Gone a little bit crazy with triangulation in Openscad

a.scad

//Scraped from postscript using pathforall

a=[
    43.9881,6.56189,"moveto",
    42.2891,5.17072,41.0949,4.67827,39.6053,4.67827,"curveto",
    37.3154,4.67827,36.626,6.06944,36.626,10.4522,"curveto",
    36.626,29.8548,"lineto",
    36.626,35.0255,36.1212,37.9186,34.6315,40.307,"curveto",
    32.4401,43.8896,28.1681,45.7732,22.2957,45.7732,"curveto",
    12.9391,45.7732,5.57699,40.898,5.57699,34.6315,"curveto",
    5.57699,32.3416,7.46061,30.3472,9.849,30.3472,"curveto",
    12.2374,30.3472,14.3303,32.3416,14.3303,34.533,"curveto",
    14.3303,34.927,14.2318,35.4318,14.1333,36.1212,"curveto",
    13.9363,37.0199,13.8378,37.8201,13.8378,38.5096,"curveto",
    13.8378,41.1934,17.0141,43.3848,21.003,43.3848,"curveto",
    25.8782,43.3848,28.5621,40.504,28.5621,35.124,"curveto",
    28.5621,29.0545,"lineto",
    13.3331,22.9851,11.5479,22.0864,7.26363,18.3068,"curveto",
    5.07223,16.3247,3.68106,12.9391,3.68106,9.65202,"curveto",
    3.68106,3.38559,8.06387,-0.997211,14.1333,-0.997211,"curveto",
    18.5038,-0.997211,22.5911,1.0957,28.6606,6.26642,"curveto",
    29.153,0.997211,30.9505,-0.997211,35.0255,-0.997211,"curveto",
    38.4111,-0.997211,40.504,0.19698,43.9881,3.97653,"curveto",
    43.9881,6.56189,"lineto",
    "closepath",
    28.5621,12.2374,"moveto",
    28.5621,9.25806,28.0573,8.16236,25.9767,6.96816,"curveto",
    23.4899,5.57699,20.7937,4.77676,18.7131,4.77676,"curveto",
    15.229,4.77676,12.4344,8.16236,12.4344,12.4344,"curveto",
    12.4344,12.8406,"lineto",
    12.5328,18.8116,16.9156,22.5911,28.5621,26.6662,"curveto",
    28.5621,12.2374,"lineto",
    "closepath"
];


function splitpaths(script,i=0)=
   ("closepath"==script[i])?
      (i==len(script)-1)?
         [[for (j=[0:i-1]) script[j]]]
      :
        concat(
            [[for (j=[0:i-1]) script[j]]],
            splitpaths([for (j=[i+1:len(script)-1]) script[j]])
        )
   :
      splitpaths(script,i+1)
;

function pathstep(path,i=0,curx,cury,steps=10)=
   (i>=len(path))?
      []
   :("moveto"==path[i])? //This should only happen when i==2
        concat(
            [[path[i-2],path[i-1]]],
            pathstep(path,i+1,path[i-2],path[i-1],steps)
        )
   :("lineto"==path[i])? //This happens later...
        concat(
            [[path[i-2],path[i-1]]],
            pathstep(path,i+1,path[i-2],path[i-1],steps)
        )
   :("curveto"==path[i])?
      concat(
         psbezier([curx,cury],[path[i-6],path[i-5]],[path[i-4],path[i-3]],[path[i-2],path[i-1]],steps),
         pathstep(path,i+1,path[i-2],path[i-1],steps)
      )
   :
      pathstep(path,i+1,curx,cury,steps);

function psbezier(a,b,c,d,steps=10) =
    let(step=1/steps)
    [for(i=[1:steps]) nbezier([a,b,c,d],step*i)]
;

function nbezier(points,t)=
      1>=len(points)?
          points[0]
      :
          nbezier(
              [for(i=[0:len(points)-2]) points[i]*(1-t)+points[i+1]*t],
              t
          );

function stripnulls(path)=
   let(pl=len(path))
   [for (i=[0:pl-1]) if((path[i]-path[(pl+i-1)%pl])*(path[i]-path[(pl+i-1)%pl])>0) path[i]]
;

function mkpoly(paths,curpoints=[],curpaths=[],i=0)=
   (i>=len(paths))?
      []
   :(i==len(paths)-1)?
      let(mypath=stripnulls(paths[i]))
      [
         concat(curpoints,mypath),
         concat(curpaths,[[for (i=[0:len(mypath)-1]) i+len(curpoints)]])
      ]
   :
      let(mypath=stripnulls(paths[i]))
      mkpoly(
         paths,
         concat(curpoints,mypath),
         concat(curpaths,[[for (i=[0:len(mypath)-1]) i+len(curpoints)]]),
         i+1
      )
;

function makesegments(poly) =
    [
        for (i=[0:len(poly[1])-1]) [
            for(j=[0:len(poly[1][i])-1])
            [
                poly[1][i][j],
                poly[1][i][(j+1)%len(poly[1][i])]
            ]
        ]
    ]
;

apaths=splitpaths(a);
arender=[for (i=[0:len(apaths)-1]) pathstep(apaths[i])];
poly=mkpoly(arender);

translate([0,0,-1]) linear_extrude(height=1) {
   polygon(points=poly[0],paths=poly[1]);
}

sweeptriangulate.scad

use<subdivision.scad>
use<FunctionalOpenSCAD/functional.scad>

//Sweep line triangulator using monotone polygons

//Requires:
//  First path to be properly wound external face.
//  Correctly wound paths (internal paths are CW, external CCW).
//  No intesecting paths
//  No vertices with more than 2 edges.


//include<a.scad>
use<a.scad>
include<text.scad>
ppaths=splitpaths(text);
prender=[for (i=[0:len(ppaths)-1]) pathstep(ppaths[i],steps=3)];
poly=mkpoly(prender);

/*
translate([0,0,-1]) linear_extrude(height=1) {
   polygon(points=poly[0],paths=poly[1]);
}
*/


maxtest=0;

triangles=triangulate(poly[0],poly[1]);

//Testing stuff...
mypoints=mk3d(poly[0]);
//subdivided=[mypoints,triangles];
stest=sphere();
subdivided=subdivide_faces(2,[mypoints,triangles]);

echo(len(subdivided[0]));

//modified=[for (point=subdivided[0]) [point[0],point[1]+point[0]/10,((point[0]-325)*(point[0]-325)+point[1]*point[1])/1000]];

function toc(point)=
   let(x=point[0],y=point[1],z=point[2])
   [-50*cos(x),-50*sin(x),y-x/3]
;

modified=[for (point=subdivided[0]) toc(point)];


polyhedron(points=modified,faces=subdivided[1]);
color("black") cylinder(r=48,h=2000,$fn=36,center=true);
//showsweep(points=modified,closed=subdivided[1],open=[]);



//This one is often handy...
module line (a=[1,1,1],b=[21,2,2],r=0.125) {
   v=b-a;
   translate(a)
       rotate(a=atan2(v[1],v[0]))
           rotate(v=[0,1,0],a=atan2(sqrt(v[0]*v[0]+v[1]*v[1]),v[2]))
               cylinder(h=sqrt(v*v),r1=r,r2=r);
}

module closedtest(pointlist,components) {
   echo("testing components");
   for(i=[0:len(components)-1]) {
      for(j=[0:len(components[i])-1]) {
         if(pointlist[components[i][j]][0]>pointlist[components[i][0]][0]) {
            echo("no start on max x",i,j,pointlist[component[i][0]],pointlist[component[i][j]]);
         }
      }
   }
}

module dot (p=[1,1,1],r=0.25) {
   translate(p) sphere(r=r);
}

module showopen(points,component) {
   list=component[0];
   prev=points[component[1]];
   next=points[component[2]];

   color("white") translate(prev) sphere(r=0.5);
   color("yellow") line(prev,points[list[0]]);
//   color("white") translate(next) sphere(r=0.25);
   color("white") line(points[list[len(list)-1]],next);

   color("black") translate(points[list[0]]) sphere(r=0.25);
   color("black") translate(points[list[len(list)-1]]) sphere(r=0.25);

//show box..
//   color("white") line(points[list[0]],points[list[len(list)-1]]);
//   color("white") line(prev,next);

//latest
   color("green") dot(points[list[component[3]]],r=0.5);

   if(len(list)>1) {
      for(j=[0:len(list)-2]) {
           color("black") line(points[list[j]],points[list[j+1]]);
      }
   }
}

module showsweep (points,closed,open,rz=0.1) {
   if(len(closed)>0) {
      for (i=[0:len(closed)-1]) {
         for(j=[0:len(closed[i])-1]) {
            color("blue") line(
               points[closed[i][j]],points[closed[i][(j+1)%len(closed[i])]]);
         }
      }
   }
   if(len(open)>0) {
      for (i=[0:len(open)-1]) {
         translate([0,0,rz*(i+1)]) showopen(points,open[i]);
      }
   }
}

//End of test/debugging section

//Requires:
//  First path to be properly wound.
//  No intesecting paths
//  No vertices with more than 2 edges.

//At this point I have monotone components. ...

function triangulate(points,paths)=
   let(
     mypoints=mk3d(points),
/*
     localz=winding_direction(mypoints,paths[0]),
     localx=nontrivialsegment(mypoints,paths[0]),
     localy=cross(localz,localx),
*/
localx=[1,0,0],localy=[0,1,0],localz=[0,0,1],

     neighborlist=mkneighborlist(mypoints,paths,localx,localy),
     sweeplist=mksweeplist(neighborlist),
     closed=sweeptriangulate(neighborlist,sweeplist,closed=[],open=[])
   )
   flatten([for (i=[0:len(closed)-1]) triangulatecomponent(neighborlist,closed[i])])

//   flatten([for (i=[0:60]) triangulatecomponent(neighborlist,closed[i])])
;

//Use a "data structure" for components:
//vertices - component body
//prev - "left" dangler
//next - "right" dangler
//latest - index of the newest vertex (typically 0 or  -1)
//pendant - undef or index of a 'roof cusp'

function flatten(list)=
   [for (a=list) for (b=a) b]
;

//Fixme: Needs a component triangulation function.
//Trapezoid partition & uni-montone components, perhaps.

function newcomponent(pointlist,point) =
   let(
      index=2,
      isexternal=5,
      a=pointlist[point[3]],
      b=pointlist[point[4]],
      swap=!point[isexternal],
      prev=swap?b[2]:a[2],
      next=swap?a[2]:b[2]
   )
   [
      [point[index]],
      prev,
      next,
      0,
      undef
   ]
;

//returns [ newclosed/undef, component ]
function componentnewprev(pointlist,component,point) =
   let(
      vertexlist=component[0],
      next=component[2],
      index=2,
      pendant=component[4],
      newprev=(vertexlist[0]==point[3])?point[4]:point[3]
   )
   (undef==pendant)? //No dangling roof pendant.
       [
          [],
          [
             concat([point[index]],vertexlist),
             newprev,
             next,
             0,
             undef
          ]
      ]
   :
     [
        [
              concat( [point[index]], sublist(vertexlist,0,pendant) )
        ],
        [
           concat( [point[index]], sublist(vertexlist,pendant,-1) ),
           newprev,
           next,
           0,
           undef
        ]
    ]
;

function componentnewnext(pointlist,component,point) =
   let(
      vertexlist=component[0],
      prev=component[1],
      index=2,
      pendant=component[4],
      newnext=(vertexlist[len(vertexlist)-1]==point[3])?point[4]:point[3]
   )
   (undef==pendant)? //No dangling roof pendant.
       [
          [],
          [
             concat(vertexlist,[point[index]]),
             prev,
             newnext,
             len(vertexlist),
             undef
          ]
      ]
   :
     [
        [
           concat( [point[index]], sublist(vertexlist,pendant,-1) )
        ],
        [
           concat( sublist(vertexlist,0,pendant), [point[index]] ),
           prev,
           newnext,
           pendant+1,
           undef
        ]
    ]
;

function componentfuse(pointlist,componentl,componentr,point)=
   let(
      pendant=4,
      index=2,
      lvertexlist=componentl[0],
      rvertexlist=componentr[0],
      newprev=componentl[1],
      newnext=componentr[2],
      lpendant=componentl[pendant],
      rpendant=componentr[pendant]
   )
   (lpendant==undef && rpendant==undef)?
      [
         [],
         [
             concat(lvertexlist,[point[index]],rvertexlist),
             newprev,
             newnext,
             len(lvertexlist),
             len(lvertexlist)
         ]
      ]
   :(rpendant==undef)?
      [
         [
//Make X-most point first in list for triangulation.
            concat([point[index]],sublist(lvertexlist,lpendant,-1))
         ],
         [
            concat(sublist(lvertexlist,0,lpendant),[point[index]],rvertexlist),
            newprev,
            newnext,
            lpendant+1, 
            lpendant+1
         ]
      ]
   :(lpendant==undef)?
      [
         [
            concat([point[index]],sublist(rvertexlist,0,rpendant))
         ],
         [
            concat(lvertexlist,[point[index]],sublist(rvertexlist,rpendant,-1)),
            newprev,
            newnext,
            len(lvertexlist),
            len(lvertexlist)
         ]
      ]
   ://both components have pendants
//fixme: I think this one still needs testing.
      [
         [
//Make x-most point first for triangulation.
            concat([point[index]],sublist(lvertices,lpendant,-1)),
            concat([point[index]],sublist(rvertexlist,0,rpendant))
         ],
         [
            concat(sublist(lvertices,0,lpendant),[point[index]],sublist(rvertexlist,rpendant,-1)),
            newprev,
            newnext,
            lpendant+1, 
            lpendant+1
         ]
      ]
;

function componentsplit (pointlist,component,point)=
   let(
      latest=component[3],
      vertexlist=component[0],
      l=pointlist[vertexlist[latest]],
      componentprev=component[1],
      componentnext=component[2],
      index=2,
      isexternal=5,
      a=pointlist[point[3]],
      b=pointlist[point[4]],


      swap=!point[isexternal],
//Reversed b/c this is inside -> outside
      pointprev=swap?a[2]:b[2],
      pointnext=swap?b[2]:a[2]
   )

   [
      [
          concat(sublist(vertexlist,0,latest),[point[index]]),
          componentprev,
          pointprev,
          latest+1,
          undef
      ],
      [
          concat([point[index]],sublist(vertexlist,latest,-1)),
          pointnext,
          componentnext,
          0,
          undef
      ]
   ]
;

function componentclose(open,point)=
   let(
      list=open[0],
      pendant=open[4],
      mypoint=point[2]
   )
   (undef==pendant)?
      [
         concat([mypoint],list)
      ]
   :
//FIXME: This may be untested.
      [
         concat([mypoint],sublist(list,0,pendant)),
         concat([mypoint],sublist(list,pendant,-1))
      ]
;


function r2ceil(x,n=1)=
   (n>x)?
      n
   :
      r2ceil(x,n=n*2)
;

function componentposition(point,neighborlist,open,i=0)=
   let(
      odd=(i%2==1),
      path=odd?(i-1)/2:i/2,
      prev=1,
      next=2,
      vlist=open[path][0],
      ai=odd?open[path][next]:open[path][prev],
      bi=odd?vlist[len(vlist)-1]:vlist[0],
      a=[neighborlist[ai][0],neighborlist[ai][1]],
      b=[neighborlist[bi][0],neighborlist[bi][1]],
      p=[point[0],point[1]]
   )
   (i>=len(open)*2)?
      i
   :cross(b-a,p-b)>0?
      i
//On the line case?
   :(a[0]==p[0] && b[0]==p[0] && ((a[1]<=p[1] && p[1]<=b[1]) || (a[1]>=p[1] && p[1]>=b[1])))?
      i
   :
      componentposition(point,neighborlist,open,i=i+1)
;

/*
FIXME: This doesn't work? - want binary search...

function componentposition(point,neighborlist,components)=
   let(
      r2c=r2ceil(2*len(components)+1) //radix 2 ceiling 
   )
   componentpositionstep(point,neighborlist,components,pos=r2c-1,i=r2c/2)
;

function componentpositionstep(point,neighborlist,components,pos=0,i=1)=
   let(
      cur=floor(pos-i),
      odd=(cur%2==1),
      path=floor(cur/2),
      prev=1,
      next=2,
      component=components[path],
      vertexlist=component[0],
      ai=odd?component[next]:component[prev],
      bi=odd?vertexlist[len(vertexlist)-1]:vertexlist[0],
      a=[neighborlist[ai][0],neighborlist[ai][1]],
      b=[neighborlist[bi][0],neighborlist[bi][1]],
      p=[point[0],point[1]]
   )
   (i<1)?
      pos
   :cur>=(len(components)*2)?
      componentpositionstep(point,neighborlist,components,pos=pos-i,i=i/2)
   :cross(b-a,p-b)>0?
      componentpositionstep(point,neighborlist,components,pos=pos-i,i=i/2)
   :
      componentpositionstep(point,neighborlist,components,pos=pos,i=i/2)
;
*/


function checkstarts(point, open,incomp)=
   let(
      tocheck=[incomp,incomp-1,incomp+1],
      mypoint=point[2],
      prev=1
   )
   (0==len(open))?
      [false]
   :(mypoint==open[tocheck[0]][prev])?
      [true,tocheck[0]]
   :(tocheck[1]>=0 && mypoint==open[tocheck[1]][prev])?
      [true,tocheck[1]]
   :(tocheck[2]<len(open) && mypoint==open[tocheck[2]][prev])?
      [true,tocheck[2]]
   :
      [false]
;

function checkends(point, open,incomp)=
   let(
      tocheck=[incomp,incomp-1,incomp+1],
      mypoint=point[2],
      next=2
   )
   (0==len(open))?
      [false]
   :(mypoint==open[tocheck[0]][next])?
      [true,tocheck[0]]
   :(tocheck[1]>=0 && mypoint==open[tocheck[1]][next])?
      [true,tocheck[1]]
   :(tocheck[2]<len(open) && mypoint==open[tocheck[2]][next])?
      [true,tocheck[2]]
   :
      [false]
;

function sweeptriangulate (neighborlist,sweeplist,closed=[],open=[],i=0)=
  let(
     a=neighborlist[sweeplist[i][3]],
     b=neighborlist[sweeplist[i][4]],
     point=sweeplist[i],
//FIXME: These need to use binary search or something
//similar if this is to be O(N log N)

     pos=componentposition(point,neighborlist,open),
     incomp=floor(pos/2),
     starts=checkstarts(point,open,incomp),
     ends=checkends(point,open,incomp),
     index=2 //Fake associative array?
  )
//Testing stub
  (maxtest>0 && i>=maxtest)?
     [closed,open,"point",point,"incomp",incomp,"pos",pos,"starts",starts,"ends",ends]
  :
  (i>len(neighborlist)-1)? 
//no more points - all the components should be closed.
     closed
  :(starts[0] && ends[0])?
     (starts[1]==ends[1])? //Current point closes off a component
        sweeptriangulate(
           neighborlist,
           sweeplist,
           closed=concat(closed,componentclose(open[starts[1]],point)),
           open=concat(
              (starts[1]>0)?
                 sublist(open,0,starts[1]-1)
              :
                 []
              ,
              (starts[1]<len(open)-1)?
                 sublist(open,starts[1]+1,len(open)-1)
              :
                 []
           ),
           i=i+1
        )
     ://Current point hooks together components.
//Should die if starts[1]!=ends[1]+1
         let(
            new=componentfuse(neighborlist,open[ends[1]],open[starts[1]],point),
            newclosed=new[0],
            newopen=new[1]
         )
         sweeptriangulate(
           neighborlist,
           sweeplist,
           closed=concat(closed,newclosed),
           open=concat(
              (ends[1]>0)?sublist(open,0,ends[1]-1):[],
              [newopen],
              (starts[1]<len(open)-1)?sublist(open,starts[1]+1,len(open)-1):[]
           ),
           i=i+1
        )
   :(starts[0])?//Current point extends the left end of a component
        let(
           new=componentnewprev(neighborlist,open[starts[1]],point),
           newclosed=new[0],
           newopen=new[1]
        )
        sweeptriangulate(
           neighborlist,
           sweeplist,
           closed=concat(closed,newclosed),
           open=concat(
              (starts[1]>0)?sublist(open,0,starts[1]-1):[],
              [newopen],
              (starts[1]<len(open)-1)?sublist(open,starts[1]+1,-1):[]
           ),
           i=i+1
        )
   :(ends[0])?//Current point extends the right end of a component
        let(
           new=componentnewnext(neighborlist,open[ends[1]],point),
           newclosed=new[0],
           newopen=new[1]
        )
        sweeptriangulate(
           neighborlist,
           sweeplist,
           closed=concat(closed,newclosed),
           open=concat(
              (ends[1]>0)?sublist(open,0,ends[1]-1):[],
              [newopen],
              (ends[1]<len(open)-1)?sublist(open,ends[1]+1,-1):[]
           ),
           i=i+1
        )
   :(1==pos%2)? // Current point is "in" a component
        let(
           newopenlist=componentsplit(neighborlist,open[incomp],point)
        )
         sweeptriangulate(
            neighborlist,
            sweeplist,
            closed=closed,
            open=concat(
               (incomp>0)?sublist(open,0,incomp-1):[],
               newopenlist,
               (incomp<len(open)-1)?sublist(open,incomp+1,-1):[]
           ),
           i=i+1
        )
   ://Current point is 'between' components.
         sweeptriangulate(
            neighborlist,
            sweeplist,
            closed=closed,
            open=concat(
               (incomp>0)?sublist(open,0,incomp-1):[],
               [
                  newcomponent(neighborlist,point)
               ],
//Since it's "between" the incompth open component is retained.
               (incomp<=len(open)-1)?sublist(open,incomp,-1):[]
           ),
           i=i+1
        )
;


function sublist (list,a,b) =
    let(
       start=(a<0)?(len(list)+a)%len(list):a,
       end=(b<0)?(len(list)+b)%len(list):b
    )
    (start<=end)?
       [for (i=[start:end]) list[i]]
    :
       []
;

function reverse(list)=
   [for (i=[1:len(list)]) list[len(list)-i]]
;

function mkums (list,splitpoints) =
   let(
      ums=[for (i=[1:len(splitpoints)-1]) sublist(list,splitpoints[i-1]-1,splitpoints[i])],
      isreturn=3
   )
   [for (i=[0:len(ums)-1]) ums[i][1][isreturn]?reverse(ums[i]):ums[i]]
;

function triangulateums (ums,stack,i=0) =
   let(
      length=len(ums),
      next=ums[i],
      last=len(stack)-1
   )
   i>=length-1?
      [for (j=[1:len(stack)-1]) [stack[j-1],stack[j],ums[length-1]]]
   :(len(stack)<2 || cross(
         [stack[last-1][0],stack[last-1][1]]-[stack[last][0],stack[last][1]],[next[0],next[1]]-[stack[last][0],stack[last][1]])<0)?
      triangulateums(ums,concat(stack,[next]),i+1)
   :
      concat(
         [[stack[last-1],stack[last],next]],
         triangulateums(ums,sublist(stack,0,-2),i=i)
      )
;

function listgt (a,b,list,i=0) =
   (i>=len(list) || i<0 || list[i]<0 || list[i]>=len(a) || list[i]>= len(b)) ?
      false
   :(a[list[i]]==b[list[i]])?
      listgt(a,b,list,i+1)
   :(a[list[i]]>b[list[i]])?
      true
   :(a[list[i]]<b[list[i]])?
      false
   :
      false
;

function listeq (a,b,list,i=0) =
   (i>=len(list) || i<0 || list[i]<0 || list[i]>=len(a) || list[i]>= len(b)) ?
      false
   :(a[list[i]]>b[list[i]])?
      false
   :(a[list[i]]<b[list[i]])?
      false
   :(i<len(list)-1)?
      listeq(a,b,list,i+1)
   :
      true
;

function listquicksort(arr,list) =
   !(len(arr)>0)?
      []
   :
      let(
         pivot   = arr[floor(len(arr)/2)],
         lesser  = [ for (y = arr) if(listgt(pivot,y,list)) y ],
         equal   = [ for (y = arr) if(listeq(pivot,y,list)) y ],
         greater = [ for (y = arr) if(listgt(y,pivot,list)) y ]
      )
      concat(
    listquicksort(lesser,list), equal, listquicksort(greater,list)
);

//Sorting by local x, then local y.
function mksweeplist(neighborlist)=
   listquicksort(neighborlist,[0,1])
;

function patharea(points,path,localx,localy) =
    let(
       da=[for (i=[0:len(path)-1]) cross(points[path[i]]-points[path[0]],points[path[(i+1)%len(path)]]-points[path[i]])]
    )
    vsum(da)
;

//FIXME: Just making unimonotone components so far.
function triangulatecomponent(points,component)=
   let(
      l=len(component),
      minxindex=minx(points,component),
//negating the x coordinates so that is a sort by decreasing x.
//second coordinate is negative on the return leg.
      sortlist=[for (i=[0:l-1]) [-points[component[i]][0],-points[component[i]][1],i>minxindex?-i:i,i>minxindex,component[i]]],
      sortedlist=listquicksort(sortlist,[0,2]),
      switchpoints=[for (i=[1:l-1]) if(i==1 || i==l-1 || sortedlist[i][3]!=sortedlist[i-1][3]) i],
//      splits=mkums(sortedlist,switchpoints),
//      cleansplits=[for (split=splits) [for (a=split) a[4]]]
      umss=mkums(sortedlist,switchpoints),
      triangulated=flatten([for (ums=umss) triangulateums(ums,[],0)]),
      cleantriangles=[for (triangle=triangulated) [for (a=triangle) a[4]]]
   )
//["component",component,"sortedlist",sortedlist,"splitpoints",switchpoints,"splits",splits,"cleansplits",cleansplits]
//   cleansplits
   cleantriangles
;

function minx(points,component,i=0)=
   (i>=len(component)-1 || points[component[i+1]][0]>points[component[i]][0])?
      i
   :
   minx(points,component,i+1)
;

function mkneighborlist(points,paths,localx,localy)=
   let(
      localpoints=[for (i=[0:len(points)-1]) [points[i]*localx,points[i]*localy]],
      areas=[for (i=[0:len(paths)-1]) patharea(localpoints,paths[i])],
      list=[
         for(i=[0:len(paths)-1])
            for(j=[0:len(paths[i])-1])
               [
//Sweep line sort values
                   localpoints[paths[i][j]][0],
                   localpoints[paths[i][j]][1],
//Index
                   paths[i][j],
//neighbors - use oriented area for consistent winding.
                   areas[i]>0? paths[i][(j+1)%len(paths[i])]: paths[i][(len(paths[i])+j-1)%len(paths[i])],
                   areas[i]>0? paths[i][(len(paths[i])+j-1)%len(paths[i])]:paths[i][(j+1)%len(paths[i])],
//path number
                   areas[i]>0
               ]
      ]
   )
//sort by point index.
   listquicksort(list,[2])
;

function nontrivialsegment(points,path,i=0)=
   let(
      count=len(path),
      v=points[path[(i+1)%count]]-points[path[i]]
   )
   (i<count-1)?
      v*v>0?
         v
      :
         nontrivialsegment(points,path,i+1)
   :
      undef
;
   
function mk3d(list)=
   (2==len(list[0]))?
      [for (i=[0:len(list)-1]) concat(list[i],[0])]
   :(3==len(list[0]))?
      list
   :
      []
;

function vsum(v,i=0) = len(v)-1 > i ? v[i] + vsum(v, i+1) : v[i];

function winding_direction(points,path)=
   let(count=len(path))
   vsum([
      for(i=[0:count-1])
      cross(
         points[path[(i+1)%count]]-points[path[0]],
         points[path[(i+2)%count]]-points[path[(i+1)%count]]
      )
   ])
;

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