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8.5
Precedence Rules of Binary Operators
METAPOST provides the classifiers primarydef, secondarydef, and tertiarydef (for def
macros, not for vardef macros) to set the level of priority of a binary operator. In the
example below, the orthogonal projection of a vector v along another vector w is defined as a
secondary binary operator.
u1
u4
2u2
u3
8.6
u2
beginfig(1);
secondarydef v projectedalong w =
if pair(v) and pair(w):
(v dotprod w) / (w dotprod w) * w
else:
errmessage "arguments must be vectors"
fi
enddef;
pair u[]; u1 = (20,80); u2 = (60,15);
drawarrow origin--u1;
drawarrow origin--u2;
drawarrow origin--2*u2;
u3 = u1 projectedalong u2;
u4 = 2*u2 projectedalong u1;
drawarrow origin--u3 withcolor blue;
draw u1--u3 dashed withdots;
draw ((1,0)--(1,1)--(0,1))
zscaled (6pt*unitvector(u2)) shifted u3;
drawarrow origin--u4 withcolor blue;
draw 2*u2--u4 dashed withdots;
draw ((1,0)--(1,1)--(0,1))
zscaled (6pt*unitvector(-u1)) shifted u4;
labeloffset := 4pt;
label.rt(btex $u_1$ etex, u1);
label.bot(btex $u_2$ etex, u2);
label.bot(btex $2u_2$ etex, 2*u2);
label.bot(btex $u_3$ etex, u3);
label.lft(btex $u_4$ etex, u4);
endfig;
end;
Recursion
A macro is defined recursively if in its definition, it makes a call to itself. Recursive definition
of a macro is possible in METAPOST. We shall illustrate this with the computation of a
Pythagorean tree.
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