On 07/03/2010 12:19 PM, Taco Hoekwater wrote:
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.
Here is a somewhat smarter version of the same macro. This one
seems ok at first glance (extensive testing will probably show
border cases that are not covered).
Best wishes,
Taco
def inside(expr j, p) =
begingroup
save n;
hide(
save L, P, t, tt,bottom, top;
boolean abort;
path L,P;
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:
P := subpath (epsilon,(length P)) of P;
L := j--(xpart j, -infinity);
forever:
t := xpart (P intersectiontimes L);
exitif t<0;
tt := t;
forever:
exitif t<0;
exitif not (xpart direction t of P = 0);
L := L shifted (-epsilon,0);
t := xpart (P intersectiontimes L);
exitif t<0;
if t<tt:
L := L shifted (3epsilon,0);
t := xpart (P intersectiontimes L);
fi
endfor
exitif t < 0;
n := n + 1;
P := subpath (t+epsilon,(length P)) of P;
endfor;
fi )
if (n>0) and (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 := ((0,0)--(10,0)--(10,10)--(0,10)--cycle) rotated 130 shifted (20,10);
% P := (10,10){down}..(30,10){up} .. (0,10){down} .. (20,10){up}..cycle;
% P := ((25,10){down}..(10,0){right}..(30,5){up}..
% (20,10){up}..(30,15){up}..(20,20){left}..cycle) shifted (0,5);
nx := 50;
ny := 40;
pair endgrid;
endgrid := (40,30);
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;
draw P withcolor red;
currentpicture := currentpicture scaled 10;
endfig;
end.
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