On 07/03/2010 10:03 AM, Taco Hoekwater wrote:
If this is too complicated, it might help if I can find out if a given
point lies inside a given cycled path.
Even this is fairly tricky. Some important questions are:
I thought this was a neat thing to try to write a macro for. Attached
is a test file that defines a macro inside() that takes two arguments:
a point and a cyclic path. It returns true if the point lies inside
that path, in most cases. There are lots of problems with it;
what happens to a point actually on the curve is basically undefined,
and self-intersects sometimes make it fail in interesting ways.
Anyway, perhaps it helps.
Best wishes,
Taco
def inside(expr j, p) =
begingroup
save n;
hide(
save done, L, P, t, bottom, top;
boolean done;
path L,P;
numeric t[];
pair bottom, top;
bottom = llcorner p;
top = urcorner p;
P := p;
n := 0;
if (xpart j <= xpart bottom) or (xpart j >= xpart top)
or (ypart j <= ypart bottom) or (ypart j >= ypart top):
else:
L := j--(xpart j, ((ypart bottom)-100));
done := false;
forever:
(t[n],whatever) = L intersectiontimes P;
if (t[n]<0) and (n>0) : % find upward match
P := reverse P;
numeric t[];
L := j--(xpart j, ((ypart bottom)-100));
forever:
(t[n],whatever) = L intersectiontimes P;
exitif t[n]<0;
L := subpath (t[n]+epsilon, length L) of L;
n := n + 1;
endfor;
done := true;
fi
exitif done;
L := subpath (t[n]+epsilon,length L) of L;
n := n + 1;
endfor;
fi )
if (n>1) and (not odd n): true else: false fi
endgroup
enddef;
beginfig(1);
path P;
% P:= (fullcircle scaled 20) shifted (20,20);
% P:= (0,10){down}..(10,10){up} .. (30,10){down} .. (20,10){up}..cycle;
% P := unitsquare scaled 10 rotated 30 shifted (20,10);
% P := (10,10){down}..(30,10){up} .. (0,10){down} .. (20,10){up}..cycle;
P := (0,10){down}..(10,0){right}..(30,5){up}..
(20,10){up}..(30,15){up}..(20,20){left}..cycle;
draw P withcolor red;
nx := 100;
ny := 100;
pair endgrid;
endgrid := (30,30);
pickup pencircle xscaled (xpart endgrid/nx) yscaled (ypart endgrid/ny);
pair J;
for k = 1 upto nx:
for l = 1 upto ny:
J := (k/nx*xpart endgrid,l/ny*ypart endgrid);
if inside(J,P):
drawdot J withcolor green;
else:
drawdot J withcolor blue;
fi
endfor;
endfor;
currentpicture := currentpicture scaled 10;
endfig;
end.
___________________________________________________________________________________
If your question is of interest to others as well, please add an entry to the
Wiki!
maillist : [email protected] / http://www.ntg.nl/mailman/listinfo/ntg-context
webpage : http://www.pragma-ade.nl / http://tex.aanhet.net
archive : http://foundry.supelec.fr/projects/contextrev/
wiki : http://contextgarden.net
___________________________________________________________________________________
