Première version Voronoi avec MetaPost

diff --git a/luamesh.lua b/luamesh.lua
index 26a3cbf..4d255a1 100644 (file)
--- 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
@@ -252,6 +327,81 @@ 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
+
+
+
+-- 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
+
+
+
 -- trace a triangulation with TikZ
 function traceMeshTikZ(listPoints, triangulation,points,color,colorBbox)
    output = ""

diff --git a/luamesh.sty b/luamesh.sty
index ae3db83..de6d9e7 100644 (file)
--- a/luamesh.sty
+++ b/luamesh.sty
@@ -153,6 +153,138 @@
   %
   \fi%
 }%
+%%%%%%%%%%%%%%%% the buildVoronoi command
+%% the user can write code (tikz or MP)
+%% before and after the generated code
+\define@boolkey{buildVoronoiInc}{tikz}[true]{}%
+%% show the bounding box for delaunay
+\define@choicekey*{buildVoronoiInc}{bbox}[\val\nr]{none, show}{%
+  \ifcase\nr\relax%
+  \def\luameshval@bvi@bbox{none}%
+  \or%
+  \def\luameshval@bvi@bbox{bbox}%
+  \fi%
+}%
+%% the scale
+\define@key{buildVoronoiInc}{scale}[1cm]{\def\luameshval@bvi@scale{#1}}%
+%% print ponits ?
+\define@choicekey*{buildVoronoiInc}{print}[\val\nr]{none, points}{%
+  \ifcase\nr\relax%
+  \def\luameshval@bvi@print{none}%
+  \or%
+  \def\luameshval@bvi@print{points}%
+  \fi%
+}%
+%% the name of the point
+\define@key{buildVoronoiInc}{meshpoint}[P]{\def\luameshval@bvi@meshpoint{#1}}%
+%% the mode for reading the points
+\define@choicekey*{buildVoronoiInc}{mode}[\val\nr]{int, ext}{%
+  \ifcase\nr\relax%
+  \def\luameshval@bvi@mode{int}%
+  \or%
+  \def\luameshval@bvi@mode{ext}%
+  \fi%
+}%
+%% the name of the color of drawing
+\define@key{buildVoronoiInc}{color}[black]{\def\luameshval@bvi@color{#1}}%
+%% the name of the color of drawing the bbox
+\define@key{buildVoronoiInc}{colorBbox}[black]{\def\luameshval@bvi@colorbbox{#1}}%
+%
+\presetkeys{buildVoronoiInc}{tikz=false,bbox=none,scale, meshpoint,mode=int,print=none,color,colorBbox}{}%
+%
+\newcommand*{\buildVoronoiBWinc}[4][]{%
+  % #1 : optionnal arguments
+  % #2 : the string containing the list of points
+  % (x1,y1);(x2,y2);... or the name file containing the points
+  % #3 : the code to place before the generated one
+  % #4 : the code to place after the generated one
+  \setkeys{buildVoronoiInc}{#1} %
+  \def\MeshPoint{\luameshval@bvi@meshpoint}%
+  \ifKV@buildVoronoiInc@tikz% if we are using tikz
+  \directlua{%
+    buildVoronoiTikZBWinc("#2","\luaescapestring{\unexpanded{#3}}","\luaescapestring{\unexpanded{#4}}","\luameshval@bvi@mode","\luameshval@bvi@print","\luameshval@bvi@bbox","\luameshval@bvi@scale","\luameshval@bvi@color","\luameshval@bvi@colorbbox")%
+  }%
+  \else % we are using MP
+  \mplibcolor{\luameshmpcolor}{\luameshval@bvi@color}%
+  \mplibcolor{\luameshmpcolorBbox}{\luameshval@bvi@colorbbox}%
+  \directlua{%
+    buildVoronoiMPBWinc("#2","\luaescapestring{\unexpanded{#3}}","\luaescapestring{\unexpanded{#4}}","\luameshval@bvi@mode","\luameshval@bvi@print","\luameshval@bvi@bbox","\luameshval@bvi@scale")%
+  }%
+  %
+  \fi%
+}%
+%
+%%%%%%%%%%%%%%%% the buildVoronoiBW command
+%% the code is complete and we don't have any callbacks
+\define@boolkey{buildVoronoi}{tikz}[true]{}%
+%% show the bounding box for delaunay
+\define@choicekey*{buildVoronoi}{bbox}[\val\nr]{none, show}{%
+  \ifcase\nr\relax%
+  \def\luameshval@bv@bbox{none}%
+  \or%
+  \def\luameshval@bv@bbox{bbox}%
+  \fi%
+}%
+%% the scale
+\define@key{buildVoronoi}{scale}[1cm]{\def\luameshval@bv@scale{#1}}%
+%% print points
+\define@choicekey*{buildVoronoi}{print}[\val\nr]{none, points}{%
+  \ifcase\nr\relax%
+  \def\luameshval@bv@print{none}%
+  \or%
+  \def\luameshval@bv@print{points}%
+  \fi%
+}%
+%% the name of the point
+\define@key{buildVoronoi}{meshpoint}[P]{\def\luameshval@bv@meshpoint{#1}}%
+%% the name of the circum point
+\define@key{buildVoronoi}{circumpoint}[P]{\def\luameshval@bv@circumpoint{#1}}%
+%% the mode for reading the points
+\define@choicekey*{buildVoronoi}{mode}[\val\nr]{int, ext}{%
+  \ifcase\nr\relax%
+  \def\luameshval@bv@mode{int}%
+  \or%
+  \def\luameshval@bv@mode{ext}%
+  \fi%
+}%
+%% the mode for reading the points
+\define@choicekey*{buildVoronoi}{delaunay}[\val\nr]{none, show}{%
+  \ifcase\nr\relax%
+  \def\luameshval@bv@delaunay{none}%
+  \or%
+  \def\luameshval@bv@delaunay{show}%
+  \fi%
+}%
+%% the name of the color of drawing
+\define@key{buildVoronoi}{color}[black]{\def\luameshval@bv@color{#1}}%
+%% the name of the color of drawing Voronoi
+\define@key{buildVoronoi}{colorVoronoi}[red]{\def\luameshval@bv@colorVoronoi{#1}}%
+%% the name of the color of drawing the bbox
+\define@key{buildVoronoi}{colorBbox}[black]{\def\luameshval@bv@colorbbox{#1}}%
+%
+\presetkeys{buildVoronoi}{tikz=false,bbox=none,scale, meshpoint,circumpoint,mode=int,print=none,color,colorVoronoi,colorBbox,delaunay=none}{}%
+%
+\newcommand{\buildVoronoiBW}[2][]{%
+  % #1 : optionnal arguments
+  % #2 : the string containing the list of points
+  % (x1,y1);(x2,y2);... or the name file containing the points
+  \setkeys{buildVoronoi}{#1} %
+  \def\MeshPoint{\luameshval@bv@meshpoint}%
+  \def\CircumPoint{\luameshval@bv@circumpoint}%
+  \ifKV@buildVoronoi@tikz% if we are using tikz
+  \directlua{%
+    buildVoronoiTikZBW("#2","\luameshval@bv@mode","\luameshval@bv@print","\luameshval@bv@bbox","\luameshval@bv@scale","\luameshval@bv@color","\luameshval@bv@colorbbox")%
+  }%
+  \else % we are using MP
+  \mplibcolor{\luameshmpcolor}{\luameshval@bv@color}%
+  \mplibcolor{\luameshmpcolorBbox}{\luameshval@bv@colorbbox}%
+  \mplibcolor{\luameshmpcolorVoronoi}{\luameshval@bv@colorVoronoi}%
+  \directlua{%
+    buildVoronoiMPBW("#2","\luameshval@bv@mode","\luameshval@bv@print","\luameshval@bv@bbox","\luameshval@bv@scale","\luameshval@bv@delaunay")%
+  }%
+  %
+  \fi%
+}%
 %
 %
 %%%%%%%%%%%%%%%%% the draw Points macro

diff --git a/test/delaunay.pdf b/test/delaunay.pdf
index 33fcbbe..f208943 100644 (file)
Binary files a/test/delaunay.pdf and b/test/delaunay.pdf differ

diff --git a/test/delaunay.tex b/test/delaunay.tex
index 3229ba1..d79b5b7 100644 (file)
--- a/test/delaunay.tex
+++ b/test/delaunay.tex
@@ -139,4 +139,14 @@ colorBbox = black
 ]
 {(0,0);(3.5,3);(7,0);(7.5,5);(1.61,3.14);(6,4)}{(3,1)}
 
+
+% \def\CircumPoint{y}
+% \luampcolor
+% \directlua{
+%   buildVoronoiMP("mesh.txt","ext","points","","1cm","show")
+% }
+\buildVoronoiBW[mode=ext]{mesh.txt}
+\buildVoronoiBW[mode=ext,delaunay=show]{mesh.txt}\par
+\buildVoronoiBW[mode=ext,print=points,delaunay=show,bbox=show]{mesh.txt}
+
 \end{document}

diff --git a/test/test.lua b/test/test.lua
new file mode 100644 (file)
index 0000000..e4e9a91
--- /dev/null
+++ b/test/test.lua
@@ -0,0 +1,20 @@
+dofile('luamesh.lua')
+
+listPoints = {{x=0, y=0},{x=1,y=1},{x=1.7,y=0.8},{x=0.6, y=2},{x=3,y=0},{x=1.9,y=2.7}}
+print("list of Points")
+
+for i=1,#listPoints do
+   print(listPoints[i].x,listPoints[i].y)
+end
+
+triangulation = BowyerWatson(listPoints, "")
+print("triangualiton")
+for i=1,#triangulation do
+   print(triangulation[i][1],triangulation[i][2],triangulation[i][3])
+end
+
+listVoronoi = buildVoronoi(listPoints, triangulation)
+print("Voronoi")
+for i=1,#listVoronoi do
+   print(listVoronoi[i][1],listVoronoi[i][2])
+end