Re: [NTG-context] Metapost: directionpoint gives unexpected point(?)

Hi, since I already started this thread, I continue here. My metapost code is still not always working, and I do not understand what is going wrong. In the example below, I draw two curves of constant width (p1 and p2), one rotated 180 degrees around the origin. Then I draw the curve (p3), constructed as follows: for each direction (phi), find the point of p1 and p2 which correspond to it, and add those points. This should result in a circle, and with the code I paste it does (hooray! see the file minkowski-good.pdf). BUT, it seems very unstable. If I change u to 0.5cm instead of 1cm, it breaks down (see minkowski-bad.pdf). If I loop over more angles phi (say step 2 instead of step 30), it gets wrong. Any ideas are welcome. /Mikael \starttext \startMPpage[offset=4bp,instance=doublefun] u:=1cm; 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; % the first curve (darkyellow) 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; % the minkowski sum (darkred) of the reulleaux curves p1 and p2. 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; % 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; dotlabel.top("$O$",origin); \stopMPpage \stoptext On Fri, Feb 5, 2021 at 5:51 PM Mikael Sundqvist wrote:

Hi,

I was too quick to push send. This must be some rounding error. Changing the instance fixes the problem. Sorry for the noise.

/Mikael

On Fri, Feb 5, 2021 at 5:48 PM Mikael Sundqvist wrote:

...

Hi,

I get sometimes the wrong directionpoint. In the example below it works for all values of direx except between 0 and 90. If I put direx to something in this interval, it seems that the point between cs and cl are chosen.

Is there a better way to construct the paths not to get this problem? Or some other way out?

/Mikael

\starttext \startMPpage[offset=3bp] u:=1cm; path cl,cs,rl,p[]; z0 = (0,6/sqrt(3)*u); z1 = z0 rotated 120; cs := (fullcircle scaled 16u) shifted z1; cs := cs cutafter point 1/6 along cs; cl := (fullcircle scaled 4u) shifted z0; cl := cl cutbefore point 1/6 along cl cutafter point 2/6 along cl;

p[0] = cs .. cl .. (cs rotated 120) .. (cl rotated 120) .. (cs rotated 240) .. (cl rotated 240) .. cycle;

draw p[0];

drawarrow cs withcolor darkblue; drawarrow cl withcolor darkred;

direx=300; z11=directionpoint dir(direx) of p[0]; drawarrow ((-u,0)--(u,0)) rotated direx shifted z11;

\stopMPpage \stoptext