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)
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 output = output .. "\\draw[color="..color.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
264 if(points=="points") then
265 for i=1,#listPoints do
266 output = output .. "\\draw[color=".."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};"
273 -- trace a triangulation with MP
274 function traceMeshMP(listPoints, triangulation,points)
276 output = output .. " pair MeshPoints[];"
277 for i=1,#listPoints do
278 output = output .. "MeshPoints[".. i .. "] = (" .. listPoints[i].x .. "," .. listPoints[i].y .. ");"
281 for i=1,#triangulation do
282 PointI = listPoints[triangulation[i][1]]
283 PointJ = listPoints[triangulation[i][2]]
284 PointK = listPoints[triangulation[i][3]]
285 if(triangulation[i].type == "bbox") then
286 output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolorBbox;"
288 output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolor;"
291 if(points=="points") then
292 for i=1,#listPoints do
293 if(listPoints[i].type == "bbox") then
294 output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolorBbox ;"
296 output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolor ;"
304 -- print points of the mesh
305 function tracePointsMP(listPoints,points)
307 output = output .. " pair MeshPoints[];"
308 for i=1,#listPoints do
309 output = output .. "MeshPoints[".. i .. "] = (" .. listPoints[i].x .. "," .. listPoints[i].y .. ");"
311 if(points=="points") then
312 for i=1,#listPoints do
313 if(listPoints[i].type == "bbox") then
314 output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolorBbox ;"
316 output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolor ;"
320 for i=1,#listPoints do
321 if(listPoints[i].type == "bbox") then
322 output = output .. "drawdot (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolorBbox ;"
324 output = output .. "drawdot (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolor ;"
333 -- buildMesh with TikZ
334 function buildMeshTikZ(chaine,mode,points,bbox,full,scale,color)
335 listPoints = buildList(chaine, mode)
336 triangulation = BowyerWatson(listPoints,bbox)
337 output = traceMeshTikZ(listPoints, triangulation,points,color)
338 if(full=="full") then
339 output = "\\noindent\\begin{tikzpicture}[x=" .. scale .. ",y=" .. scale .."]" .. output .."\\end{tikzpicture}"
346 function buildMeshMPBW(chaine,mode,points,bbox,scale)
347 listPoints = buildList(chaine, mode)
348 triangulation = BowyerWatson(listPoints,bbox)
349 output = traceMeshMP(listPoints, triangulation,points)
350 output = "\\leavevmode\\begin{mplibcode}beginfig(0);u:="..scale.. ";" .. output .."endfig;\\end{mplibcode}"
354 -- print points to mesh
355 function printPointsMP(chaine,mode,points,bbox,scale)
356 listPoints = buildList(chaine, mode)
357 if(bbox == "bbox" ) then
358 listPoints = buildBoundingBox(listPoints)
360 output = tracePointsMP(listPoints,points)
361 output = "\\leavevmode\\begin{mplibcode}beginfig(0);u:="..scale.. ";" .. output .."endfig;\\end{mplibcode}"
366 -- print points to mesh
367 function printPointsMPinc(chaine,beginning, ending, mode,points,bbox,scale)
368 listPoints = buildList(chaine, mode)
369 if(bbox == "bbox" ) then
370 listPoints = buildBoundingBox(listPoints)
372 output = tracePointsMP(listPoints,points)
373 output = "\\begin{mplibcode}u:="..scale..";"..beginning .. output .. ending .. "\\end{mplibcode}"
378 -- buildMesh with MP include code
379 function buildMeshMPBWinc(chaine,beginning, ending,mode,points,bbox,scale)
380 listPoints = buildList(chaine, mode)
381 triangulation = BowyerWatson(listPoints,bbox)
382 output = traceMeshMP(listPoints, triangulation,points)
383 output = "\\begin{mplibcode}u:="..scale..";"..beginning .. output .. ending .. "\\end{mplibcode}"
388 function buildRect(largeur,a,b,nbrA, nbrB)
389 listPoints = rectangleList(a,b,nbrA,nbrB)
390 triangulation = BowyerWatson(listPoints,"none")
391 traceTikZ(listPoints, triangulation,largeur,"none")
394 local function shallowCopy(original)
396 for key, value in pairs(original) do
402 -- function give a real polygon without repeting points
403 function cleanPoly(polygon)
405 polyCopy = shallowCopy(polygon)
408 table.insert(polyNew, e1)
409 table.insert(polyNew, e2)
410 table.remove(polyCopy,1)
415 while (i<=#polyCopy and find==false) do
417 bool1 = (polyCopy[i][1] == polyNew[j])
418 bool2 = (polyCopy[i][2] == polyNew[j])
419 if(bool1 or bool2) then -- the edge has a common point with polyNew[j]
421 table.insert(polyNew, polyCopy[i][1])
423 table.remove(polyCopy,i)
425 elseif(not bool2) then
426 table.insert(polyNew, polyCopy[i][2])
428 table.remove(polyCopy,i)
438 function TeXaddOnePointTikZ(chaine,point,step,color,colorBack, colorNew, colorCircle)
439 Sx,Sy=string.match(point,"%((.+),(.+)%)")
442 listPoints = buildList(chaine, "int")
443 -- build the triangulation
444 triangulation = BowyerWatson(listPoints,"none")
445 badTriangles = buildBadTriangles(P,triangulation)
446 if(step == "badT") then
448 for i=1,#triangulation do
449 PointI = listPoints[triangulation[i][1]]
450 PointJ = listPoints[triangulation[i][2]]
451 PointK = listPoints[triangulation[i][3]]
452 output = output .. "\\draw[color="..color.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
454 -- draw and fill the bad triangle
455 for i=1,#badTriangles do
456 PointI = listPoints[triangulation[badTriangles[i]][1]]
457 PointJ = listPoints[triangulation[badTriangles[i]][2]]
458 PointK = listPoints[triangulation[badTriangles[i]][3]]
459 output = output .. "\\draw[fill="..colorBack.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
461 -- draw the circoncircle
462 for i=1,#badTriangles do
463 PointI = listPoints[triangulation[badTriangles[i]][1]]
464 PointJ = listPoints[triangulation[badTriangles[i]][2]]
465 PointK = listPoints[triangulation[badTriangles[i]][3]]
466 center, radius = circoncircle(PointI, PointJ, PointK)
467 output = output .. "\\draw[dashed, color="..colorCircle.."] ("..center.x .. "," .. center.y .. ") circle ("..radius ..");"
470 for i=1,#listPoints do
471 output = output .. "\\draw[color ="..color.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};"
473 -- mark the point to add
474 output = output .. "\\draw[color="..colorNew.."] (" .. P.x ..",".. P.y .. ") node {$\\bullet$} node[anchor=north east] {$\\NewPoint$};"
475 elseif(step == "cavity") then
476 polygon = buildCavity(badTriangles, triangulation)
477 polyNew = cleanPoly(polygon)
478 -- remove the bad triangles
479 for j=1,#badTriangles do
480 table.remove(triangulation,badTriangles[j]-(j-1))
482 -- draw the triangles
483 for i=1,#triangulation do
484 PointI = listPoints[triangulation[i][1]]
485 PointJ = listPoints[triangulation[i][2]]
486 PointK = listPoints[triangulation[i][3]]
487 output = output .. "\\draw[color="..color.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
489 -- fill and draw the cavity
492 PointI = listPoints[polyNew[i]]
493 path = path .. "(".. PointI.x ..",".. PointI.y ..")--"
495 output = output .. "\\draw[color="..colorNew..",fill ="..colorBack..", thick] " .. path .. "cycle;"
496 -- mark the points of the mesh
497 for i=1,#listPoints do
498 output = output .. "\\draw[color="..color.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};"
500 -- mark the adding point
501 output = output .. "\\draw[color="..colorNew.."] (" .. P.x ..",".. P.y .. ") node {$\\bullet$} node[anchor=north east] {$\\NewPoint$};"
502 elseif(step == "newT") then
503 polygon = buildCavity(badTriangles, triangulation)
504 polyNew = cleanPoly(polygon)
505 -- remove the bad triangles
506 for j=1,#badTriangles do
507 table.remove(triangulation,badTriangles[j]-(j-1))
509 -- draw the triangle of the triangulation
510 for i=1,#triangulation do
511 PointI = listPoints[triangulation[i][1]]
512 PointJ = listPoints[triangulation[i][2]]
513 PointK = listPoints[triangulation[i][3]]
514 output = output .. "\\draw[color ="..color.."] (".. PointI.x ..",".. PointI.y ..")--("..PointJ.x..",".. PointJ.y ..")--("..PointK.x..",".. PointK.y ..")--cycle;"
516 -- fill and draw the cavity
519 PointI = listPoints[polyNew[i]]
520 path = path .. "(".. PointI.x ..",".. PointI.y ..")--"
522 output = output .. "\\draw[color="..colorNew..",fill ="..colorBack..", thick] " .. path .. "cycle;"
523 -- draw the new triangles composed by the edges of the polygon and the added point
525 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 ..");"
526 output = output .. "\\draw[color="..colorNew..", thick]".."(".. listPoints[polygon[i][1]].x .. "," .. listPoints[polygon[i][1]].y .. ") -- (" .. P.x .. "," .. P.y ..");"
527 output = output .. "\\draw[color="..colorNew..", thick]".."(".. listPoints[polygon[i][2]].x .. "," .. listPoints[polygon[i][2]].y .. ") -- (" .. P.x .. "," .. P.y ..");"
530 for i=1,#listPoints do
531 output = output .. "\\draw[color="..color.."] (" .. listPoints[i].x ..",".. listPoints[i].y .. ") node {$\\bullet$} node[anchor=north east] {$\\MeshPoint_{" .. i .. "}$};"
533 -- mark the added point
534 output = output .. "\\draw[color="..colorNew.."] (" .. P.x ..",".. P.y .. ") node {$\\bullet$} node[anchor=north east] {$\\NewPoint$};"
539 function TeXaddOnePointMPBW(listPoints,P,step,bbox)
541 output = output .. "pair MeshPoints[];"
542 -- build the triangulation
543 triangulation = BowyerWatson(listPoints,bbox)
544 badTriangles = buildBadTriangles(P,triangulation)
545 for i=1,#listPoints do
546 output = output .. "MeshPoints[".. i .. "] = (" .. listPoints[i].x .. "," .. listPoints[i].y .. ");"
548 if(step == "badT") then
550 for i=1,#triangulation do
551 PointI = listPoints[triangulation[i][1]]
552 PointJ = listPoints[triangulation[i][2]]
553 PointK = listPoints[triangulation[i][3]]
554 if(triangulation[i].type == "bbox") then
555 output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolorBbox;"
557 output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolor;"
560 -- draw and fill the bad triangle
561 for i=1,#badTriangles do
562 PointI = listPoints[triangulation[badTriangles[i]][1]]
563 PointJ = listPoints[triangulation[badTriangles[i]][2]]
564 PointK = listPoints[triangulation[badTriangles[i]][3]]
565 output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolor;"
566 output = output .. "fill (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolorBack;"
568 -- draw the circoncircle
569 for i=1,#badTriangles do
570 PointI = listPoints[triangulation[badTriangles[i]][1]]
571 PointJ = listPoints[triangulation[badTriangles[i]][2]]
572 PointK = listPoints[triangulation[badTriangles[i]][3]]
573 center, radius = circoncircle(PointI, PointJ, PointK)
574 output = output .. "draw fullcircle scaled ("..radius .."*2u) shifted ("..center.x .. "*u," .. center.y .. "*u) dashed evenly withcolor \\luameshmpcolorCircle;"
577 for i=1,#listPoints do
578 if(listPoints[i].type == "bbox") then
579 output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolorBbox ;"
581 output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolor ;"
584 -- mark the point to add
585 output = output .. "dotlabel.llft (btex $\\NewPoint$ etex,(" .. P.x ..",".. P.y .. ")*u) withcolor \\luameshmpcolorNew;"
586 elseif(step == "cavity") then
587 polygon = buildCavity(badTriangles, triangulation)
588 polyNew = cleanPoly(polygon)
589 -- remove the bad triangles
590 for j=1,#badTriangles do
591 table.remove(triangulation,badTriangles[j]-(j-1))
593 -- draw the triangles
594 for i=1,#triangulation do
595 PointI = listPoints[triangulation[i][1]]
596 PointJ = listPoints[triangulation[i][2]]
597 PointK = listPoints[triangulation[i][3]]
598 if(triangulation[i].type == "bbox") then
599 output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolorBbox;"
601 output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolor;"
604 -- fill and draw the cavity
607 PointI = listPoints[polyNew[i]]
608 path = path .. "(".. PointI.x ..",".. PointI.y ..")*u--"
610 output = output .. "fill " .. path .. "cycle withcolor \\luameshmpcolorBack;"
611 output = output .. "draw " .. path .. "cycle withcolor \\luameshmpcolorNew withpen pencircle scaled 1pt;"
612 -- mark the points of the mesh
613 for i=1,#listPoints do
614 if(listPoints[i].type == "bbox") then
615 output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolorBbox ;"
617 output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolor ;"
620 -- mark the adding point
621 output = output .. "dotlabel.llft (btex $\\NewPoint$ etex,(" .. P.x ..",".. P.y .. ")*u) withcolor \\luameshmpcolorNew ;"
622 elseif(step == "newT") then
623 polygon = buildCavity(badTriangles, triangulation)
624 polyNew = cleanPoly(polygon)
625 -- remove the bad triangles
626 for j=1,#badTriangles do
627 table.remove(triangulation,badTriangles[j]-(j-1))
629 -- draw the triangle of the triangulation
630 for i=1,#triangulation do
631 PointI = listPoints[triangulation[i][1]]
632 PointJ = listPoints[triangulation[i][2]]
633 PointK = listPoints[triangulation[i][3]]
634 if(triangulation[i].type == "bbox") then
635 output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolorBbox;"
637 output = output .. "draw (".. PointI.x ..",".. PointI.y ..")*u--("..PointJ.x..",".. PointJ.y ..")*u--("..PointK.x..",".. PointK.y ..")*u--cycle withcolor \\luameshmpcolor;"
643 PointI = listPoints[polyNew[i]]
644 path = path .. "(".. PointI.x ..",".. PointI.y ..")*u--"
646 output = output .. "fill " .. path .. "cycle withcolor \\luameshmpcolorBack;"
647 -- draw the new triangles composed by the edges of the polygon and the added point
649 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;"
650 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;"
651 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;"
654 for i=1,#listPoints do
655 if(listPoints[i].type == "bbox") then
656 output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolorBbox ;"
658 output = output .. "dotlabel.llft (btex $\\MeshPoint_{" .. i .. "}$ etex, (" .. listPoints[i].x ..",".. listPoints[i].y .. ")*u ) withcolor \\luameshmpcolor ;"
661 -- mark the added point
662 output = output .. "dotlabel.llft (btex $\\NewPoint$ etex,(" .. P.x ..",".. P.y .. ")*u) withcolor \\luameshmpcolorNew ;"
668 -- build the list of points extern and stop at nbr
669 function buildListExt(chaine, stop)
671 io.input(chaine) -- open the file
673 lines=string.explode(text,"\n+") -- all the lines
674 for i=1,tonumber(stop) do
675 xy=string.explode(lines[i]," +")
676 table.insert(listPoints,{x=tonumber(xy[1]),y=tonumber(xy[2])})
678 xy=string.explode(lines[stop+1]," +")
679 point={x=tonumber(xy[1]),y=tonumber(xy[2])}
680 return point, listPoints
684 function TeXOnePointTikZ(chaine,point,step,color,colorBack,colorNew,colorCircle,scale)
685 output = TeXaddOnePointTikZ(chaine,point,step,color,colorBack,colorNew,colorCircle)
686 output = "\\noindent\\begin{tikzpicture}[x="..scale..",y="..scale.."]".. output .. "\\end{tikzpicture}"
690 function TeXOnePointMPBW(chaine,point,step,scale,mode,bbox)
692 Sx,Sy=string.match(point,"%((.+),(.+)%)")
694 listPoints = buildList(chaine, mode)
697 P, listPoints = buildListExt(chaine,tonumber(point))
699 output = TeXaddOnePointMPBW(listPoints,P,step,bbox)
700 output = "\\leavevmode\\begin{mplibcode}beginfig(0);u:="..scale..";".. output .. "endfig;\\end{mplibcode}"
704 function TeXOnePointMPBWinc(chaine,point,beginning,ending,step,scale,mode,bbox)
706 Sx,Sy=string.match(point,"%((.+),(.+)%)")
708 listPoints = buildList(chaine, mode)
711 P, listPoints = buildListExt(chaine,tonumber(point))
713 output = TeXaddOnePointMPBW(listPoints,P,step,bbox)
714 output = "\\begin{mplibcode}u:="..scale..";"..beginning .. output .. ending .. "\\end{mplibcode}"