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On 2/12/2021 9:35 AM, Taco Hoekwater wrote:
Hi,
On 11 Feb 2021, at 17:41, Mikael Sundqvist
wrote: Thanks for your investigation and extended example!
So, if I understand it correctly, the problem occurs where the different circles are glued together with the .. construction.
Took me a while to get it, but the problem is the definition of p0:
p[0] := cs .. cl .. (cs rotated 120) .. (cl rotated 120) .. (cs rotated 240) .. (cl rotated 240) .. cycle;
Here are cs and cl after your earlier definition:
cs := (141.73224999999996,-49.097491614210789) ..(75.312386775380347,111.25424516116959) ..(28.347427842053655,147.2925755432174);
cl := (28.346108531095332,147.29283827977969) ..(0,154.88788322842163) ..(-28.346108531095332,147.29283827977969);
Note how the last point of cs and the first point of cl are nearly the same. When you combine these bits into p0, p0 becomes a cyclic path with 18 points (where you really want/need only 12 points).
The micro-segments between these nearly-identical paths are the problem. At smaller u values the differences between the points become zero, and the directionpoint of a path of length zero is mathematically undefined.
I do not know a quick generic solution off hand, but that is what the issue is. Brilliant, as usual. So, now I can kick in with the dirty hackery (can be some proper thing but that's for later):
\starttext \startluacode function mp.foo() local p = mp.scan.path() local r = math.round local d = 100000 for i=1,#p do local pi = p[i] pi[1] = r(pi[1] * d) / d pi[2] = r(pi[2] * d) / d end local x1 = r(p[1][1]) local y1 = r(p[1][2]) local n = 1 local t = { p[1], cycle = p.cycle } for i=2,#p do local x2 = r(p[i][1]) local y2 = r(p[i][2]) if x1 ~= x2 or y1 ~= y2 then n = n + 1 t[n] = p[i] x1 = x2 y1 = y2 end end -- inspect(t) mp.inject.path(t) end \stopluacode \startMPdefinitions{doublefun} def FOO(expr u) = path p[]; % This defines the reulleaux curves % p[0] is a "base" reulleaux curve path cl,cs,rl ; z0 = (0,6/sqrt(3)*u); z1 = z0 rotated 120; cl := (fullcircle scaled 4u) shifted z0; cl := cl cutbefore point 1/6 along cl cutafter point 2/6 along cl; cs := (fullcircle scaled 16u) shifted z1; cs := cs cutafter point 1/6 along cs; p[0] := cs .. cl .. (cs rotated 120) .. (cl rotated 120) .. (cs rotated 240) .. (cl rotated 240) .. cycle; % p[0] := runscript("mp.foo()") p[0]; % the first curve (darkyellow) % p[1] := p[0] rotated 27 shifted (-10u,2u); p[1] := p[0] rotated 27 shifted (-10u,2u); draw p1 withpen pencircle scaled 2bp withcolor darkyellow; % the second curve (darkblue) p[2] := p[1] rotated 180; draw p2 withpen pencircle scaled 2bp withcolor darkblue; if true : p[1] := runscript("mp.foo()") p[1]; p[2] := runscript("mp.foo()") p[2]; p3 := for phi=0 step 30 until 360: ((directionpoint dir(phi) of p1) shifted (directionpoint dir(phi) of p2)) .. endfor cycle; draw p3 withpen pencircle scaled 2bp withcolor darkred; else : drawarrow for phi=0 step 30 until 360: (directionpoint dir(phi) of p1) -- endfor cycle withpen pencircle scaled 1bp withcolor darkgreen; drawarrow for phi=0 step 30 until 360: (directionpoint dir(phi) of p2) -- endfor cycle withpen pencircle scaled 1bp withcolor darkmagenta; drawarrow for phi=0 step 30 until 360: ((directionpoint dir(phi) of p1) shifted (directionpoint dir(phi) of p2)) -- endfor cycle withpen pencircle scaled 1bp withcolor darkred; fi ; % We give one direction as example % These are merely here to show the construction of the curve % But they also show what is going wrong direx:=40; z11=directionpoint dir(direx) of p1; z22=directionpoint dir(direx) of p2; p4 = ((-u,0)--(u,0)) rotated direx; % These arrows should be tangent drawarrow p4 shifted z11; drawarrow p4 shifted z22; drawarrow p4 shifted (z11 shifted z22); % Draw the parallelogram. draw origin -- z11 dashed evenly; draw origin -- z22 dashed evenly; draw z11 -- (z11 shifted z22) dashed evenly; draw z22 -- (z11 shifted z22) dashed evenly; enddef ; \stopMPdefinitions \startMPpage[offset=4bp,instance=doublefun] FOO(1cm); \stopMPpage \startMPpage[offset=4bp,instance=doublefun] FOO(.8cm); \stopMPpage \startMPpage[offset=4bp,instance=doublefun] FOO(.5cm); \stopMPpage \startMPpage[offset=4bp,instance=doublefun] FOO(.2cm); \stopMPpage \stoptext ----------------------------------------------------------------- Hans Hagen | PRAGMA ADE Ridderstraat 27 | 8061 GH Hasselt | The Netherlands tel: 038 477 53 69 | www.pragma-ade.nl | www.pragma-pod.nl -----------------------------------------------------------------