1 -- Bowyer and Watson algorithm
3 function BowyerWatson (listPoints,bbox)
4 local triangulation = {}
5 local lgth = #listPoints
6 -- add four points to listPoints to have a bounding box
7 listPoints = buildBoundingBox(listPoints)
9 triangulation[1] = {lgth+1, lgth+2, lgth+3,type="bbox"}
10 -- the second triangle
11 triangulation[2] = {lgth+1, lgth+3, lgth+4,type="bbox"}
12 -- add points one by one
14 -- find the triangles which the circumcircle contained the point to add
15 badTriangles = buildBadTriangles(listPoints[i],triangulation)
16 -- build the polygon of the cavity containing the point to add
17 polygon = buildCavity(badTriangles, triangulation)
18 -- remove the bad triangles
19 for j=1,#badTriangles do
20 table.remove(triangulation,badTriangles[j]-(j-1))
22 -- build the new triangles and add them to triangulation
24 if((polygon[j][1]>lgth) or (polygon[j][2]>lgth) or (i>lgth)) then
25 table.insert(triangulation,{polygon[j][1],polygon[j][2],i,type="bbox"})
27 table.insert(triangulation,{polygon[j][1],polygon[j][2],i,type="in"})
30 end -- end adding points of the listPoints
31 -- remove bounding box
32 if(bbox ~= "bbox") then
33 triangulation = removeBoundingBox(triangulation,lgth)
34 table.remove(listPoints,lgth+1)
35 table.remove(listPoints,lgth+1)
36 table.remove(listPoints,lgth+1)
37 table.remove(listPoints,lgth+1)
43 function buildBoundingBox(listPoints)
44 -- listPoints : list of points
45 -- epsV : parameter for the distance of the bounding box
46 local xmin, xmax, ymin, ymax, eps
51 for i=1,#listPoints do
52 if (listPoints[i].x < xmin) then
53 xmin = listPoints[i].x
55 if (listPoints[i].x > xmax) then
56 xmax = listPoints[i].x
58 if (listPoints[i].y < ymin) then
59 ymin = listPoints[i].y
61 if (listPoints[i].y > ymax) then
62 ymax = listPoints[i].y
65 eps = math.max(math.abs(xmax-xmin),math.abs(ymax-ymin))*0.15
70 -- add points of the bounding box in last positions
71 table.insert(listPoints,{x=xmin,y=ymin,type="bbox"})
72 table.insert(listPoints,{x=xmin,y=ymax,type="bbox"})
73 table.insert(listPoints,{x=xmax,y=ymax,type="bbox"})
74 table.insert(listPoints,{x=xmax,y=ymin,type="bbox"})
78 function removeBoundingBox(triangulation,lgth)
79 -- build the four bounding box edge
86 for i=1,#triangulation do
87 boolE1 = pointInTriangle(point1,triangulation[i])
88 boolE2 = pointInTriangle(point2,triangulation[i])
89 boolE3 = pointInTriangle(point3,triangulation[i])
90 boolE4 = pointInTriangle(point4,triangulation[i])
91 if((not boolE1) and (not boolE2) and (not boolE3) and (not boolE4)) then
92 table.insert(newTriangulation,triangulation[i])
95 return newTriangulation
99 function buildBadTriangles(point, triangulation)
101 for j=1,#triangulation do -- for all triangles
102 A = listPoints[triangulation[j][1]]
103 B = listPoints[triangulation[j][2]]
104 C = listPoints[triangulation[j][3]]
105 center, radius = circoncircle(A,B,C)
106 CP = Vector(center,point)
107 if(VectorNorm(CP)<radius) then -- the point belongs to the circoncirle
108 table.insert(badTriangles,j)
114 -- construction of the cavity composed by the bad triangles around the point to add
115 function buildCavity(badTriangles, triangulation)
117 for j=1,#badTriangles do -- for all bad triangles
118 ind = badTriangles[j]
119 for k=1,3 do -- for all edges
120 edge = {triangulation[ind][k],triangulation[ind][k%3+1]}
122 for l = 1,#badTriangles do -- for all badtriangles
123 badInd = badTriangles[l]
124 if(badInd ~= ind) then -- if not the current one
125 edgeBord = edgeBord or edgeInTriangle(edge,triangulation[badInd])
128 -- if the edge does not belong to another bad triangle
129 if(edgeBord == false) then
130 -- insert the edge to the cavity
131 table.insert(polygon,edge)
138 function edgeInTriangle(e,t)
153 function pointInTriangle(e,t)
165 local out = {x = B.x - A.x, y = B.y - A.y}
169 function VectorNorm(NP)
170 return math.sqrt(NP.x*NP.x +NP.y*NP.y)
174 function circoncircle(M, N, P)
175 -- Compute center and radius of the circoncircle of the triangle M N P
177 -- return : (center [Point],radius [float])
179 local MN = Vector(M,N)
180 local NP = Vector(N,P)
181 local PM = Vector(P,M)
182 m = VectorNorm(NP) -- |NP|
183 n = VectorNorm(PM) -- |PM|
184 p = VectorNorm(MN) -- |MN|
186 d = (m + n + p) * (-m + n + p) * (m - n + p) * (m + n - p)
188 rad = m * n * p / math.sqrt(d)
192 d = -2 * (M.x * NP.y + N.x * PM.y + P.x * MN.y)
197 om2 = math.pow(VectorNorm(OM),2) -- |OM|**2
198 on2 = math.pow(VectorNorm(ON),2) -- |ON|**2
199 op2 = math.pow(VectorNorm(OP),2) -- |OP|**2
200 x0 = -(om2 * NP.y + on2 * PM.y + op2 * MN.y) / d
201 y0 = (om2 * NP.x + on2 * PM.x + op2 * MN.x) / d
207 return Out, rad -- (center [Point], R [float])
211 -------------------------- TeX
212 -- build the list of points
213 function buildList(chaine, mode)
214 -- if mode = int : the list is given in the chaine string (x1,y1);(x2,y2);...;(xn,yn)
215 -- if mode = ext : the list is given in a file line by line with space separation
217 if mode == "int" then
218 local points = string.explode(chaine, ";")
221 Sx,Sy=string.match(points[i],"%((.+),(.+)%)")
222 listPoints[i]={x=tonumber(Sx),y=tonumber(Sy)}
224 elseif mode == "ext" then
225 io.input(chaine) -- open the file
227 lines=string.explode(text,"\n+") -- all the lines
230 xy=string.explode(lines[i]," +")
231 listPoints[i]={x=tonumber(xy[1]),y=tonumber(xy[2])}
234 print("Non existing mode")
241 function rectangleList(a,b,nbrA,nbrB)
248 listPoints[k] = {x = (i-1)*stepA, y=(j-1)*stepB}
255 -- trace a triangulation with TikZ
256 function traceMeshTikZ(listPoints, triangulation,points,color,colorBbox)
258 for i=1,#triangulation do
259 PointI = listPoints[triangulation[i][1]]
260 PointJ = listPoints[triangulation[i][2]]
261 PointK = listPoints[triangulation[i][3]]
262 if(triangulation[i].type == "bbox") then
263 output = output .. "\\draw[color="..colorBbox.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
265 output = output .. "\\draw[color="..color.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
268 if(points=="points") then
269 for i=1,#listPoints do
270 if(listPoints[i].type == "bbox") then
271 output = output .. "\\draw[color="..colorBbox.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};"
273 output = output .. "\\draw[color="..color.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};"
281 -- trace a triangulation with MP
282 function traceMeshMP(listPoints, triangulation,points)
284 output = output .. " pair MeshPoints[];"
285 for i=1,#listPoints do
286 output = output .. "MeshPoints[".. i .. "] = (" .. listPoints[i].x .. "," .. listPoints[i].y .. ");"
289 for i=1,#triangulation do
290 PointI = listPoints[triangulation[i][1]]
291 PointJ = listPoints[triangulation[i][2]]
292 PointK = listPoints[triangulation[i][3]]
293 if(triangulation[i].type == "bbox") then
294 output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolorBbox;"
296 output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolor;"
299 if(points=="points") then
301 for i=1,#listPoints do
302 if(listPoints[i].type == "bbox") then
303 output = output .. "dotlabel.llft (btex $\\MeshPoint^{*}_{"..j.."}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolorBbox ;"
306 output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolor ;"
315 function buildMeshMPBW(chaine,mode,points,bbox,scale)
316 listPoints = buildList(chaine, mode)
317 triangulation = BowyerWatson(listPoints,bbox)
318 output = traceMeshMP(listPoints, triangulation,points)
319 output = "\\leavevmode\\begin{mplibcode}beginfig(0);u:="..scale.. ";" .. output .."endfig;\\end{mplibcode}"
323 -- buildMesh with MP include code
324 function buildMeshMPBWinc(chaine,beginning, ending,mode,points,bbox,scale)
325 listPoints = buildList(chaine, mode)
326 triangulation = BowyerWatson(listPoints,bbox)
327 output = traceMeshMP(listPoints, triangulation,points)
328 output = "\\leavevmode\\begin{mplibcode}u:="..scale..";"..beginning .. output .. ending .. "\\end{mplibcode}"
332 -- buildMesh with TikZ
333 function buildMeshTikZBW(chaine,mode,points,bbox,scale,color,colorBbox)
334 listPoints = buildList(chaine, mode)
335 triangulation = BowyerWatson(listPoints,bbox)
336 output = traceMeshTikZ(listPoints, triangulation,points,color,colorBbox)
337 output = "\\noindent\\begin{tikzpicture}[x=" .. scale .. ",y=" .. scale .."]" .. output .."\\end{tikzpicture}"
341 -- buildMesh with TikZ
342 function buildMeshTikZBWinc(chaine,beginning, ending,mode,points,bbox,scale,color,colorBbox)
343 listPoints = buildList(chaine, mode)
344 triangulation = BowyerWatson(listPoints,bbox)
345 output = traceMeshTikZ(listPoints, triangulation,points,color,colorBbox)
346 output = "\\noindent\\begin{tikzpicture}[x=" .. scale .. ",y=" .. scale .."]" ..beginning.. output..ending .."\\end{tikzpicture}"
351 -- print points of the mesh
352 function tracePointsMP(listPoints,points)
354 output = output .. " pair MeshPoints[];"
355 for i=1,#listPoints do
356 output = output .. "MeshPoints[".. i .. "] = (" .. listPoints[i].x .. "," .. listPoints[i].y .. ");"
358 if(points=="points") then
360 for i=1,#listPoints do
361 if(listPoints[i].type == "bbox") then
362 output = output .. "dotlabel.llft (btex $\\MeshPoint^{*}_{" .. j .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolorBbox ;"
365 output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolor ;"
369 for i=1,#listPoints do
370 if(listPoints[i].type == "bbox") then
371 output = output .. "drawdot (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u withcolor \\luameshmpcolorBbox withpen pencircle scaled 3;"
373 output = output .. "drawdot (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u withcolor \\luameshmpcolor withpen pencircle scaled 3;"
380 -- print points of the mesh
381 function tracePointsTikZ(listPoints,points,color,colorBbox)
383 if(points=="points") then
384 for i=1,#listPoints do
385 if(listPoints[i].type == "bbox") then
386 output = output .. "\\draw[color="..colorBbox.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};"
388 output = output .. "\\draw[color="..color.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};"
392 for i=1,#listPoints do
393 if(listPoints[i].type == "bbox") then
394 output = output .. "\\draw[color="..colorBbox.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} ;"
396 output = output .. "\\draw[color="..color.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} ;"
403 -- print points to mesh
404 function printPointsMP(chaine,mode,points,bbox,scale)
405 listPoints = buildList(chaine, mode)
406 if(bbox == "bbox" ) then
407 listPoints = buildBoundingBox(listPoints)
409 output = tracePointsMP(listPoints,points)
410 output = "\\leavevmode\\begin{mplibcode}beginfig(0);u:="..scale.. ";" .. output .."endfig;\\end{mplibcode}"
415 -- print points to mesh
416 function printPointsMPinc(chaine,beginning, ending, mode,points,bbox,scale)
417 listPoints = buildList(chaine, mode)
418 if(bbox == "bbox" ) then
419 listPoints = buildBoundingBox(listPoints)
421 output = tracePointsMP(listPoints,points)
422 output = "\\begin{mplibcode}u:="..scale..";"..beginning .. output .. ending .. "\\end{mplibcode}"
426 -- print points to mesh
427 function printPointsTikZ(chaine,mode,points,bbox,scale,color,colorBbox)
428 listPoints = buildList(chaine, mode)
429 if(bbox == "bbox" ) then
430 listPoints = buildBoundingBox(listPoints)
432 output = tracePointsTikZ(listPoints,points,color,colorBbox)
433 output = "\\noindent\\begin{tikzpicture}[x=" .. scale .. ",y=" .. scale .."]" .. output .."\\end{tikzpicture}"
438 -- print points to mesh
439 function printPointsTikZinc(chaine,beginning, ending, mode,points,bbox,scale,color,colorBbox)
440 listPoints = buildList(chaine, mode)
441 if(bbox == "bbox" ) then
442 listPoints = buildBoundingBox(listPoints)
444 output = tracePointsTikZ(listPoints,points,color,colorBbox)
445 output = "\\noindent\\begin{tikzpicture}[x=" .. scale .. ",y=" .. scale .."]" ..beginning.. output..ending .."\\end{tikzpicture}"
451 function buildRect(largeur,a,b,nbrA, nbrB)
452 listPoints = rectangleList(a,b,nbrA,nbrB)
453 triangulation = BowyerWatson(listPoints,"none")
454 traceTikZ(listPoints, triangulation,largeur,"none")
457 local function shallowCopy(original)
459 for key, value in pairs(original) do
465 -- function give a real polygon without repeting points
466 function cleanPoly(polygon)
468 polyCopy = shallowCopy(polygon)
471 table.insert(polyNew, e1)
472 table.insert(polyNew, e2)
473 table.remove(polyCopy,1)
478 while (i<=#polyCopy and find==false) do
479 bool1 = (polyCopy[i][1] == polyNew[j])
480 bool2 = (polyCopy[i][2] == polyNew[j])
481 if(bool1 or bool2) then -- the edge has a common point with polyNew[j]
483 table.insert(polyNew, polyCopy[i][1])
485 table.remove(polyCopy,i)
487 elseif(not bool2) then
488 table.insert(polyNew, polyCopy[i][2])
490 table.remove(polyCopy,i)
501 function TeXaddOnePointTikZ(chaine,point,step,color,colorBack, colorNew, colorCircle,colorBbox)
503 -- build the triangulation
504 triangulation = BowyerWatson(listPoints,"none")
505 badTriangles = buildBadTriangles(P,triangulation)
506 if(step == "badT") then
508 for i=1,#triangulation do
509 PointI = listPoints[triangulation[i][1]]
510 PointJ = listPoints[triangulation[i][2]]
511 PointK = listPoints[triangulation[i][3]]
512 if(triangulation[i].type == "bbox") then
513 output = output .. "\\draw[color="..colorBbox.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
515 output = output .. "\\draw[color="..color.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
518 -- draw and fill the bad triangle
519 for i=1,#badTriangles do
520 PointI = listPoints[triangulation[badTriangles[i]][1]]
521 PointJ = listPoints[triangulation[badTriangles[i]][2]]
522 PointK = listPoints[triangulation[badTriangles[i]][3]]
523 output = output .. "\\draw[fill="..colorBack.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
525 -- draw the circoncircle
526 for i=1,#badTriangles do
527 PointI = listPoints[triangulation[badTriangles[i]][1]]
528 PointJ = listPoints[triangulation[badTriangles[i]][2]]
529 PointK = listPoints[triangulation[badTriangles[i]][3]]
530 center, radius = circoncircle(PointI, PointJ, PointK)
531 output = output .. "\\draw[dashed, color="..colorCircle.."] ("..center.x .. "," .. center.y .. ") circle ("..radius ..");"
534 for i=1,#listPoints do
535 if(listPoints[i].type == "bbox") then
536 output = output .. "\\draw[color="..colorBbox.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};"
538 output = output .. "\\draw[color="..color.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};"
541 -- mark the point to add
542 output = output .. "\\draw[color="..colorNew.."] (" .. P.x ..",".. P.y .. ") node {$\\bullet$} node[anchor=north east] {$\\NewPoint$};"
543 elseif(step == "cavity") then
544 polygon = buildCavity(badTriangles, triangulation)
545 polyNew = cleanPoly(polygon)
546 -- remove the bad triangles
547 for j=1,#badTriangles do
548 table.remove(triangulation,badTriangles[j]-(j-1))
550 -- draw the triangles
551 for i=1,#triangulation do
552 PointI = listPoints[triangulation[i][1]]
553 PointJ = listPoints[triangulation[i][2]]
554 PointK = listPoints[triangulation[i][3]]
555 if(triangulation[i].type == "bbox") then
556 output = output .. "\\draw[color="..colorBbox.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
558 output = output .. "\\draw[color="..color.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
561 -- fill and draw the cavity
564 PointI = listPoints[polyNew[i]]
565 path = path .. "(".. PointI.x ..",".. PointI.y ..")--"
567 output = output .. "\\draw[color="..colorNew..",fill ="..colorBack..", thick] " .. path .. "cycle;"
568 -- mark the points of the mesh
569 for i=1,#listPoints do
570 if(listPoints[i].type == "bbox") then
571 output = output .. "\\draw[color="..colorBbox.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};"
573 output = output .. "\\draw[color="..color.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};"
576 -- mark the adding point
577 output = output .. "\\draw[color="..colorNew.."] (" .. P.x ..",".. P.y .. ") node {$\\bullet$} node[anchor=north east] {$\\NewPoint$};"
578 elseif(step == "newT") then
579 polygon = buildCavity(badTriangles, triangulation)
580 polyNew = cleanPoly(polygon)
581 -- remove the bad triangles
582 for j=1,#badTriangles do
583 table.remove(triangulation,badTriangles[j]-(j-1))
585 -- draw the triangle of the triangulation
586 for i=1,#triangulation do
587 PointI = listPoints[triangulation[i][1]]
588 PointJ = listPoints[triangulation[i][2]]
589 PointK = listPoints[triangulation[i][3]]
590 if(triangulation[i].type == "bbox") then
591 output = output .. "\\draw[color="..colorBbox.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
593 output = output .. "\\draw[color="..color.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
596 -- fill and draw the cavity
599 PointI = listPoints[polyNew[i]]
600 path = path .. "(".. PointI.x ..",".. PointI.y ..")--"
602 output = output .. "\\draw[color="..colorNew..",fill ="..colorBack..", thick] " .. path .. "cycle;"
603 -- draw the new triangles composed by the edges of the polygon and the added point
605 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 ..");"
606 output = output .. "\\draw[color="..colorNew..", thick]".."(".. listPoints[polygon[i][1]].x .. "," .. listPoints[polygon[i][1]].y .. ") -- (" .. P.x .. "," .. P.y ..");"
607 output = output .. "\\draw[color="..colorNew..", thick]".."(".. listPoints[polygon[i][2]].x .. "," .. listPoints[polygon[i][2]].y .. ") -- (" .. P.x .. "," .. P.y ..");"
610 for i=1,#listPoints do
611 if(listPoints[i].type == "bbox") then
612 output = output .. "\\draw[color="..colorBbox.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};"
614 output = output .. "\\draw[color="..color.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};"
617 -- mark the added point
618 output = output .. "\\draw[color="..colorNew.."] (" .. P.x ..",".. P.y .. ") node {$\\bullet$} node[anchor=north east] {$\\NewPoint$};"
623 function TeXaddOnePointMPBW(listPoints,P,step,bbox)
625 output = output .. "pair MeshPoints[];"
626 -- build the triangulation
627 triangulation = BowyerWatson(listPoints,bbox)
628 badTriangles = buildBadTriangles(P,triangulation)
629 for i=1,#listPoints do
630 output = output .. "MeshPoints[".. i .. "] = (" .. listPoints[i].x .. "," .. listPoints[i].y .. ");"
632 if(step == "badT") then
634 for i=1,#triangulation do
635 PointI = listPoints[triangulation[i][1]]
636 PointJ = listPoints[triangulation[i][2]]
637 PointK = listPoints[triangulation[i][3]]
638 if(triangulation[i].type == "bbox") then
639 output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolorBbox;"
641 output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolor;"
644 -- draw and fill the bad triangle
645 for i=1,#badTriangles do
646 PointI = listPoints[triangulation[badTriangles[i]][1]]
647 PointJ = listPoints[triangulation[badTriangles[i]][2]]
648 PointK = listPoints[triangulation[badTriangles[i]][3]]
649 output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolor;"
650 output = output .. "fill (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolorBack;"
652 -- draw the circoncircle
653 for i=1,#badTriangles do
654 PointI = listPoints[triangulation[badTriangles[i]][1]]
655 PointJ = listPoints[triangulation[badTriangles[i]][2]]
656 PointK = listPoints[triangulation[badTriangles[i]][3]]
657 center, radius = circoncircle(PointI, PointJ, PointK)
658 output = output .. "draw fullcircle scaled ("..radius .."*2u) shifted ("..center.x .. "*u," .. center.y .. "*u) dashed evenly withcolor \\luameshmpcolorCircle;"
662 for i=1,#listPoints do
663 if(listPoints[i].type == "bbox") then
664 output = output .. "dotlabel.llft (btex $\\MeshPoint^{*}_{" .. j .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolorBbox ;"
667 output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolor ;"
670 -- mark the point to add
671 output = output .. "dotlabel.llft (btex $\\NewPoint$ etex,(" .. P.x ..",".. P.y .. ")*u) withcolor \\luameshmpcolorNew;"
672 elseif(step == "cavity") then
673 polygon = buildCavity(badTriangles, triangulation)
674 polyNew = cleanPoly(polygon)
675 -- remove the bad triangles
676 for j=1,#badTriangles do
677 table.remove(triangulation,badTriangles[j]-(j-1))
679 -- draw the triangles
680 for i=1,#triangulation do
681 PointI = listPoints[triangulation[i][1]]
682 PointJ = listPoints[triangulation[i][2]]
683 PointK = listPoints[triangulation[i][3]]
684 if(triangulation[i].type == "bbox") then
685 output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolorBbox;"
687 output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolor;"
690 -- fill and draw the cavity
693 PointI = listPoints[polyNew[i]]
694 path = path .. "(".. PointI.x ..",".. PointI.y ..")*u--"
696 output = output .. "fill " .. path .. "cycle withcolor \\luameshmpcolorBack;"
697 output = output .. "draw " .. path .. "cycle withcolor \\luameshmpcolorNew withpen pencircle scaled 1pt;"
698 -- mark the points of the mesh
700 for i=1,#listPoints do
701 if(listPoints[i].type == "bbox") then
702 output = output .. "dotlabel.llft (btex $\\MeshPoint^{*}_{" .. j .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolorBbox ;"
705 output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolor ;"
708 -- mark the adding point
709 output = output .. "dotlabel.llft (btex $\\NewPoint$ etex,(" .. P.x ..",".. P.y .. ")*u) withcolor \\luameshmpcolorNew ;"
710 elseif(step == "newT") then
711 polygon = buildCavity(badTriangles, triangulation)
712 polyNew = cleanPoly(polygon)
713 -- remove the bad triangles
714 for j=1,#badTriangles do
715 table.remove(triangulation,badTriangles[j]-(j-1))
717 -- draw the triangle of the triangulation
718 for i=1,#triangulation do
719 PointI = listPoints[triangulation[i][1]]
720 PointJ = listPoints[triangulation[i][2]]
721 PointK = listPoints[triangulation[i][3]]
722 if(triangulation[i].type == "bbox") then
723 output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolorBbox;"
725 output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolor;"
731 PointI = listPoints[polyNew[i]]
732 path = path .. "(".. PointI.x ..",".. PointI.y ..")*u--"
734 output = output .. "fill " .. path .. "cycle withcolor \\luameshmpcolorBack;"
735 -- draw the new triangles composed by the edges of the polygon and the added point
737 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;"
738 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;"
739 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;"
743 for i=1,#listPoints do
744 if(listPoints[i].type == "bbox") then
745 output = output .. "dotlabel.llft (btex $\\MeshPoint^{*}_{" .. j .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolorBbox ;"
748 output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolor ;"
751 -- mark the added point
752 output = output .. "dotlabel.llft (btex $\\NewPoint$ etex,(" .. P.x ..",".. P.y .. ")*u) withcolor \\luameshmpcolorNew ;"
758 -- build the list of points extern and stop at nbr
759 function buildListExt(chaine, stop)
761 io.input(chaine) -- open the file
763 lines=string.explode(text,"\n+") -- all the lines
764 for i=1,tonumber(stop) do
765 xy=string.explode(lines[i]," +")
766 table.insert(listPoints,{x=tonumber(xy[1]),y=tonumber(xy[2])})
768 xy=string.explode(lines[stop+1]," +")
769 point={x=tonumber(xy[1]),y=tonumber(xy[2])}
770 return point, listPoints
774 function TeXOnePointTikZBW(chaine,point,step,scale,mode,bbox,color,colorBack,colorNew,colorCircle,colorBbox)
776 Sx,Sy=string.match(point,"%((.+),(.+)%)")
778 listPoints = buildList(chaine, mode)
781 P, listPoints = buildListExt(chaine,tonumber(point))
783 output = TeXaddOnePointTikZ(chaine,point,step,color,colorBack,colorNew,colorCircle,colorBbox)
784 output = "\\noindent\\begin{tikzpicture}[x="..scale..",y="..scale.."]".. output .. "\\end{tikzpicture}"
788 function TeXOnePointTikZBWinc(chaine,point,beginning, ending,step,scale,mode,bbox,color,colorBack,colorNew,colorCircle,colorBbox)
790 Sx,Sy=string.match(point,"%((.+),(.+)%)")
792 listPoints = buildList(chaine, mode)
795 P, listPoints = buildListExt(chaine,tonumber(point))
797 output = TeXaddOnePointTikZ(chaine,point,step,color,colorBack,colorNew,colorCircle,colorBbox)
798 output = "\\noindent\\begin{tikzpicture}[x="..scale..",y="..scale.."]".. beginning..output ..ending.. "\\end{tikzpicture}"
802 function TeXOnePointMPBW(chaine,point,step,scale,mode,bbox)
804 Sx,Sy=string.match(point,"%((.+),(.+)%)")
806 listPoints = buildList(chaine, mode)
809 P, listPoints = buildListExt(chaine,tonumber(point))
811 output = TeXaddOnePointMPBW(listPoints,P,step,bbox)
812 output = "\\leavevmode\\begin{mplibcode}beginfig(0);u:="..scale..";".. output .. "endfig;\\end{mplibcode}"
816 function TeXOnePointMPBWinc(chaine,point,beginning,ending,step,scale,mode,bbox)
818 Sx,Sy=string.match(point,"%((.+),(.+)%)")
820 listPoints = buildList(chaine, mode)
823 P, listPoints = buildListExt(chaine,tonumber(point))
825 output = TeXaddOnePointMPBW(listPoints,P,step,bbox)
826 output = "\\begin{mplibcode}u:="..scale..";"..beginning .. output .. ending .. "\\end{mplibcode}"