=Sx, y=Sy}