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Ft(78)253 974 y Fk(h)p Ft(if)13 b(test)r Fk(i)e(!)g Fo(if)p Fk(h)p Ft(b)q(o)q(olean)i(expression)r Fk(i)p Fo(:)p Fk(h)p Ft(balanced)h(tok)o(ens)p Fk(ih)p Ft(alternativ)o(es)q Fk(i)p Fo(fi)253 1024 y Fk(h)p Ft(alternativ)o(es)q Fk(i)d(!)g(h)p Ft(empt)o(y)o Fk(i)348 1073 y(j)g Fo(else:)o Fk(h)p Ft(balanced)j(tok)o(ens)p Fk(i)348 1123 y(j)d Fo(elseif)p Fk(h)p Ft(b)q(o)q(olean)h(expression)q Fk(i)q Fo(:)o Fk(h)p Ft(balanced)j(tok)o(ens)p Fk(ih)p Ft(alternativ)o(es)q Fk(i)253 1223 y(h)p Ft(lo)q(op)p Fk(i)c(!)g(h)p Ft(lo)q(op)j(header)q Fk(i)p Fo(:)p Fk(h)p Ft(lo)q(op)f(text)p Fk(i)q Fo(endfor)253 1273 y Fk(h)p Ft(lo)q(op)g(header)r Fk(i)e(!)g Fo(for)p Fk(h)p Ft(sym)o(b)q(olic)h(tok)o(en)p Fk(i)p Fo(=)p Fk(h)p Ft(progression)q Fk(i)348 1323 y(j)f Fo(for)p Fk(h)p Ft(sym)o(b)q(olic)g(tok)o(en)q Fk(i)p Fo(=)p Fk(h)p Ft(for)i(list)p Fk(i)348 1372 y(j)e Fo(forsuffixes)p Fk(h)p Ft(sym)n(b)q(oli)o(c)h(tok)o(en)p Fk(i)p Fo(=)p Fk(h)p Ft(su\016x)i(list)o Fk(i)348 1422 y(j)d Fo(forever)253 1472 y Fk(h)p Ft(progression)q Fk(i)h(!)f(h)p Ft(n)o(umeric)i(expression)q Fk(i)p Fo(upto)p Fk(h)p Ft(n)o(umeric)g(expression)q Fk(i)348 1522 y(j)e(h)p Ft(n)o(umeric)i(expression)q Fk(i)p Fo(downto)p Fk(h)p Ft(n)o(umeric)f(expression)r Fk(i)348 1572 y(j)f(h)p Ft(n)o(umeric)i(expression)q Fk(i)p Fo(step)p Fk(h)p Ft(n)o(umeric)g (expression)q Fk(i)p Fo(until)p Fk(h)p Ft(n)o(umeric)f(expression)r Fk(i)253 1621 y(h)p Ft(for)i(list)o Fk(i)e(!)f(h)p Ft(expression)r Fk(i)g(j)g(h)p Ft(for)j(list)p Fk(i)p Fo(,)o Fk(h)p Ft(expression)r Fk(i)253 1671 y(h)p Ft(su\016x)g(list)p Fk(i)d(!)g(h)p Ft(su\016x)q Fk(i)g(j)g(h)p Ft(su\016x)j(list)p Fk(i)p Fo(,)p Fk(h)p Ft(su\016x)p Fk(i)530 1804 y Ft(Figure)g(61:)k(The)c(syn)o(tax)g(for)f(conditionals)g(and) h(lo)q(ops)p eop %%Page: 77 11 bop 75 -54 a Fq(A)14 b(User's)h(Man)o(ual)e(for)g(MetaP)o(ost)1203 b Ft(77)329 376 y Fk(h)p Ft(command)m Fk(i)12 b(!)f Fo(clip)p Fk(h)p Ft(picture)j(v)n(ariable)o Fk(i)p Fo(to)p Fk(h)p Ft(path)g(expression) q Fk(i)424 426 y(j)d 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y(j)e Fo(addto)p Fk(h)p Ft(picture)j(v)n (ariable)o Fk(i)p Fo(doublepath)p Fk(h)p Ft(path)e(expression)q Fk(ih)p Ft(option)h(list)p Fk(i)329 1821 y(h)p Ft(option)g(list)p Fk(i)f(!)f(h)p Ft(empt)o(y)o Fk(i)g(j)h(h)p Ft(dra)o(wing)h(option)o Fk(ih)p Ft(option)g(list)p Fk(i)329 1870 y(h)p Ft(dra)o(wing)g(option)p Fk(i)e(!)g Fo(withcolor)p Fk(h)p Ft(color)h(expression)q Fk(i)424 1920 y(j)f Fo(withpen)p Fk(h)p Ft(p)q(en)i(expression)q Fk(i)f(j)f Fo(dashed)p Fk(h)p Ft(picture)j(expression)q Fk(i)329 2020 y(h)p Ft(dra)o(wing)f(command)n Fk(i)e(!)g Fo(draw)p Fk(h)p Ft(picture)j(expression)r Fk(ih)p Ft(with)f(list)p Fk(i)424 2070 y(j)e(h)p Ft(\014ll)i(t)o(yp)q(e)p Fk(ih)p Ft(path)h(expression)r Fk(ih)p Ft(with)g(list)o Fk(i)329 2120 y(h)p Ft(\014ll)f(t)o(yp)q(e)q Fk(i)e(!)g Fo(fill)g Fk(j)g Fo(draw)g Fk(j)g Fo(filldraw)f Fk(j)h Fo(unfill)f Fk(j)h Fo(undraw)g Fk(j)g Fo(unfilldraw)424 2169 y Fk(j)g Fo(drawarrow)e Fk(j)i Fo(drawdblarrow)e Fk(j)i Fo(cutdraw)329 2269 y Fk(h)p Ft(tracing)j(command)m 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Fk(i)e(!)g(h)p Ft(primary)o Fk(i)367 2452 y Ft(Figure)j(58:)k(Miscellaneous)c (pro)q(ductions)g(needed)i(to)d(complete)h(the)g(BNF)p eop %%Page: 74 14 bop 75 -54 a Fq(A)14 b(User's)h(Man)o(ual)e(for)g(MetaP)o(ost)1203 b Ft(74)285 152 y Fk(h)p Ft(transformer)p Fk(i)11 b(!)g Fo(rotated)p Fk(h)p Ft(n)o(umeric)h(primary)n Fk(i)379 202 y(j)f Fo(scaled)p Fk(h)p Ft(n)o(umeric)h(primary)o Fk(i)379 252 y(j)f Fo(shifted)p Fk(h)p Ft(pair)i(primary)n Fk(i)379 301 y(j)e Fo(slanted)p Fk(h)p Ft(n)o(umeric)h(primary)o Fk(i)379 351 y(j)f Fo(transformed)p Fk(h)p Ft(transform)g(primary)n Fk(i)379 401 y(j)g Fo(xscaled)p Fk(h)p Ft(n)o(umeric)h(primary)o Fk(i)379 451 y(j)f Fo(yscaled)p Fk(h)p Ft(n)o(umeric)h(primary)o Fk(i)379 501 y(j)f Fo(zscaled)p Fk(h)p Ft(pair)i(primary)n Fk(i)379 550 y(j)e Fo(reflectedabout\()m Fk(h)p Ft(pair)j(expression)q Fk(i)p Fo(,)p Fk(h)p Ft(pair)g(expression)q Fk(i)p Fo(\))379 600 y Fk(j)d Fo(rotatedaround\()n Fk(h)p Ft(pair)i (expression)q Fk(i)q Fo(,)o Fk(h)p Ft(n)o(umeric)h(expression)q Fk(i)p Fo(\))285 700 y Fk(h)p Ft(n)o(ullary)f(op)p Fk(i)e(!)g Fo(false)g Fk(j)g Fo(normaldeviate)e Fk(j)i Fo(nullpicture)e Fk(j)i Fo(pencircle)379 750 y Fk(j)g Fo(true)g Fk(j)g Fo(whatever)285 800 y Fk(h)p Ft(unary)j(op)p Fk(i)d(!)g(h)p Ft(t)o(yp)q(e)q Fk(i)379 849 y(j)g Fo(abs)g Fk(j)g Fo(angle)g Fk(j)g Fo(arclength)f Fk(j)h Fo(ASCII)f Fk(j)h Fo(bbox)g Fk(j)g Fo(bluepart)f Fk(j)h Fo(bot)g Fk(j)g Fo(ceiling)379 899 y Fk(j)g Fo(center)g Fk(j)g Fo(char)g Fk(j)g Fo(cosd)f Fk(j)h Fo(cycle)g Fk(j)g Fo(decimal)f Fk(j)h Fo(dir)g Fk(j)g Fo(floor)g Fk(j)g Fo(fontsize)379 949 y Fk(j)g Fo(greenpart)f Fk(j)h Fo(hex)g Fk(j)g Fo(inverse)f Fk(j)h Fo(known)g Fk(j)g Fo(length)f Fk(j)h Fo(lft)g Fk(j)g Fo(llcorner)379 999 y Fk(j)g Fo(lrcorner)f Fk(j)h Fo(makepath)f Fk(j)h Fo(makepen)f Fk(j)i Fo(mexp)e Fk(j)h Fo(mlog)g Fk(j)g Fo(not)g Fk(j)g Fo(oct)g Fk(j)g Fo(odd)379 1049 y Fk(j)g Fo(redpart)g Fk(j)g Fo(reverse)f Fk(j)h Fo(round)f Fk(j)h Fo(rt)g Fk(j)h Fo(sind)e Fk(j)h 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Fk(j)g Fo(>)g Fk(j)g Fo(>=)379 1547 y Fk(j)g Fo(cutafter)f Fk(j)h Fo(cutbefore)285 1597 y Fk(h)p Ft(of)i(op)q(erator)q Fk(i)f(!)f Fo(arctime)f Fk(j)h Fo(direction)e Fk(j)i Fo(directiontime)e Fk(j)i Fo(directionpoint)379 1646 y Fk(j)g Fo(penoffset)f Fk(j)h Fo(point)g Fk(j)g Fo(postcontrol)e Fk(j)i Fo(precontrol)f Fk(j)h Fo(subpath)379 1696 y Fk(j)g Fo(substring)285 1796 y Fk(h)p Ft(v)n(ariable)o Fk(i)h(!)f(h)p Ft(tag)o Fk(i)q(h)p Ft(su\016x)p Fk(i)285 1846 y(h)p Ft(su\016x)p Fk(i)h(!)f(h)p Ft(empt)o(y)o Fk(i)h(j)f(h)p Ft(su\016x)p Fk(ih)p Ft(subscript)q Fk(i)h(j)f(h)p Ft(su\016x)p Fk(ih)p Ft(tag)p Fk(i)379 1895 y(j)g(h)p Ft(su\016x)j(parameter) p Fk(i)285 1945 y(h)p Ft(subscript)q Fk(i)e(!)f(h)p Ft(n)o(um)o(b)q(er)p Fk(i)g(j)g Fo([)p Fk(h)p Ft(n)o(umeric)i(expression)r Fk(i)p Fo(])285 2045 y Fk(h)p Ft(in)o(ternal)h(v)n(ariable)n Fk(i)e(!)f Fo(ahangle)f Fk(j)h Fo(ahlength)f Fk(j)h Fo(bboxmargin)379 2095 y Fk(j)g Fo(charcode)f Fk(j)h Fo(day)g Fk(j)g Fo(defaultpen)f Fk(j)h Fo(defaultscale)e Fk(j)i Fo(labeloffset)379 2144 y Fk(j)g Fo(linecap)g Fk(j)g Fo(linejoin)f Fk(j)h Fo(miterlimit)e Fk(j)i Fo(month)g Fk(j)g Fo(pausing)379 2194 y Fk(j)g Fo(prologues)f Fk(j)h Fo(showstopping)e Fk(j)i Fo(time)g Fk(j)g Fo(tracingoutput)379 2244 y Fk(j)g Fo(tracingcapsules)e Fk(j)i Fo(tracingchoices)e Fk(j)i Fo(tracingcommands)379 2294 y Fk(j)g Fo(tracingequations)e Fk(j)i Fo(tracinglostchars)d Fk(j)j Fo(tracingmacros)379 2344 y Fk(j)g Fo(tracingonline)e Fk(j)i Fo(tracingrestores)e Fk(j)i Fo(tracingspecs)379 2394 y Fk(j)g Fo(tracingstats)f Fk(j)h Fo(tracingtitles)d Fk(j)k Fo(truecorners)379 2443 y Fk(j)f Fo(warningcheck)f Fk(j)h Fo(year)379 2493 y Fk(j)g(h)p Ft(sym)o(b)q(olic)i (tok)o(en)h(de\014ned)h(b)o(y)e Fo(newinternal)n Fk(i)551 2626 y Ft(Figure)h(56:)j(P)o(art)d(2)g(of)f(the)h(syn)o(tax)g(for)g(expressions)p eop %%Page: 73 15 bop 75 -54 a Fq(A)14 b(User's)h(Man)o(ual)e(for)g(MetaP)o(ost)1203 b Ft(73)308 126 y Fk(h)p Ft(atom)n Fk(i)12 b(!)f(h)p Ft(v)n(ariable)o Fk(i)h(j)f(h)p Ft(argumen)o(t)o Fk(i)402 176 y(j)g(h)p Ft(n)o(um)o(b)q(er)j (or)f(fraction)p Fk(i)402 226 y(j)e(h)p Ft(in)o(ternal)j(v)n(ariable)o Fk(i)402 276 y(j)d Fo(\()p Fk(h)p Ft(expression)q Fk(i)q Fo(\))402 325 y Fk(j)g Fo(begingroup)p Fk(h)p Ft(statemen)o(t)h(list)p Fk(ih)p Ft(expression)q Fk(i)p Fo(endgroup)402 375 y Fk(j)f(h)p Ft(n)o(ullary)i(op)p Fk(i)402 425 y(j)e Fo(btex)p Fk(h)p Ft(t)o(yp)q (esetting)j(commands)n Fk(i)p Fo(etex)402 475 y Fk(j)d(h)p Ft(pseudo)k(function)p Fk(i)308 525 y(h)p Ft(primary)n Fk(i)d(!)f(h)p Ft(atom)n Fk(i)402 575 y(j)g Fo(\()p Fk(h)p Ft(n)o(umeric)i(expression)r Fk(i)p Fo(,)p Fk(h)p Ft(n)o(umeric)g(expression)q Fk(i)p Fo(\))402 624 y Fk(j)e Fo(\()p Fk(h)p Ft(n)o(umeric)i(expression)r Fk(i)p Fo(,)p Fk(h)p Ft(n)o(umeric)g(expression)q Fk(i)p Fo(,)p Fk(h)p Ft(n)o(umeric)g(expression)q Fk(i)p Fo(\))402 674 y Fk(j)e(h)p Ft(of)j(op)q(erator)p Fk(ih)p Ft(expression)r Fk(i)p Fo(of)p Fk(h)p Ft(primary)n Fk(i)402 724 y(j)d(h)p Ft(unary)j(op)p Fk(ih)p Ft(primary)o Fk(i)402 774 y(j)d Fo(str)p Fk(h)p Ft(su\016x)p Fk(i)402 824 y(j)g Fo(z)p Fk(h)p Ft(su\016x)p Fk(i)402 873 y(j)g(h)p Ft(n)o(umeric)j(atom)n Fk(i)p Fo([)p Fk(h)p Ft(expression)q Fk(i)p Fo(,)p Fk(h)p Ft(expression)q Fk(i)q Fo(])402 923 y Fk(j)d(h)p Ft(scalar)j(m)o(ultiplication)d(op)p Fk(ih)p Ft(primary)n Fk(i)308 973 y(h)p Ft(secondary)q Fk(i)h(!)f(h)p Ft(primary)n Fk(i)402 1023 y(j)g(h)p Ft(secondary)r Fk(ih)p Ft(primary)h(binop)p Fk(ih)p Ft(primary)n Fk(i)402 1073 y(j)f(h)p Ft(secondary)r Fk(ih)p Ft(transformer)o Fk(i)308 1122 y(h)p Ft(tertiary)p Fk(i)h(!)f(h)p Ft(secondary)q Fk(i)402 1172 y(j)g(h)p Ft(tertiary)q Fk(ih)p Ft(secondary)k(binop)p Fk(ih)p Ft(secondary)q Fk(i)308 1222 y(h)p Ft(sub)q(expression)r Fk(i)c(!)g(h)p Ft(tertiary)q Fk(i)402 1272 y(j)g(h)p Ft(path)j(expression)r Fk(ih)p Ft(path)g(join)o Fk(ih)p Ft(path)g(knot)p Fk(i)308 1322 y(h)p Ft(expression)q Fk(i)e(!)f(h)p Ft(sub)q(expression)r Fk(i)402 1372 y(j)g(h)p Ft(expression)r Fk(ih)p Ft(tertiary)j(binop)p Fk(ih)p Ft(tertiary)p Fk(i)402 1421 y(j)d(h)p Ft(path)j(sub)q(expression)r Fk(ih)p Ft(direction)h(sp)q(eci\014er)q Fk(i)402 1471 y(j)c(h)p Ft(path)j(sub)q (expression)r Fk(ih)p Ft(path)g(join)o Fk(i)q Fo(cycle)308 1571 y Fk(h)p Ft(path)g(knot)p Fk(i)d(!)g(h)p Ft(tertiary)q Fk(i)308 1621 y(h)p Ft(path)j(join)o Fk(i)d(!)g(\000\000)402 1670 y(j)g(h)p Ft(direction)k(sp)q(eci\014er)q Fk(ih)p Ft(basic)g(path)e (join)p Fk(ih)p Ft(direction)h(sp)q(eci\014er)r Fk(i)308 1720 y(h)p Ft(direction)g(sp)q(eci\014er)r Fk(i)d(!)g(h)p Ft(empt)o(y)p Fk(i)402 1770 y(j)g(f)p Fo(curl)p Fk(h)p Ft(n)o(umeric)h(expression)r Fk(ig)402 1820 y(j)f(fh)p Ft(pair)j(expression)q Fk(ig)402 1870 y(j)d(fh)p Ft(n)o(umeric)i(expression)r Fk(i)p Fo(,)o Fk(h)p Ft(n)o(umeric)h(expression)q Fk(ig)308 1919 y(h)p Ft(basic)g(path)g (join)o Fk(i)d(!)g Fo(..)h Fk(j)f Fo(...)g Fk(j)g Fo(..)o Fk(h)p Ft(tension)q Fk(i)p Fo(..)g Fk(j)g Fo(..)p Fk(h)p Ft(con)o(trols)p Fk(i)p Fo(..)308 1969 y Fk(h)p Ft(tension)p Fk(i)h(!)f Fo(tension)p Fk(h)p Ft(n)o(umeric)h(primary)n Fk(i)402 2019 y(j)f Fo(tension)p Fk(h)p Ft(n)o(umeric)h(primary)n Fk(i)q Fo(and)p Fk(h)p Ft(n)o(umeric)g (primary)o Fk(i)308 2069 y(h)p Ft(con)o(trols)p Fk(i)g(!)f Fo(controls)p Fk(h)p Ft(pair)h(primary)n Fk(i)402 2119 y(j)f Fo(controls)p Fk(h)p Ft(pair)h(primary)o Fk(i)p Fo(and)p Fk(h)p Ft(pair)h(primary)n Fk(i)308 2218 y(h)p Ft(argumen)o(t)o Fk(i)e(!)g(h)p Ft(sym)o(b)q(olic)i(tok)o(en)p Fk(i)308 2268 y(h)p Ft(n)o(um)o(b)q(er)g(or)h (fraction)p Fk(i)d(!)g(h)p Ft(n)o(um)o(b)q(er)p Fk(i)p Fo(/)p Fk(h)p Ft(n)o(um)o(b)q(er)o Fk(i)402 2318 y(j)g(h)p Ft(n)o(um)o(b)q(er)j(not) f(follo)o(w)o(ed)g(b)o(y)g(`)p Fo(/)p Fk(h)p Ft(n)o(um)o(b)q(er)p Fk(i)p Ft(')o Fk(i)308 2368 y(h)p Ft(scalar)h(m)o(ultiplicatio)o(n)d(op)p Fk(i)h(!)f Ft(+)h Fk(j)f(\000)402 2418 y(j)g(h)p Ft(`)p Fk(h)p Ft(n)o(um)o(b)q(er)i(or)h(fraction)p Fk(i)p Ft(')f(not)h(follo)o(w)o(ed)e(b)o (y)i(`)p Fk(h)p Ft(add)f(op)p Fk(ih)p Ft(n)o(um)o(b)q(er)p Fk(i)p Ft(')p Fk(i)551 2550 y 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w(Argumen)o(t/result)g(t)o(yp)q(es)p 1044 269 V 159 w(P)o(age)p 1181 269 V 262 w(Explanation)p 1876 269 V 365 271 681 2 v 74 319 2 50 v 364 319 V 389 304 a(Left)p 590 319 V 154 w(Righ)o(t)p 817 319 V 125 w(Result)p 1044 319 V 1181 319 V 1876 319 V 75 321 1802 2 v 75 331 V 74 381 2 50 v 100 366 a Fo(string)p 364 381 V 157 w Ft({)p 590 381 V 206 w(an)o(y)p 817 381 V 162 w(b)q(o)q(olean)p 1044 381 V 131 w(16)p 1181 381 V 49 w(Is)h(the)f(expression)h(of)e(t)o(yp)q (e)i(string?)p 1876 381 V 75 382 1802 2 v 74 432 2 50 v 100 417 a Fo(subpath)p 364 432 V 135 w Ft(pair)p 590 432 V 155 w(path)p 817 432 V 144 w(path)p 1044 432 V 189 w(28)p 1181 432 V 49 w(P)o(ortion)f(of)f(a)h(path)g(for)f(giv)o(en)g(range)p 1876 432 V 74 482 V 100 467 a Fo(of)p 364 482 V 590 482 V 817 482 V 1044 482 V 1181 482 V 1062 w Ft(of)h(time)e(v)n(alues)p 1876 482 V 75 484 1802 2 v 74 533 2 50 v 100 518 a Fo(substring)p 364 533 V 91 w Ft(pair)p 590 533 V 155 w(string)p 817 533 V 123 w(string)p 1044 533 V 168 w(14)p 1181 533 V 49 w(Substring)j(b)q(ounded)f (b)o(y)g(giv)o(en)f(indices)p 1876 533 V 74 583 V 100 568 a Fo(of)p 364 583 V 590 583 V 817 583 V 1044 583 V 1181 583 V 1876 583 V 75 585 1802 2 v 74 635 2 50 v 100 620 a Fk(y)p Fo(top)p 364 635 V 205 w Ft({)p 590 635 V 206 w(n)o(umeric)p 817 635 V 82 w(n)o(umeric)p 1044 635 V 127 w(38)p 1181 635 V 49 w(T)m(op)h(of)f (curren)o(t)i(p)q(en)g(when)f(cen)o(tered)p 1876 635 V 74 685 V 364 685 V 590 685 V 616 670 a(pair)p 817 685 V 155 w(pair)p 1044 685 V 1181 685 V 291 w(at)g(the)h(giv)o(en)e(co)q(ordinate\(s\))p 1876 685 V 75 686 1802 2 v 74 736 2 50 v 100 721 a Fo(transform)p 364 736 V 91 w Ft({)p 590 736 V 206 w(an)o(y)p 817 736 V 162 w(b)q(o)q(olean)p 1044 736 V 131 w(16)p 1181 736 V 49 w(Is)i(the)f(argumen)o (t)f(of)g(t)o(yp)q(e)i(transform?)p 1876 736 V 75 738 1802 2 v 74 787 2 50 v 100 773 a Fo(transformed)p 364 787 V 47 w Ft(picture)p 590 787 V 101 w(transform)p 817 787 V 49 w(picture)p 1044 787 V 146 w(31)p 1181 787 V 49 w(Apply)f(the)g(giv)o(en)g(transform)f (to)g(all)p 1876 787 V 74 837 V 364 837 V 389 822 a(path)p 590 837 V 817 837 V 371 w(path)p 1044 837 V 1181 837 V 280 w(co)q(ordinates)p 1876 837 V 74 887 V 364 887 V 389 872 a(pair)p 590 887 V 817 887 V 382 w(pair)p 1044 887 V 1181 887 V 1876 887 V 74 937 V 364 937 V 389 922 a(p)q(en)p 590 937 V 817 937 V 389 w(p)q(en)p 1044 937 V 1181 937 V 1876 937 V 74 987 V 364 987 V 389 972 a(transform)p 590 987 V 817 987 V 276 w(transform)p 1044 987 V 1181 987 V 1876 987 V 75 988 1802 2 v 74 1038 2 50 v 100 1023 a Fo(ulcorner)p 364 1038 V 113 w Ft({)p 590 1038 V 206 w(picture)p 817 1038 V 101 w(pair)p 1044 1038 V 200 w(22)p 1181 1038 V 49 w(Upp)q(er-left)i(corner)g(of)e(b)q(ounding)h(b)q(o)o(x)p 1876 1038 V 74 1088 V 364 1088 V 590 1088 V 616 1073 a(path)p 817 1088 V 1044 1088 V 1181 1088 V 1876 1088 V 74 1138 V 364 1138 V 590 1138 V 616 1123 a(p)q(en)p 817 1138 V 1044 1138 V 1181 1138 V 1876 1138 V 75 1139 1802 2 v 74 1189 2 50 v 100 1174 a Fo(uniform-)p 364 1189 V 113 w Ft({)p 590 1189 V 206 w(n)o(umeric)p 817 1189 V 82 w(n)o(umeric)p 1044 1189 V 148 w({)p 1181 1189 V 49 w(Random)e(n)o(um)o(b)q(er)h(b)q(et)o(w)o(een)i(zero)g (and)p 1876 1189 V 74 1239 V 100 1224 a Fo(deviate)p 364 1239 V 590 1239 V 817 1239 V 1044 1239 V 1181 1239 V 952 w Ft(the)g(v)n(alue)e(of) g(the)i(argumen)o(t)p 1876 1239 V 75 1241 1802 2 v 74 1291 2 50 v 100 1276 a Fk(y)p Fo(unitvector)p 364 1291 V 51 w Ft({)p 590 1291 V 206 w(pair)p 817 1291 V 155 w(pair)p 1044 1291 V 200 w(15)p 1181 1291 V 49 w(Rescale)g(a)e(v)o(ector)i(so)f(its)g(length)g(is) f(1)p 1876 1291 V 75 1292 1802 2 v 74 1342 2 50 v 100 1327 a Fo(unknown)p 364 1342 V 135 w Ft({)p 590 1342 V 206 w(an)o(y)p 817 1342 V 162 w(b)q(o)q(olean)p 1044 1342 V 131 w(16)p 1181 1342 V 49 w(Is)i(the)f(v)n(alue)f(unkno)o(wn?)p 1876 1342 V 75 1344 1802 2 v 74 1394 2 50 v 100 1379 a Fo(urcorner)p 364 1394 V 113 w Ft({)p 590 1394 V 206 w(picture)p 817 1394 V 101 w(pair)p 1044 1394 V 200 w(22)p 1181 1394 V 49 w(Upp)q(er-left)i(corner)g(of) e(b)q(ounding)h(b)q(o)o(x)p 1876 1394 V 74 1443 V 364 1443 V 590 1443 V 616 1428 a(path)p 817 1443 V 1044 1443 V 1181 1443 V 1876 1443 V 74 1493 V 364 1493 V 590 1493 V 616 1478 a(p)q(en)p 817 1493 V 1044 1493 V 1181 1493 V 1876 1493 V 75 1495 1802 2 v 74 1545 2 50 v 100 1530 a Fk(y)p Fo(whatever)p 364 1545 V 95 w Ft({)p 590 1545 V 206 w({)p 817 1545 V 206 w(n)o(umeric)p 1044 1545 V 127 w(10)p 1181 1545 V 49 w(Create)h(a)f(new)g (anon)o(ymous)e(unkno)o(wn)p 1876 1545 V 75 1546 1802 2 v 74 1596 2 50 v 100 1581 a Fo(xpart)p 364 1596 V 179 w Ft({)p 590 1596 V 206 w(pair)p 817 1596 V 155 w(n)o(um)o(b)q(er)p 1044 1596 V 134 w(16)p 1181 1596 V 49 w Fp(x)i Ft(or)g Fp(t)1310 1587 y Fh(x)1345 1581 y Ft(comp)q(onen)o(t)p 1876 1596 V 74 1646 V 364 1646 V 590 1646 V 616 1631 a(transform)p 817 1646 V 1044 1646 V 1181 1646 V 1876 1646 V 75 1648 1802 2 v 74 1697 2 50 v 100 1682 a Fo(xscaled)p 364 1697 V 135 w Ft(picture)p 590 1697 V 101 w(n)o(umeric)p 817 1697 V 82 w(picture)p 1044 1697 V 146 w(30)p 1181 1697 V 49 w(Scale)g(all)f Fp(x)h Ft(co)q(ordinates)g (b)o(y)g(the)p 1876 1697 V 74 1747 V 364 1747 V 389 1732 a(path)p 590 1747 V 817 1747 V 371 w(path)p 1044 1747 V 1181 1747 V 280 w(giv)o(en)g(amoun)o(t)p 1876 1747 V 74 1797 V 364 1797 V 389 1782 a(pair)p 590 1797 V 817 1797 V 382 w(pair)p 1044 1797 V 1181 1797 V 1876 1797 V 74 1847 V 364 1847 V 389 1832 a(p)q(en)p 590 1847 V 817 1847 V 389 w(p)q(en)p 1044 1847 V 1181 1847 V 1876 1847 V 74 1897 V 364 1897 V 389 1882 a(transform)p 590 1897 V 817 1897 V 276 w(transform)p 1044 1897 V 1181 1897 V 1876 1897 V 75 1898 1802 2 v 74 1948 2 50 v 100 1933 a Fo(xxpart)p 364 1948 V 157 w Ft({)p 590 1948 V 206 w(transform)p 817 1948 V 49 w(n)o(um)o(b)q(er)p 1044 1948 V 134 w(32)p 1181 1948 V 49 w Fp(t)1221 1939 y Fh(xx)1275 1933 y Ft(en)o(try)g(in)g(transformation)e (matrix)p 1876 1948 V 75 1950 1802 2 v 74 2000 2 50 v 100 1985 a Fo(xypart)p 364 2000 V 157 w Ft({)p 590 2000 V 206 w(transform)p 817 2000 V 49 w(n)o(um)o(b)q(er)p 1044 2000 V 134 w(32)p 1181 2000 V 49 w Fp(t)1221 1991 y Fh(xy)1274 1985 y Ft(en)o(try)j(in)e (transformation)f(matrix)p 1876 2000 V 75 2001 1802 2 v 74 2051 2 50 v 100 2036 a Fo(ypart)p 364 2051 V 179 w Ft({)p 590 2051 V 206 w(pair)p 817 2051 V 155 w(n)o(um)o(b)q(er)p 1044 2051 V 134 w(16)p 1181 2051 V 49 w Fp(y)k Ft(or)e Fp(t)1308 2042 y Fh(y)1342 2036 y Ft(comp)q(onen)o(t)p 1876 2051 V 74 2101 V 364 2101 V 590 2101 V 616 2086 a(transform)p 817 2101 V 1044 2101 V 1181 2101 V 1876 2101 V 75 2103 1802 2 v 74 2152 2 50 v 100 2137 a Fo(yscaled)p 364 2152 V 135 w Ft(picture)p 590 2152 V 101 w(n)o(umeric)p 817 2152 V 82 w(picture)p 1044 2152 V 146 w(30)p 1181 2152 V 49 w(Scale)g(all)f Fp(y)j Ft(co)q(ordinates)e (b)o(y)g(the)p 1876 2152 V 74 2202 V 364 2202 V 389 2187 a(path)p 590 2202 V 817 2202 V 371 w(path)p 1044 2202 V 1181 2202 V 280 w(giv)o(en)g(amoun)o(t)p 1876 2202 V 74 2252 V 364 2252 V 389 2237 a(pair)p 590 2252 V 817 2252 V 382 w(pair)p 1044 2252 V 1181 2252 V 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w(Rotate)i(and)g(scale)g(all)f(co)q(ordinates)h (so)p 1876 2506 V 74 2556 V 364 2556 V 389 2541 a(path)p 590 2556 V 817 2556 V 371 w(path)p 1044 2556 V 1181 2556 V 280 w(that)g(\(1)p Fp(;)7 b Ft(0\))13 b(is)h(mapp)q(ed)f(in)o(to)g(the)p 1876 2556 V 74 2606 V 364 2606 V 389 2591 a(pair)p 590 2606 V 817 2606 V 382 w(pair)p 1044 2606 V 1181 2606 V 291 w(giv)o(en)h(pair;)f (i.e.,)f(do)i(complex)p 1876 2606 V 74 2655 V 364 2655 V 389 2641 a(p)q(en)p 590 2655 V 817 2655 V 389 w(p)q(en)p 1044 2655 V 1181 2655 V 298 w(m)o(ultiplication.)p 1876 2655 V 74 2705 V 364 2705 V 389 2690 a(transform)p 590 2705 V 817 2705 V 276 w(transform)p 1044 2705 V 1181 2705 V 1876 2705 V 75 2707 1802 2 v eop %%Page: 69 19 bop 75 -54 a Fq(A)14 b(User's)h(Man)o(ual)e(for)g(MetaP)o(ost)1203 b Ft(69)721 122 y(T)m(able)13 b(8:)18 b(Op)q(erators)e(\(P)o(art)e(3\))p 75 220 1802 2 v 74 269 2 50 v 167 254 a(Name)p 364 269 V 208 w(Argumen)o(t/result)g(t)o(yp)q(es)p 1011 269 V 142 w(P)o(age)p 1148 269 V 278 w(Explanation)p 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V 75 743 1802 2 v 74 792 2 50 v 100 778 a Fo(penoffset)p 364 792 V 91 w Ft(pair)p 590 792 V 155 w(p)q(en)p 784 792 V 129 w(pair)p 1011 792 V 221 w({)p 1148 792 V 50 w(P)o(oin)o(t)f(on) h(the)g(p)q(en)h(furthest)g(to)f(the)p 1875 792 V 74 842 V 100 827 a Fo(of)p 364 842 V 590 842 V 784 842 V 1011 842 V 1148 842 V 1030 w Ft(righ)o(t)f(of)g(the)i(giv)o(en)e(direction)p 1875 842 V 75 844 1802 2 v 74 894 2 50 v 100 879 a Fo(picture)p 364 894 V 135 w Ft({)p 590 894 V 206 w(an)o(y)p 784 894 V 129 w(b)q(o)q(olean)p 1011 894 V 131 w(16)p 1148 894 V 50 w(Is)h(the)g (expression)i(of)d(t)o(yp)q(e)h(picture?)p 1875 894 V 75 895 1802 2 v 74 945 2 50 v 100 930 a Fo(point)21 b(of)p 364 945 V 114 w Ft(n)o(umeric)p 590 945 V 82 w(path)p 784 945 V 111 w(pair)p 1011 945 V 200 w(27)p 1148 945 V 50 w(P)o(oin)o(t)13 b(on)h(a)f(path)h(giv)o(en)g(a)f(time)g(v)n(alue)p 1875 945 V 75 947 1802 2 v 74 997 2 50 v 100 982 a Fo(postcontrol)p 364 997 V 47 w Ft(n)o(umeric)p 590 997 V 82 w(path)p 784 997 V 111 w(pair)p 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V 135 w Ft({)p 590 1251 V 206 w(path)p 784 1251 V 111 w(path)p 1011 1251 V 189 w(37)p 1148 1251 V 50 w(`time'-rev)o(ersed)e(path)h(with)g(b)q(eginning)p 1875 1251 V 74 1301 V 364 1301 V 590 1301 V 784 1301 V 1011 1301 V 1148 1301 V 1174 1286 a(sw)o(app)q(ed)g(with)g(ending)p 1875 1301 V 75 1302 1802 2 v 74 1352 2 50 v 100 1337 a Fo(rotated)p 364 1352 V 135 w Ft(picture)p 590 1352 V 101 w(n)o(umeric)p 784 1352 V 49 w(picture)p 1011 1352 V 146 w(30)p 1148 1352 V 50 w(Rotate)f(clo)q(c)o(kwise)i(a)e(giv)o(en)h(n)o(um)o(b)q(er)p 1875 1352 V 74 1402 V 364 1402 V 389 1387 a(path)p 590 1402 V 784 1402 V 338 w(path)p 1011 1402 V 1148 1402 V 281 w(of)f(degrees)p 1875 1402 V 74 1452 V 364 1452 V 389 1437 a(pair)p 590 1452 V 784 1452 V 349 w(pair)p 1011 1452 V 1148 1452 V 1875 1452 V 74 1501 V 364 1501 V 389 1487 a(p)q(en)p 590 1501 V 784 1501 V 356 w(p)q(en)p 1011 1501 V 1148 1501 V 1875 1501 V 74 1551 V 364 1551 V 389 1536 a(transform)p 590 1551 V 784 1551 V 243 w(transform)p 1011 1551 V 1148 1551 V 1875 1551 V 75 1553 1802 2 v 74 1603 2 50 v 100 1588 a Fk(y)p Fo(round)p 364 1603 V 161 w Ft({)p 590 1603 V 206 w(n)o(umeric)p 784 1603 V 49 w(n)o(umeric)p 1011 1603 V 127 w(15)p 1148 1603 V 50 w(round)h(eac)o(h)g(comp)q(onen)o(t)f (to)h(the)h(nearest)p 1875 1603 V 74 1653 V 364 1653 V 590 1653 V 616 1638 a(pair)p 784 1653 V 122 w(pair)p 1011 1653 V 1148 1653 V 292 w(in)o(teger)p 1875 1653 V 75 1654 1802 2 v 74 1704 2 50 v 100 1689 a Fk(y)p Fo(rt)p 364 1704 V 227 w Ft({)p 590 1704 V 206 w(n)o(umeric)p 784 1704 V 49 w(n)o(umeric)p 1011 1704 V 127 w(38)p 1148 1704 V 50 w(Righ)o(t)e(side)h(of)f(curren)o(t)i (p)q(en)g(when)p 1875 1704 V 74 1754 V 364 1754 V 590 1754 V 616 1739 a(pair)p 784 1754 V 122 w(pair)p 1011 1754 V 1148 1754 V 292 w(cen)o(tered)h(at)e(giv)o(en)f(co)q(ordinate\(s\))p 1875 1754 V 75 1755 1802 2 v 74 1805 2 50 v 100 1790 a Fo(scaled)p 364 1805 V 157 w Ft(picture)p 590 1805 V 101 w(n)o(umeric)p 784 1805 V 49 w(picture)p 1011 1805 V 146 w(30)p 1148 1805 V 50 w(Scale)h(all)f(co)q(ordinates)h(b)o(y)g(the)g(giv)o(en)p 1875 1805 V 74 1855 V 364 1855 V 389 1840 a(path)p 590 1855 V 784 1855 V 338 w(path)p 1011 1855 V 1148 1855 V 281 w(amoun)o(t)p 1875 1855 V 74 1905 V 364 1905 V 389 1890 a(pair)p 590 1905 V 784 1905 V 349 w(pair)p 1011 1905 V 1148 1905 V 1875 1905 V 74 1955 V 364 1955 V 389 1940 a(p)q(en)p 590 1955 V 784 1955 V 356 w(p)q(en)p 1011 1955 V 1148 1955 V 1875 1955 V 74 2005 V 364 2005 V 389 1990 a(transform)p 590 2005 V 784 2005 V 243 w(transform)p 1011 2005 V 1148 2005 V 1875 2005 V 75 2006 1802 2 v 74 2056 2 50 v 100 2041 a Fo(shifted)p 364 2056 V 135 w Ft(picture)p 590 2056 V 101 w(pair)p 784 2056 V 122 w(picture)p 1011 2056 V 146 w(30)p 1148 2056 V 50 w(Add)g(the)g(giv)o(en)g(shift)f(amoun) o(t)f(to)i(eac)o(h)p 1875 2056 V 74 2106 V 364 2106 V 389 2091 a(path)p 590 2106 V 784 2106 V 338 w(path)p 1011 2106 V 1148 2106 V 281 w(pair)f(of)g(co)q(ordinates)p 1875 2106 V 74 2156 V 364 2156 V 389 2141 a(pair)p 590 2156 V 784 2156 V 349 w(pair)p 1011 2156 V 1148 2156 V 1875 2156 V 74 2205 V 364 2205 V 389 2191 a(p)q(en)p 590 2205 V 784 2205 V 356 w(p)q(en)p 1011 2205 V 1148 2205 V 1875 2205 V 74 2255 V 364 2255 V 389 2240 a(transform)p 590 2255 V 784 2255 V 243 w(transform)p 1011 2255 V 1148 2255 V 1875 2255 V 75 2257 1802 2 v 74 2307 2 50 v 100 2292 a Fo(sind)p 364 2307 V 201 w Ft({)p 590 2307 V 206 w(n)o(umeric)p 784 2307 V 49 w(n)o(umeric)p 1011 2307 V 127 w(15)p 1148 2307 V 50 w(Sine)h(of)f(an)h (angle)f(in)g(degrees)p 1875 2307 V 75 2308 1802 2 v 74 2358 2 50 v 100 2343 a Fo(slanted)p 364 2358 V 135 w Ft(picture)p 590 2358 V 101 w(n)o(umeric)p 784 2358 V 49 w(picture)p 1011 2358 V 146 w(30)p 1148 2358 V 50 w(Apply)g(the)i(slan)o(ting)e (transformation)p 1875 2358 V 74 2408 V 364 2408 V 389 2393 a(path)p 590 2408 V 784 2408 V 338 w(path)p 1011 2408 V 1148 2408 V 281 w(that)h(maps)e(\()p Fp(x;)7 b(y)q Ft(\))14 b(in)o(to)g(\()p Fp(x)9 b Ft(+)g Fp(sy)q(;)e(y)q Ft(\),)p 1875 2408 V 74 2458 V 364 2458 V 389 2443 a(pair)p 590 2458 V 784 2458 V 349 w(pair)p 1011 2458 V 1148 2458 V 292 w(where)15 b Fp(s)f Ft(is)g(the)g(n)o(umeric)f (argumen)o(t)p 1875 2458 V 74 2508 V 364 2508 V 389 2493 a(p)q(en)p 590 2508 V 784 2508 V 356 w(p)q(en)p 1011 2508 V 1148 2508 V 1875 2508 V 74 2557 V 364 2557 V 389 2543 a(transform)p 590 2557 V 784 2557 V 243 w(transform)p 1011 2557 V 1148 2557 V 1875 2557 V 75 2559 1802 2 v 74 2609 2 50 v 100 2594 a Fo(sqrt)p 364 2609 V 201 w Ft({)p 590 2609 V 206 w(n)o(umeric)p 784 2609 V 49 w(n)o(umeric)p 1011 2609 V 127 w(15)p 1148 2609 V 50 w(Square)h(ro)q(ot) p 1875 2609 V 75 2611 1802 2 v 74 2660 2 50 v 100 2645 a Fo(str)p 364 2660 V 223 w Ft({)p 590 2660 V 206 w(su\016x)p 784 2660 V 98 w(string)p 1011 2660 V 168 w(50)p 1148 2660 V 50 w(String)f(represen)o (tation)j(for)d(a)h(su\016x)p 1875 2660 V 75 2662 1802 2 v eop %%Page: 68 20 bop 75 -54 a Fq(A)14 b(User's)h(Man)o(ual)e(for)g(MetaP)o(ost)1203 b Ft(68)721 122 y(T)m(able)13 b(7:)18 b(Op)q(erators)e(\(P)o(art)e(2\))p 76 220 1798 2 v 75 269 2 50 v 167 254 a(Name)p 362 269 V 206 w(Argumen)o(t/result)g(t)o(yp)q(es)p 1009 269 V 142 w(P)o(age)p 1146 269 V 278 w(Explanation)p 1873 269 V 363 271 648 2 v 75 319 2 50 v 362 319 V 387 304 a(Left)p 556 319 V 121 w(Righ)o(t)p 782 319 V 125 w(Result)p 1009 319 V 1146 319 V 1873 319 V 76 321 1798 2 v 76 331 V 75 381 2 50 v 101 366 a Fo(char)p 362 381 V 198 w Ft({)p 556 381 V 173 w(n)o(umeric)p 782 381 V 82 w(string)p 1009 381 V 168 w(22)p 1146 381 V 50 w(Character)h(with)e(a)h(giv)o (en)f(ASCI)q(I)h(co)q(de)p 1873 381 V 76 382 1798 2 v 75 432 2 50 v 101 417 a Fo(color)p 362 432 V 176 w Ft({)p 556 432 V 173 w(an)o(y)p 782 432 V 162 w(b)q(o)q(olean)p 1009 432 V 131 w(16)p 1146 432 V 50 w(Is)g(the)g(expression)h(of)f(t)o(yp)q(e)g(color?)p 1873 432 V 76 434 1798 2 v 75 484 2 50 v 101 469 a Fo(cosd)p 362 484 V 198 w Ft({)p 556 484 V 173 w(n)o(umeric)p 782 484 V 82 w(n)o(umeric)p 1009 484 V 127 w(15)p 1146 484 V 50 w(Cosine)g(of)f (angle)g(in)h(degrees)p 1873 484 V 76 485 1798 2 v 75 535 2 50 v 101 520 a Fk(y)q Fo(cutafter)p 362 535 V 91 w Ft(path)p 556 535 V 111 w(path)p 782 535 V 144 w(path)p 1009 535 V 189 w(28)p 1146 535 V 50 w(Left)g(argumen)o(t)f(with)g(part)h(after)g(the)p 1873 535 V 75 585 V 362 585 V 556 585 V 782 585 V 1009 585 V 1146 585 V 1172 570 a(in)o(tersection)h(dropp)q(ed)p 1873 585 V 76 587 1798 2 v 75 636 2 50 v 101 621 a Fk(y)q Fo(cutbefore)p 362 636 V 69 w Ft(path)p 556 636 V 111 w(path)p 782 636 V 144 w(path)p 1009 636 V 189 w(28)p 1146 636 V 50 w(Left)f(argumen)o(t)f(with)g (part)h(b)q(efore)h(the)p 1873 636 V 75 686 V 362 686 V 556 686 V 782 686 V 1009 686 V 1146 686 V 1172 671 a(in)o(tersection)g(dropp)q (ed)p 1873 686 V 76 688 1798 2 v 75 738 2 50 v 101 723 a Fo(cycle)p 362 738 V 176 w Ft({)p 556 738 V 173 w(path)p 782 738 V 144 w(b)q(o)q(olean)p 1009 738 V 131 w(15)p 1146 738 V 50 w(Determines)f(whether) h(a)e(path)h(is)g(cyclic)p 1873 738 V 76 739 1798 2 v 75 789 2 50 v 101 774 a Fo(decimal)p 362 789 V 132 w Ft({)p 556 789 V 173 w(n)o(umeric)p 782 789 V 82 w(string)p 1009 789 V 168 w(15)p 1146 789 V 50 w(The)g(decimal)e(represen)o(tation)p 1873 789 V 76 791 1798 2 v 75 841 2 50 v 101 826 a Fk(y)q Fo(dir)p 362 841 V 201 w Ft({)p 556 841 V 173 w(n)o(umeric)p 782 841 V 82 w(pair)p 1009 841 V 221 w(6)p 1146 841 V 50 w(\(cos)7 b Fp(\022)q(;)g Ft(sin)g Fp(\022)q Ft(\))15 b(giv)o(en)e Fp(\022)j Ft(in)d(degrees)p 1873 841 V 76 842 1798 2 v 75 892 2 50 v 101 877 a Fk(y)q Fo(direction)p 362 892 V 69 w Ft(n)o(umeric)p 556 892 V 49 w(path)p 782 892 V 144 w(pair)p 1009 892 V 200 w(28)p 1146 892 V 50 w(The)h(direction)g(of)f(a)h(path)g(at)g(a)f(giv)o(en)p 1873 892 V 75 942 V 123 927 a Fo(of)p 362 942 V 556 942 V 782 942 V 1009 942 V 1146 942 V 1005 w Ft(`time')p 1873 942 V 76 944 1798 2 v 75 993 2 50 v 101 978 a Fk(y)q Fo(direction-)p 362 993 V 47 w Ft(pair)p 556 993 V 122 w(path)p 782 993 V 144 w(n)o(umeric)p 1009 993 V 127 w(30)p 1146 993 V 50 w(P)o(oin)o(t)g(where)i(a) f(path)g(has)g(a)f(giv)o(en)p 1873 993 V 75 1043 V 101 1028 a Fo(point)21 b(of)p 362 1043 V 556 1043 V 782 1043 V 1009 1043 V 1146 1043 V 896 w Ft(direction)p 1873 1043 V 76 1045 1798 2 v 75 1095 2 50 v 101 1080 a Fo(direction-)p 362 1095 V 66 w Ft(pair)p 556 1095 V 122 w(path)p 782 1095 V 144 w(n)o(umeric)p 1009 1095 V 127 w(28)p 1146 1095 V 50 w(`Time')11 b(when)k(a)e(path)h(has)g (a)g(giv)o(en)p 1873 1095 V 75 1144 V 101 1130 a Fo(time)21 b(of)p 362 1144 V 556 1144 V 782 1144 V 1009 1144 V 1146 1144 V 918 w Ft(direction)p 1873 1144 V 76 1146 1798 2 v 75 1196 2 50 v 101 1181 a Fk(y)q Fo(div)p 362 1196 V 201 w Ft(n)o(umeric)p 556 1196 V 49 w(n)o(umeric)p 782 1196 V 82 w(n)o(umeric)p 1009 1196 V 148 w({)p 1146 1196 V 50 w(In)o(teger)15 b(division)d Fk(b)p Fp(l)q(=r)q Fk(c)p 1873 1196 V 76 1198 1798 2 v 75 1247 2 50 v 101 1232 a(y)q Fo(dotprod)p 362 1247 V 113 w Ft(pair)p 556 1247 V 122 w(pair)p 782 1247 V 155 w(n)o(umeric)p 1009 1247 V 127 w(13)p 1146 1247 V 50 w(v)o(ector)i(dot)g(pro)q(duct)p 1873 1247 V 76 1249 1798 2 v 75 1299 2 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Ft(string)p 556 1505 V 90 w(string)p 782 1505 V 123 w(picture)p 1009 1505 V 146 w(22)p 1146 1505 V 50 w(T)o(yp)q(eset)j(string)f(in)f(giv)o (en)h(fon)o(t)p 1873 1505 V 76 1506 1798 2 v 75 1556 2 50 v 101 1541 a Fk(y)q Fo(intersec-)p 362 1556 V 69 w Ft(path)p 556 1556 V 111 w(path)p 782 1556 V 144 w(pair)p 1009 1556 V 200 w(27)p 1146 1556 V 50 w(An)g(in)o(tersection)h(p)q(oin)o(t)p 1873 1556 V 75 1606 V 123 1591 a Fo(tionpoint)p 362 1606 V 556 1606 V 782 1606 V 1009 1606 V 1146 1606 V 1873 1606 V 76 1608 1798 2 v 75 1658 2 50 v 101 1643 a(intersec-)p 362 1658 V 88 w Ft(path)p 556 1658 V 111 w(path)p 782 1658 V 144 w(pair)p 1009 1658 V 200 w(27)p 1146 1658 V 50 w(Times)e(\()p Fp(t)1328 1649 y Fh(l)1340 1643 y Fp(;)7 b(t)1374 1649 y Fh(r)1392 1643 y Ft(\))14 b(on)g(paths)g Fp(l)h Ft(and)f Fp(r)p 1873 1658 V 75 1707 V 101 1692 a Fo(tiontimes)p 362 1707 V 556 1707 V 782 1707 V 1009 1707 V 1146 1707 V 873 w Ft(when)g(the)h(paths)f(in)o (tersect)p 1873 1707 V 76 1709 1798 2 v 75 1759 2 50 v 101 1744 a Fk(y)q Fo(inverse)p 362 1759 V 113 w Ft({)p 556 1759 V 173 w(transform)p 782 1759 V 49 w(transform)p 1009 1759 V 94 w(31)p 1146 1759 V 50 w(In)o(v)o(ert)g(a)g(transformation)p 1873 1759 V 76 1760 1798 2 v 75 1810 2 50 v 101 1795 a Fo(known)p 362 1810 V 176 w Ft({)p 556 1810 V 173 w(an)o(y)p 782 1810 V 162 w(b)q(o)q(olean)p 1009 1810 V 131 w(16)p 1146 1810 V 50 w(Do)q(es)g(argumen)o(t)f(ha)o(v)o(e)g(a)h(kno)o(wn)g(v)n(alue?)p 1873 1810 V 76 1812 1798 2 v 75 1862 2 50 v 101 1847 a Fo(length)p 362 1862 V 154 w Ft({)p 556 1862 V 173 w(path)p 782 1862 V 144 w(n)o(umeric)p 1009 1862 V 127 w(28)p 1146 1862 V 50 w(Num)o(b)q(er)f(of) g(arcs)i(in)f(a)f(path)p 1873 1862 V 76 1863 1798 2 v 75 1913 2 50 v 101 1898 a Fk(y)q Fo(lft)p 362 1913 V 201 w Ft({)p 556 1913 V 173 w(n)o(umeric)p 782 1913 V 82 w(n)o(umeric)p 1009 1913 V 127 w(38)p 1146 1913 V 50 w(Left)h(side)g(of)f(curren)o(t)j(p)q(en)e (when)h(its)p 1873 1913 V 75 1963 V 362 1963 V 556 1963 V 581 1948 a(pair)p 782 1963 V 155 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1798 2 v 75 2317 2 50 v 101 2302 a Fo(makepath)p 362 2317 V 110 w Ft({)p 556 2317 V 173 w(p)q(en)p 782 2317 V 162 w(path)p 1009 2317 V 189 w(39)p 1146 2317 V 50 w(Cyclic)g(path)h(b)q (ounding)g(the)g(p)q(en)h(shap)q(e)p 1873 2317 V 76 2318 1798 2 v 75 2368 2 50 v 101 2353 a Fo(makepen)p 362 2368 V 132 w Ft({)p 556 2368 V 173 w(path)p 782 2368 V 144 w(p)q(en)p 1009 2368 V 207 w(39)p 1146 2368 V 50 w(A)f(p)q(olygonal)e(p)q(en)i(made)f(from)f (the)p 1873 2368 V 75 2418 V 362 2418 V 556 2418 V 782 2418 V 1009 2418 V 1146 2418 V 1172 2403 a(con)o(v)o(ex)i(h)o(ull)f(of)g(the)h (path)g(knots)p 1873 2418 V 76 2420 1798 2 v 75 2469 2 50 v 101 2455 a Fo(mexp)p 362 2469 V 198 w Ft({)p 556 2469 V 173 w(n)o(umeric)p 782 2469 V 82 w(n)o(umeric)p 1009 2469 V 148 w({)p 1146 2469 V 50 w(The)g(function)g(exp\()p Fp(x=)p Ft(256\))p 1873 2469 V 76 2471 1798 2 v 75 2521 2 50 v 101 2506 a Fo(mlog)p 362 2521 V 198 w Ft({)p 556 2521 V 173 w(n)o(umeric)p 782 2521 V 82 w(n)o(umeric)p 1009 2521 V 148 w({)p 1146 2521 V 50 w(The)g(function)g (256)7 b(ln)n(\()p Fp(x)p Ft(\))p 1873 2521 V 76 2523 1798 2 v 75 2572 2 50 v 101 2557 a Fk(y)q Fo(mod)p 362 2572 V 201 w Ft({)p 556 2572 V 173 w(n)o(umeric)p 782 2572 V 82 w(n)o(umeric)p 1009 2572 V 148 w({)p 1146 2572 V 50 w(The)14 b(remainder)f(function)h Fp(l)c Fk(\000)g Fp(r)q Fk(b)p Fp(l)q(=r)q Fk(c)p 1873 2572 V 76 2574 1798 2 v 75 2624 2 50 v 101 2609 a Fo(normal-)p 362 2624 V 132 w Ft({)p 556 2624 V 173 w({)p 782 2624 V 206 w(n)o(umeric)p 1009 2624 V 148 w({)p 1146 2624 V 50 w(Cho)q(ose)k(a)g(random)e(n)o(um)o(b)q (er)h(with)p 1873 2624 V 75 2674 V 101 2659 a Fo(deviate)p 362 2674 V 556 2674 V 782 2674 V 1009 2674 V 1146 2674 V 917 w Ft(mean)f(0)i(and)g(standard)g(deviation)f(1)p 1873 2674 V 76 2675 1798 2 v eop %%Page: 67 21 bop 75 -54 a Fq(A)14 b(User's)h(Man)o(ual)e(for)g(MetaP)o(ost)1203 b Ft(67)721 122 y(T)m(able)13 b(6:)18 b(Op)q(erators)e(\(P)o(art)e(1\))p 83 220 1784 2 v 82 269 2 50 v 154 254 a(Name)p 328 269 V 186 w(Argumen)o(t/result)f(t)o(yp)q(es)p 976 269 V 143 w(P)o(age)p 1113 269 V 291 w(Explanation)p 1866 269 V 329 271 648 2 v 82 319 2 50 v 328 319 V 354 304 a(Left)p 555 319 V 154 w(Righ)o(t)p 782 319 V 125 w(Result)p 976 319 V 1113 319 V 1866 319 V 83 321 1784 2 v 83 331 V 82 381 2 50 v 108 366 a Fo(&)p 328 381 V 224 w Ft(string)p 555 381 V 123 w(string)p 782 381 V 123 w(string)p 976 381 V 135 w(14)p 1113 381 V 50 w(Concatenation|w)o(orks)g(for) g(paths)i Fp(l)q Fo(&)p Fp(r)f Ft(if)p 1866 381 V 82 430 V 328 430 V 354 416 a(path)p 555 430 V 144 w(path)p 782 430 V 144 w(path)p 976 430 V 1113 430 V 248 w Fp(r)g Ft(starts)h(exactly)f(where)h (the)g Fp(l)g Ft(ends)p 1866 430 V 83 432 1784 2 v 82 482 2 50 v 108 467 a Fo(*)p 328 482 V 224 w Ft(n)o(umeric)p 555 482 V 82 w(color)p 782 482 V 139 w(color)p 976 482 V 151 w(13)p 1113 482 V 50 w(Multiplication)p 1866 482 V 82 532 V 328 532 V 555 532 V 581 517 a(n)o(umeric)p 782 532 V 82 w(n)o(umeric)p 976 532 V 1113 532 V 1866 532 V 82 582 V 328 582 V 555 582 V 581 567 a(pair)p 782 582 V 155 w(pair)p 976 582 V 1113 582 V 1866 582 V 83 583 1784 2 v 82 633 2 50 v 108 618 a Fo(*)p 328 633 V 224 w Ft(color)p 555 633 V 139 w(n)o(umeric)p 782 633 V 82 w(color)p 976 633 V 151 w(13)p 1113 633 V 50 w(Multiplication)p 1866 633 V 82 683 V 328 683 V 354 668 a(n)o(umeric)p 555 683 V 782 683 V 309 w(n)o(umeric)p 976 683 V 1113 683 V 1866 683 V 82 733 V 328 733 V 354 718 a(pair)p 555 733 V 782 733 V 382 w(pair)p 976 733 V 1113 733 V 1866 733 V 83 734 1784 2 v 82 784 2 50 v 108 769 a Fo(**)p 328 784 V 202 w Ft(n)o(umeric)p 555 784 V 82 w(n)o(umeric)p 782 784 V 82 w(n)o(umeric)p 976 784 V 94 w(13)p 1113 784 V 50 w(Exp)q(onen)o(tiation)p 1866 784 V 83 786 1784 2 v 82 836 2 50 v 108 821 a Fo(+)p 328 836 V 224 w Ft(color)p 555 836 V 139 w(color)p 782 836 V 139 w(color)p 976 836 V 151 w(13)p 1113 836 V 50 w(Addition)p 1866 836 V 82 885 V 328 885 V 354 870 a(n)o(umeric)p 555 885 V 82 w(n)o(umeric)p 782 885 V 82 w(n)o(umeric)p 976 885 V 1113 885 V 1866 885 V 82 935 V 328 935 V 354 920 a(pair)p 555 935 V 155 w(pair)p 782 935 V 155 w(pair)p 976 935 V 1113 935 V 1866 935 V 83 937 1784 2 v 82 990 2 53 v 108 975 a Fo(++)p 328 990 V 202 w Ft(n)o(umeric)p 555 990 V 82 w(n)o(umeric)p 782 990 V 82 w(n)o(umeric)p 976 990 V 94 w(14)p 1113 990 V 50 w(Pythagorean)f(addition)1546 940 y Fk(p)p 1581 940 122 2 v 35 x Fp(l)1594 963 y Fn(2)1622 975 y Ft(+)9 b Fp(r)1683 963 y Fn(2)p 1866 990 2 53 v 83 991 1784 2 v 82 1044 2 53 v 108 1029 a Fo(+-+)p 328 1044 V 180 w Ft(n)o(umeric)p 555 1044 V 82 w(n)o(umeric)p 782 1044 V 82 w(n)o(umeric)p 976 1044 V 94 w(14)p 1113 1044 V 50 w(Pythagorean)14 b(subtraction)1602 995 y Fk(p)p 1637 995 122 2 v 34 x Fp(l)1650 1017 y Fn(2)1678 1029 y Fk(\000)9 b Fp(r)1739 1017 y Fn(2)p 1866 1044 2 53 v 83 1046 1784 2 v 82 1096 2 50 v 108 1081 a Fo(-)p 328 1096 V 224 w Ft(color)p 555 1096 V 139 w(color)p 782 1096 V 139 w(color)p 976 1096 V 151 w(13)p 1113 1096 V 50 w(Subtraction)p 1866 1096 V 82 1146 V 328 1146 V 354 1131 a(n)o(umeric)p 555 1146 V 82 w(n)o(umeric)p 782 1146 V 82 w(n)o(umeric)p 976 1146 V 1113 1146 V 1866 1146 V 82 1195 V 328 1195 V 354 1180 a(pair)p 555 1195 V 155 w(pair)p 782 1195 V 155 w(pair)p 976 1195 V 1113 1195 V 1866 1195 V 83 1197 1784 2 v 82 1247 2 50 v 108 1232 a Fo(-)p 328 1247 V 224 w Ft({)p 555 1247 V 206 w(color)p 782 1247 V 139 w(color)p 976 1247 V 151 w(13)p 1113 1247 V 50 w(Negation)p 1866 1247 V 82 1297 V 328 1297 V 555 1297 V 581 1282 a(n)o(umeric)p 782 1297 V 82 w(n)o(umeric)p 976 1297 V 1113 1297 V 1866 1297 V 82 1346 V 328 1346 V 555 1346 V 581 1332 a(pair)p 782 1346 V 155 w(pair)p 976 1346 V 1113 1346 V 1866 1346 V 83 1348 1784 2 v 82 1398 2 50 v 108 1383 a Fo(/)p 328 1398 V 224 w Ft(color)p 555 1398 V 139 w(n)o(umeric)p 782 1398 V 82 w(color)p 976 1398 V 151 w(13)p 1113 1398 V 50 w(Division)p 1866 1398 V 82 1448 V 328 1448 V 354 1433 a(n)o(umeric)p 555 1448 V 782 1448 V 309 w(n)o(umeric)p 976 1448 V 1113 1448 V 1866 1448 V 82 1498 V 328 1498 V 354 1483 a(pair)p 555 1498 V 782 1498 V 382 w(pair)p 976 1498 V 1113 1498 V 1866 1498 V 83 1499 1784 2 v 82 1549 2 50 v 108 1534 a Fo(<)22 b(=)f(>)p 328 1549 V 137 w Ft(string)p 555 1549 V 123 w(string)p 782 1549 V 123 w(b)q(o)q(olean)p 976 1549 V 98 w(13)p 1113 1549 V 50 w(Comparison)12 b(op)q(erators)p 1866 1549 V 82 1599 V 108 1584 a Fo(<=)22 b(>=)p 328 1599 V 136 w Ft(n)o(umeric)p 555 1599 V 82 w(n)o(umeric)p 782 1599 V 976 1599 V 1113 1599 V 1866 1599 V 82 1649 V 108 1634 a Fo(<>)p 328 1649 V 202 w Ft(pair)p 555 1649 V 155 w(pair)p 782 1649 V 976 1649 V 1113 1649 V 1866 1649 V 82 1698 V 328 1698 V 354 1684 a(color)p 555 1698 V 139 w(color)p 782 1698 V 976 1698 V 1113 1698 V 1866 1698 V 82 1748 V 328 1748 V 354 1733 a(transform)p 555 1748 V 49 w(transform)p 782 1748 V 976 1748 V 1113 1748 V 1866 1748 V 83 1750 1784 2 v 82 1800 2 50 v 108 1785 a Fk(y)q Fo(abs)p 328 1800 V 161 w Ft({)p 555 1800 V 206 w(n)o(umeric)p 782 1800 V 82 w(n)o(umeric)p 976 1800 V 94 w(15)p 1113 1800 V 50 w(Absolute)14 b(v)n(alue)p 1866 1800 V 82 1850 V 328 1850 V 555 1850 V 581 1835 a(pair)p 782 1850 V 976 1850 V 1113 1850 V 1866 1850 V 83 1851 1784 2 v 82 1901 2 50 v 108 1886 a Fo(and)p 328 1901 V 180 w Ft(b)q(o)q(olean)p 555 1901 V 86 w(b)q(o)q(olean)p 782 1901 V 86 w(b)q(o)q(olean)p 976 1901 V 98 w(13)p 1113 1901 V 50 w(Logical)e(and)p 1866 1901 V 83 1903 1784 2 v 82 1953 2 50 v 108 1938 a Fo(angle)p 328 1953 V 136 w Ft({)p 555 1953 V 206 w(pair)p 782 1953 V 155 w(n)o(umeric)p 976 1953 V 94 w(15)p 1113 1953 V 50 w(2-argumen)o(t)g(arctangen)o(t)i(\(in)g(degrees\))p 1866 1953 V 83 1954 1784 2 v 82 2004 2 50 v 108 1989 a Fo(arclength)p 328 2004 V 48 w Ft({)p 555 2004 V 206 w(path)p 782 2004 V 144 w(n)o(umeric)p 976 2004 V 94 w(30)p 1113 2004 V 50 w(Arc)g(length)g(of)f(a)h (path)p 1866 2004 V 83 2006 1784 2 v 82 2055 2 50 v 108 2041 a Fo(arctime)p 328 2055 V 92 w Ft(n)o(umeric)p 555 2055 V 82 w(path)p 782 2055 V 144 w(n)o(umeric)p 976 2055 V 94 w(30)p 1113 2055 V 50 w(Time)e(on)i(a)f(path)h(where)h(arclength)f(from)p 1866 2055 V 82 2105 V 108 2090 a Fo(of)p 328 2105 V 555 2105 V 782 2105 V 976 2105 V 1113 2105 V 987 w Ft(the)g(start)h(reac)o(hes)g(a)f (giv)o(en)f(v)n(alue)p 1866 2105 V 83 2107 1784 2 v 82 2157 2 50 v 108 2142 a Fo(ASCII)p 328 2157 V 136 w Ft({)p 555 2157 V 206 w(string)p 782 2157 V 123 w(n)o(umeric)p 976 2157 V 115 w({)p 1113 2157 V 50 w(ASCI)q(I)h(v)n(alue)f(of)g(\014rst)i(c)o(haracter)g (in)f(string)p 1866 2157 V 83 2158 1784 2 v 82 2208 2 50 v 108 2193 a Fk(y)q Fo(bbox)p 328 2208 V 139 w Ft({)p 555 2208 V 206 w(picture)p 782 2208 V 101 w(path)p 976 2208 V 156 w(22)p 1113 2208 V 50 w(A)g(rectangular)g(path)g(for)f(the)i(b)q(ounding)p 1866 2208 V 82 2258 V 328 2258 V 555 2258 V 581 2243 a(path)p 782 2258 V 976 2258 V 1113 2258 V 475 w(b)q(o)o(x)p 1866 2258 V 82 2308 V 328 2308 V 555 2308 V 581 2293 a(p)q(en)p 782 2308 V 976 2308 V 1113 2308 V 1866 2308 V 83 2310 1784 2 v 82 2359 2 50 v 108 2344 a Fo(bluepart)p 328 2359 V 70 w Ft({)p 555 2359 V 206 w(color)p 782 2359 V 139 w(n)o(umeric)p 976 2359 V 94 w(16)p 1113 2359 V 50 w(Extracts)g(the)f(third)g(comp)q(onen)o(t)p 1866 2359 V 83 2361 1784 2 v 82 2411 2 50 v 108 2396 a Fo(boolean)p 328 2411 V 92 w Ft({)p 555 2411 V 206 w(an)o(y)p 782 2411 V 162 w(b)q(o)q(olean)p 976 2411 V 98 w(16)p 1113 2411 V 50 w(Is)g(the)g (expression)h(of)f(t)o(yp)q(e)g(b)q(o)q(olean?)p 1866 2411 V 83 2412 1784 2 v 82 2462 2 50 v 108 2447 a Fo(bot)p 328 2462 V 180 w Ft({)p 555 2462 V 206 w(n)o(umeric)p 782 2462 V 82 w(n)o(umeric)p 976 2462 V 94 w(38)p 1113 2462 V 50 w(Bottom)e(of)h(curren)o (t)j(p)q(en)e(when)h(cen)o(tered)p 1866 2462 V 82 2512 V 328 2512 V 555 2512 V 581 2497 a(pair)p 782 2512 V 155 w(pair)p 976 2512 V 1113 2512 V 259 w(at)e(the)i(giv)o(en)e(co)q(ordinate\(s\))p 1866 2512 V 83 2514 1784 2 v 82 2564 2 50 v 108 2549 a Fk(y)q Fo(ceiling)p 328 2564 V 73 w Ft({)p 555 2564 V 206 w(n)o(umeric)p 782 2564 V 82 w(n)o(umeric)p 976 2564 V 94 w(15)p 1113 2564 V 50 w(Least)h(in)o(teger)g(greater)h(than)f(or)g(equal)g(to)p 1866 2564 V 83 2565 1784 2 v 82 2615 2 50 v 108 2600 a Fk(y)q Fo(center)p 328 2615 V 95 w Ft({)p 555 2615 V 206 w(picture)p 782 2615 V 101 w(pair)p 976 2615 V 167 w(22)p 1113 2615 V 50 w(Cen)o(ter)h(of)e(the)h(b)q(ounding)g(b)q(o)o(x)p 1866 2615 V 82 2665 V 328 2665 V 555 2665 V 581 2650 a(path)p 782 2665 V 976 2665 V 1113 2665 V 1866 2665 V 82 2715 V 328 2715 V 555 2715 V 581 2700 a(p)q(en)p 782 2715 V 976 2715 V 1113 2715 V 1866 2715 V 83 2716 1784 2 v eop %%Page: 66 22 bop 75 -54 a Fq(A)14 b(User's)h(Man)o(ual)e(for)g(MetaP)o(ost)1203 b Ft(66)699 285 y(T)m(able)13 b(5:)18 b(Prede\014ned)e(Constan)o(ts)p 142 382 1667 2 v 141 432 2 50 v 265 417 a(Name)p 493 432 V 189 w(T)o(yp)q(e)p 719 432 V 92 w(P)o(age)p 856 432 V 390 w(Explanation)p 1807 432 V 142 433 1667 2 v 142 443 V 141 493 2 50 v 167 478 a Fk(y)p Fo(beveled)p 493 493 V 179 w Ft(n)o(umeric)p 719 493 V 128 w(35)p 856 493 V 49 w Fo(linejoin)c Ft(v)n(alue)h(for)h(b)q(ev)o(eled)h (joins)e([2])p 1807 493 V 142 495 1667 2 v 141 545 2 50 v 167 530 a Fk(y)p Fo(black)p 493 545 V 223 w Ft(color)p 719 545 V 185 w(12)p 856 545 V 49 w(Equiv)n(alen)o(t)g(to)h Fo(\(0,0,0\))p 1807 545 V 142 546 1667 2 v 141 596 2 50 v 167 581 a Fk(y)p Fo(blue)p 493 596 V 245 w Ft(color)p 719 596 V 185 w(12)p 856 596 V 49 w(Equiv)n(alen)o(t)f(to)h Fo(\(0,0,1\))p 1807 596 V 142 598 1667 2 v 141 648 2 50 v 167 633 a Fk(y)p Fo(bp)p 493 648 V 289 w Ft(n)o(umeric)p 719 648 V 148 w(2)p 856 648 V 50 w(One)h(P)o(ostScript)f(p)q(oin)o(t)g(in)f Fo(bp)g Ft(units)h([1])p 1807 648 V 142 649 1667 2 v 141 699 2 50 v 167 684 a Fk(y)p Fo(butt)p 493 699 V 245 w Ft(n)o(umeric)p 719 699 V 128 w(35)p 856 699 V 49 w Fo(linecap)e Ft(v)n(alue)i(for)f(butt)h(end)h(caps)f([0])p 1807 699 V 142 701 1667 2 v 141 751 2 50 v 167 736 a Fk(y)p Fo(cc)p 493 751 V 289 w Ft(n)o(umeric)p 719 751 V 148 w({)p 856 751 V 50 w(One)h(cicero)f(in)g Fo(bp)f Ft(units)h([12.79213])p 1807 751 V 142 752 1667 2 v 141 802 2 50 v 167 787 a Fk(y)p Fo(cm)p 493 802 V 289 w Ft(n)o(umeric)p 719 802 V 148 w(2)p 856 802 V 50 w(One)h(cen)o(timeter)f(in)f Fo(bp)h Ft(units)g([28.34645])p 1807 802 V 142 804 1667 2 v 141 854 2 50 v 167 839 a Fk(y)p Fo(dd)p 493 854 V 289 w Ft(n)o(umeric)p 719 854 V 148 w({)p 856 854 V 50 w(One)h(didot)e(p)q(oin)o(t)g(in)h Fo(bp)f Ft(units)h([1.06601]) p 1807 854 V 142 855 1667 2 v 141 905 2 50 v 167 890 a Fk(y)p Fo(ditto)p 493 905 V 223 w Ft(string)p 719 905 V 189 w({)p 856 905 V 50 w(The)g Fo(")g Ft(c)o(haracter)h(as)f(a)g(string)g(of)f(length)h (1)p 1807 905 V 142 907 1667 2 v 141 957 2 50 v 167 942 a Fk(y)p Fo(down)p 493 957 V 245 w Ft(pair)p 719 957 V 221 w(6)p 856 957 V 50 w(Do)o(wn)o(w)o(ard)f(direction)h(v)o(ector)h(\(0)p Fp(;)7 b Fk(\000)p Ft(1\))p 1807 957 V 142 958 1667 2 v 141 1008 2 51 v 167 993 a Fk(y)p Fo(epsilon)p 493 1008 V 179 w Ft(n)o(umeric)p 719 1008 V 148 w({)p 856 1008 V 50 w(Smallest)12 b(p)q(ositiv)o(e)i(MetaP)o(ost)g(n)o(um)o(b)q(er)g([)1590 977 y Fn(1)p 1557 984 83 2 v 1557 1008 a(65536)1645 993 y Ft(])p 1807 1008 2 51 v 142 1010 1667 2 v 141 1060 2 50 v 167 1045 a Fk(y)p Fo(evenly)p 493 1060 V 201 w Ft(picture)p 719 1060 V 147 w(32)p 856 1060 V 49 w(Dash)g(pattern)g(for)g(equal)f(length)h(dashes)p 1807 1060 V 142 1061 1667 2 v 141 1111 2 50 v 167 1096 a Fo(false)p 493 1111 V 241 w Ft(b)q(o)q(olean)p 719 1111 V 132 w(13)p 856 1111 V 49 w(The)g(b)q(o)q(olean)g(v)n(alue)f Fu(false)p 1807 1111 V 142 1113 1667 2 v 141 1163 2 50 v 167 1148 a Fk(y)p Fo(fullcircle)p 493 1163 V 113 w Ft(path)p 719 1163 V 190 w(23)p 856 1163 V 49 w(Circle)h(of)f(diameter)g(1)h(cen)o(tered)i(on)e(\(0)p Fp(;)7 b Ft(0\))p 1807 1163 V 142 1164 1667 2 v 141 1214 2 50 v 167 1199 a Fk(y)p Fo(green)p 493 1214 V 223 w Ft(color)p 719 1214 V 185 w(12)p 856 1214 V 49 w(Equiv)n(alen)o(t)13 b(to)h Fo(\(0,1,0\))p 1807 1214 V 142 1216 1667 2 v 141 1266 2 50 v 167 1251 a Fk(y)p Fo(halfcircle)p 493 1266 V 113 w Ft(path)p 719 1266 V 190 w(23)p 856 1266 V 49 w(Upp)q(er)h(half)e(of)g(a)h(circle)g(of) f(diameter)g(1)p 1807 1266 V 142 1267 1667 2 v 141 1317 2 50 v 167 1302 a Fk(y)p Fo(identity)p 493 1317 V 157 w Ft(transform)p 719 1317 V 95 w(31)p 856 1317 V 49 w(Iden)o(tit)o(y)h(transformation)p 1807 1317 V 142 1319 1667 2 v 141 1368 2 50 v 167 1354 a Fk(y)p Fo(in)p 493 1368 V 289 w Ft(n)o(umeric)p 719 1368 V 148 w(2)p 856 1368 V 50 w(One)h(inc)o(h)e(in)h Fo(bp)f Ft(units)h([72])p 1807 1368 V 142 1370 1667 2 v 141 1420 2 50 v 167 1405 a Fk(y)p Fo(infinity)p 493 1420 V 157 w Ft(n)o(umeric)p 719 1420 V 128 w(28)p 856 1420 V 49 w(Large)g(p)q(ositiv)o(e)f(v)n(alue)h([4095.99998])p 1807 1420 V 142 1422 1667 2 v 141 1471 2 50 v 167 1456 a Fk(y)p Fo(left)p 493 1471 V 245 w Ft(pair)p 719 1471 V 221 w(6)p 856 1471 V 50 w(Left)o(w)o(ard)g(direction)g(\()p Fk(\000)p Ft(1)p Fp(;)7 b Ft(0\))p 1807 1471 V 142 1473 1667 2 v 141 1523 2 50 v 167 1508 a Fk(y)p Fo(mitered)p 493 1523 V 179 w Ft(n)o(umeric)p 719 1523 V 128 w(35)p 856 1523 V 49 w Fo(linejoin)12 b Ft(v)n(alue)h(for)h (mitered)f(joins)g([0])p 1807 1523 V 142 1525 1667 2 v 141 1574 2 50 v 167 1559 a Fk(y)p Fo(mm)p 493 1574 V 289 w Ft(n)o(umeric)p 719 1574 V 148 w(2)p 856 1574 V 50 w(One)i(milli)o(m)o(eter)d(in)h Fo(bp)h Ft(units)g([2.83464])p 1807 1574 V 142 1576 1667 2 v 141 1626 2 50 v 167 1611 a Fo(nullpicture)p 493 1626 V 109 w Ft(picture)p 719 1626 V 147 w(14)p 856 1626 V 49 w(Empt)o(y)f(picture)p 1807 1626 V 142 1628 1667 2 v 141 1677 2 50 v 167 1662 a Fo(origin)p 493 1677 V 219 w Ft(pair)p 719 1677 V 221 w({)p 856 1677 V 50 w(The)h(pair)g(\(0)p Fp(;)7 b Ft(0\))p 1807 1677 V 142 1679 1667 2 v 141 1729 2 50 v 167 1714 a Fk(y)p Fo(pc)p 493 1729 V 289 w Ft(n)o(umeric)p 719 1729 V 148 w({)p 856 1729 V 50 w(One)15 b(pica)e(in)h Fo(bp)f Ft(units)h([11.95517])p 1807 1729 V 142 1730 1667 2 v 141 1780 2 50 v 167 1765 a Fo(pencircle)p 493 1780 V 153 w Ft(p)q(en)p 719 1780 V 208 w(38)p 856 1780 V 49 w(Circular)g(p)q(en)g(of)f(diameter)g(1)p 1807 1780 V 142 1782 1667 2 v 141 1832 2 50 v 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b(4)h(lists)f(prede\014ned)j(v)n(ariables)e(of)75 2349 y(other)i(t)o(yp)q(es.)22 b(T)m(able)14 b(5)h(lists)g(prede\014ned)h (constan)o(ts.)23 b(Some)13 b(of)i(these)h(are)f(implemen)o(ted)e(as)i(v)n (ariables)f(whose)75 2399 y(v)n(alues)g(are)g(in)o(tended)g(to)g(b)q(e)h (left)e(unc)o(hanged.)137 2474 y(T)m(ables)c(6{9)g(summarize)f(MetaP)o(ost)i (op)q(erators)g(and)g(list)f(the)h(p)q(ossible)g(argumen)o(t)e(and)i(result)g (t)o(yp)q(es)g(for)f(eac)o(h)75 2524 y(one.)22 b(A)15 b(\\{")f(en)o(try)h (for)g(the)h(left)e(argumen)o(t)g(indicates)h(a)g(unary)g(op)q(erator;)h (\\{")e(en)o(tries)i(for)f(b)q(oth)g(argumen)o(ts)75 2573 y(indicate)j(a)g(n) o(ullary)f(op)q(erator.)32 b(Op)q(erators)19 b(that)g(tak)o(e)f(su\016x)g (parameters)g(are)h(not)f(listed)g(in)g(these)i(tables)75 2623 y(b)q(ecause)c(they)e(are)g(treated)h(as)f(\\function-lik)o(e)f(macros".)p eop %%Page: 61 27 bop 75 -54 a Fq(A)14 b(User's)h(Man)o(ual)e(for)g(MetaP)o(ost)1203 b Ft(61)75 91 y(in)o(ternal)17 b(v)n(ariable)f 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y(e.g.,)h(there)i(is)f(no)f(\\)p Fo(primaryvardef)p Ft(.")137 1530 y(Th)o(us)22 b(macro)f(de\014nitions)h(can) g(b)q(e)g(in)o(tro)q(duced)h(b)o(y)e Fo(def)p Ft(,)i Fo(vardef)p Ft(,)f Fo(primarydef)p Ft(,)f Fo(secondarydef)p Ft(,)g(or)75 1580 y Fo(tertiarydef)p Ft(.)33 b(A)20 b Fk(h)p Ft(replacemen)o(t)f(text)p Fk(i)i Ft(is)e(an)o(y)g(list)g(of)g(tok)o(ens)h(that)g(is)g(balanced)f(with)g (resp)q(ect)j(to)e Fo(def)p Ft(-)75 1629 y Fo(enddef)9 b Ft(pairs)i(where)g (all)e(\014v)o(e)i(macro)e(de\014nition)h(tok)o(ens)h(are)g(treated)h(lik)o (e)e Fo(def)f Ft(for)i(the)g(purp)q(ose)g(of)f Fo(def)p Ft(-)p Fo(enddef)75 1679 y Ft(matc)o(hing.)137 1753 y(The)17 b(rest)g(of)f(the)h (syn)o(tax)f(for)g(macro)f(de\014nitions)h(is)g(summarized)f(in)g(Figure)i (46.)24 b(The)17 b(syn)o(tax)f(con)o(tains)75 1803 y(a)j(few)g(surprises.)34 b(The)20 b(macro)d(parameters)i(can)g(ha)o(v)o(e)g(a)g Fk(h)p Ft(delimited)e(part)p Fk(i)i Ft(and)g(an)g Fk(h)p Ft(undelimited)e(part)p Fk(i)p Ft(.)75 1853 y(Normally)m(,)10 b(one)k(of)g(these)h(is)f Fk(h)p Ft(empt)o(y)p Fk(i)p Ft(,)e(but)j(it)e(is)h(p)q(ossible)g(to)g(ha)o(v) o(e)f(b)q(oth)h(parts)h(nonempt)o(y:)462 1943 y Fo(def)21 b(foo\(text)f(a\))i (expr)f(b)g(=)7 b Fk(h)p Ft(replacemen)o(t)14 b(text)q Fk(i)7 b Fo(enddef;)75 2033 y Ft(This)14 b(de\014nes)h(a)f(macro)e Fo(foo)i Ft(to)f(tak)o(e)h(a)g(text)g(parameter)g(in)f(paren)o(theses)j (follo)o(w)o(ed)d(b)o(y)g(an)h(expression.)137 2107 y(The)i(syn)o(tax)g(also) f(allo)o(ws)f(the)i Fk(h)p Ft(undelimited)e(part)p Fk(i)i Ft(to)f(sp)q(ecify) h(an)f(argumen)o(t)g(t)o(yp)q(e)h(of)f Fo(suffix)f Ft(or)h Fo(text)p Ft(.)75 2157 y(An)g(example)f(of)g(a)h(macro)e(with)i(an)g (undelimited)e(su\016x)i(parameter)f(is)h(the)h(prede\014ned)g(macro)e Fo(incr)g Ft(that)h(is)75 2207 y(actually)e(de\014ned)i(lik)o(e)e(this:)539 2296 y Fo(vardef)21 b(incr)g(suffix)f($)i(=)f($:=$+1;)g($)g(enddef;)75 2386 y Ft(This)16 b(mak)o(es)g Fo(incr)g Ft(a)g(function)g(that)h(tak)o(es)g (a)f(v)n(ariable,)g(incremen)o(ts)g(it,)h(and)f(returns)i(the)g(new)f(v)n (alue.)25 b(Un-)75 2436 y(delimited)14 b(su\016x)i(parameters)g(ma)o(y)e(b)q (e)i(paren)o(thesized,)i(so)e Fo(incr)21 b(a)16 b Ft(and)f Fo(incr\(a\))g Ft(are)h(b)q(oth)g(legal)f(if)g Fo(a)h Ft(is)f(a)75 2486 y(n)o(umeric)e(v)n(ariable.)k(There)e(is)f(also)f(a)h(similar)d (prede\014ned)16 b(macro)c Fo(decr)h Ft(that)h(subtracts)i(1.)137 2560 y(Undelimited)c(text)h(parameters)g(run)h(to)f(the)g(end)h(of)e(a)h (statemen)o(t.)k(More)d(precisely)m(,)f(an)g(undelimited)e(text)75 2610 y(parameter)j(is)h(the)g(list)f(of)g(tok)o(ens)h(follo)o(wing)c(the)16 b(macro)d(call)h(up)g(to)g(the)i(\014rst)f(\\)p Fo(;)p Ft(")f(or)g(\\)p Fo(endgroup)p Ft(")f(or)h(\\)p Fo(end)p Ft(")75 2660 y(except)k(that)e(an)g (argumen)o(t)g(con)o(taining)f(\\)p Fo(begingroup)p Ft(")f(will)g(alw)o(a)o (ys)i(include)g(the)h(matc)o(hing)e(\\)p Fo(endgroup)p Ft(.")p eop %%Page: 50 38 bop 75 -54 a Fq(A)14 b(User's)h(Man)o(ual)e(for)g(MetaP)o(ost)1203 b Ft(50)137 91 y(If)19 b(the)h(macro)d(had)i(b)q(een)i Fo(a.b[])p Ft(,)d Fo(#@)h Ft(w)o(ould)f(alw)o(a)o(ys)g(b)q(e)i Fo(a.b)e Ft(and)h(the)h Fo(@)f Ft(parameter)g(w)o(ould)f(giv)o(e)g(the)75 141 y(n)o(umeric)f(subscript.)30 b(Then)18 b Fo(a@)g Ft(w)o(ould)e(refer)j (to)f(an)f(elemen)o(t)g(of)g(the)h(arra)o(y)g Fo(a[])p Ft(.)28 b(Note)18 b(that)g Fo(@)f Ft(is)h(a)f(su\016x)75 191 y(parameter,)h(not)h(an) f(expr)g(parameter,)h(so)f(an)g(expression)h(lik)o(e)f Fo(@+1)f Ft(w)o(ould)h(b)q(e)h(illegal.)29 b(The)18 b(only)g(w)o(a)o(y)f(to)75 241 y(get)e(at)g(the)g(n)o(umeric)g(v)n(alues)f(of)g(subscripts)j(in)d(a)h (su\016x)g(parameter)f(is)h(b)o(y)g(extracting)g(them)f(from)f(the)j(string) 75 291 y(returned)g(b)o(y)e(the)h Fo(str)f Ft(op)q(erator.)21 b(This)14 b(op)q(erator)h(tak)o(es)g(a)f(su\016x)g(and)h(returns)h(a)e (string)g(represen)o(tation)i(of)e(a)75 340 y(su\016x.)22 b(Th)o(us)15 b Fo(str)21 b(@)15 b Ft(w)o(ould)f(b)q(e)i Fo("3")e Ft(in)h Fo(a.b3)f Ft(and)h Fo("3.14")f Ft(in)g Fo(a.b3.14)g Ft(or)h Fo(a.b[3.14])p Ft(.)20 b(Since)15 b(the)h(syn)o(tax)75 390 y(for)g(a)f Fk(h)p Ft(su\016x)p Fk(i)i Ft(in)e(Figure)h(16)g(requires)h (negativ)o(e)f(subscripts)i(to)e(b)q(e)g(in)g(brac)o(k)o(ets,)h Fo(str)k(@)16 b Ft(returns)i Fo("[-3]")c Ft(in)75 440 y Fo(a.b[-3])p Ft(.)137 515 y(The)h Fo(str)f Ft(op)q(erator)h(is)f(generally)g(for)g (emergency)h(use)g(only)m(.)k(It)14 b(is)g(b)q(etter)i(to)f(use)g(su\016x)f (parameters)h(only)75 565 y(as)f(v)n(ariable)f(names)h(or)g(su\016xes.)19 b(The)c(b)q(est)g(example)e(of)g(a)h(v)n(ardef)g(macro)f(in)o(v)o(olving)f (su\016xes)j(is)f(the)g Fo(z)g Ft(macro)75 614 y(that)j(de\014nes)i(the)e Fo(z)g Ft(con)o(v)o(en)o(tion.)27 b(The)18 b(de\014nition)e(in)o(v)o(olv)o (es)g(a)h(sp)q(ecial)g(tok)o(en)g Fo(@#)g Ft(that)g(refers)i(to)d(the)i (su\016x)75 664 y(follo)o(wing)11 b(the)k(macro)d(name:)670 714 y Fo(vardef)20 b(z@#=\(x@#,y@#\))g(enddef;)75 789 y Ft(This)14 b(means)g(that)g(an)o(y)g(v)n(ariable)f(name)g(whose)i(\014rst)g(tok)o(en)f (is)g Fo(z)h Ft(is)f(equiv)n(alen)o(t)f(to)h(a)g(pair)g(of)g(v)n(ariables)f (whose)75 839 y(names)e(are)h(obtained)g(b)o(y)g(replacing)g Fo(z)f Ft(with)h Fo(x)f Ft(and)h Fo(y)p Ft(.)17 b(F)m(or)12 b(instance,)h Fo(z.a1)e Ft(calls)g(the)i Fo(z)e Ft(macro)g(with)h(the)g (su\016x)75 888 y(parameter)i Fo(@#)f Ft(set)i(to)f Fo(a1)p Ft(.)137 963 y(In)g(general,)727 1013 y Fo(vardef)6 b Fk(h)p Ft(generic)14 b(v)n(ariable)o Fk(i)q Fo(@#)75 1088 y Ft(is)k(an)f(alternativ) o(e)h(to)g Fo(vardef)f Fk(h)p Ft(generic)i(v)n(ariable)p Fk(i)e Ft(that)h(causes)h(the)f(MetaP)o(ost)h(in)o(terpreter)h(to)e(lo)q(ok)f(for)g (a)75 1137 y(su\016x)11 b(follo)o(wing)e(the)k(name)d(giv)o(en)h(in)g(the)h (macro)f(call)f(and)i(mak)o(es)e(this)i(a)o(v)n(ailable)d(as)j(the)g Fo(@#)f Ft(su\016x)h(parameter.)137 1212 y(T)m(o)h(summarize)f(the)i(sp)q (ecial)g(features)g(of)f(v)n(ardef)h(macros,)e(they)i(allo)o(w)e(a)h(broad)h (class)g(of)f(macro)f(names)h(as)75 1262 y(w)o(ell)d(as)h(macro)e(names)h (follo)o(w)o(ed)f(b)o(y)i(a)f(sp)q(ecial)h(su\016x)g(parameter.)17 b(F)m(urthermore,)10 b Fo(begingroup)f Ft(and)i Fo(endgroup)75 1312 y Ft(are)j(automatically)c(added)j(to)h(the)g Fk(h)p Ft(replacemen)o(t)f (text)p Fk(i)h Ft(of)f(a)g(v)n(ardef)g(macro.)j(Th)o(us)e(using)f Fo(vardef)f Ft(instead)i(of)75 1362 y Fo(def)h Ft(to)g(de\014ne)i(the)f Fo(joinup)e Ft(macro)h(in)g(Figure)g(45)g(w)o(ould)g(ha)o(v)o(e)h(a)o(v)o (oided)e(the)i(need)h(to)e(include)h Fo(begingroup)75 1411 y Ft(and)e Fo(endgroup)e Ft(explicitly)h(in)g(the)i(macro)d(de\014nition.)137 1486 y(In)i(fact,)g(most)f(of)h(the)h(macro)e(de\014nitions)h(giv)o(en)g(in)f (previous)i(examples)e(could)h(equally)g(w)o(ell)f(use)i Fo(vardef)75 1536 y Ft(instead)j(of)f Fo(def)p Ft(.)28 b(It)18 b(usually)f(do)q(es)h(not)g (matter)e(v)o(ery)i(m)o(uc)o(h)f(whic)o(h)g(y)o(ou)g(use,)i(but)f(a)f(go)q(o) q(d)g(general)h(rule)g(is)75 1586 y(to)f(use)h Fo(vardef)e Ft(if)g(y)o(ou)g(in)o(tend)h(the)h(macro)e(to)h(b)q(e)g(used)h(lik)o(e)f(a)f (function)h(or)g(a)g(subroutine.)28 b(The)18 b(follo)o(wing)75 1636 y(comparison)12 b(should)i(help)g(in)f(deciding)h(when)h(to)e(use)i Fo(vardef)p Ft(.)137 1752 y Fk(\017)21 b Ft(V)m(ardef)13 b(macros)h(are)g (automatically)d(surrounded)k(b)o(y)e Fo(begingroup)f Ft(and)i Fo(endgroup)p Ft(.)137 1835 y Fk(\017)21 b Ft(The)14 b(name)f(of)g(a)h(v)n (ardef)f(macro)g(can)h(b)q(e)h(more)d(than)i(one)g(tok)o(en)g(long)f(and)h (it)g(can)g(con)o(tain)f(subscripts.)137 1918 y Fk(\017)21 b Ft(A)14 b(v)n(ardef)h(macro)e(can)h(ha)o(v)o(e)h(access)h(to)e(the)h (su\016x)g(that)f(follo)o(ws)f(the)i(macro)f(name)f(when)i(the)g(macro)e(is) 179 1968 y(called.)137 2051 y Fk(\017)21 b Ft(When)15 b(a)h(sym)o(b)q(olic)d (tok)o(en)j(is)f(used)i(in)e(the)h(name)e(of)h(a)g(v)n(ardef)h(macro)e(it)h (remains)f(a)i(tag)f(and)g(can)h(still)179 2100 y(b)q(e)h(used)g(in)f(other)g (v)n(ariable)f(names.)25 b(Th)o(us)16 b Fo(p5dir)f Ft(is)h(a)g(legal)g(v)n (ariable)f(name)g(ev)o(en)i(though)f Fo(dir)f Ft(is)h(a)179 2150 y(v)n(ardef)d(macro,)e(but)j(an)f(ordinary)f(macro)g(suc)o(h)i(as)g Fo(...)j Ft(cannot)d(b)q(e)f(used)i(in)d(a)h(v)n(ariable)f(name.)17 b(\(This)c(is)179 2200 y(fortunate)g(since)g Fo(z5...z6)e Ft(is)i(supp)q (osed)h(to)e(b)q(e)h(a)g(path)f(expression,)i(not)f(an)f(elab)q(orate)h(v)n (ariable)e(name\).)75 2341 y Fg(9.5)56 b(De\014ning)18 b(Unary)g(and)i (Binary)e(Macros)75 2443 y Ft(It)h(has)f(b)q(een)i(men)o(tioned)d(sev)o(eral) j(times)d(that)i(some)e(of)h(the)h(op)q(erators)h(and)e(commands)e(discussed) 21 b(so)d(far)75 2493 y(are)h(actually)f(prede\014ned)j(macros.)33 b(These)20 b(include)f(unary)g(op)q(erators)h(suc)o(h)g(as)f Fo(round)f Ft(and)h Fo(unitvector)p Ft(,)75 2542 y(statemen)o(ts)13 b(suc)o(h)g(as)g Fo(fill)f Ft(and)g Fo(draw)p Ft(,)f(and)i(binary)f(op)q (erators)h(suc)o(h)h(as)e Fo(dotprod)g Ft(and)g Fo(intersectionpoint)o Ft(.)75 2592 y(The)19 b(main)d(di\013erence)k(b)q(et)o(w)o(een)g(these)g (macros)e(and)g(the)h(ones)g(w)o(e)g(already)f(kno)o(w)g(ho)o(w)g(to)g (de\014ne)h(is)g(their)75 2642 y(argumen)o(t)13 b(syn)o(tax.)p eop %%Page: 49 39 bop 75 -54 a Fq(A)14 b(User's)h(Man)o(ual)e(for)g(MetaP)o(ost)1203 b Ft(49)75 91 y(In)15 b(fact,)g(b)q(oth)g(forms)e(are)i(acceptable.)23 b(P)o(arameters)15 b(in)f(a)h(macro)e(call)h(can)i(b)q(e)f(separated)h(b)o(y) f(commas)d(or)j(b)o(y)75 141 y Fo(\)\()e Ft(pairs.)18 b(The)c(only)e (restriction)j(is)e(that)g(a)g(text)i(parameter)e(m)o(ust)f(b)q(e)i(follo)o (w)o(ed)e(b)o(y)h(a)g(righ)o(t)g(paren)o(thesis.)19 b(F)m(or)75 191 y(instance,)14 b(a)g(macro)e Fo(foo)i Ft(with)f(one)h(text)h(parameter)e (and)h(one)g(expr)h(parameter)e(can)h(b)q(e)h(called)855 282 y Fo(foo\(a,b\)\(c\))75 374 y Ft(in)e(whic)o(h)h(case)h(the)g(text)f (parameter)g(is)f(\\)p Fo(a,b)p Ft(")g(and)h(the)g(expr)h(parameter)e(is)h Fo(c)p Ft(,)f(but)866 465 y Fo(foo\(a,b,c\))75 556 y Ft(sets)18 b(the)f(text)g(parameter)g(to)f(\\)p Fo(a,b,c)p Ft(")f(and)h(lea)o(v)o(es)h (the)g(MetaP)o(ost)h(in)o(terpreter)g(still)e(lo)q(oking)f(for)h(the)h(expr) 75 606 y(parameter.)75 747 y Fg(9.4)56 b(V)-5 b(ardef)19 b(Macros)75 849 y Ft(A)e(macro)f(de\014nition)h(can)g(b)q(egin)g(with)g Fo(vardef)f Ft(instead)i(of)e Fo(def)p Ft(.)27 b(Macros)18 b(de\014ned)g(in)f(this)g(w)o(a)o(y)g(are)g(called)75 899 y(v)n(ardef)f (macros.)23 b(They)16 b(are)g(particularly)f(w)o(ell-suited)h(to)f (applications)g(where)i(macros)e(are)h(b)q(eing)g(used)h(lik)o(e)75 948 y(functions)d(or)g(subroutines.)19 b(The)14 b(main)e(idea)i(is)f(that)h (a)g(v)n(ardef)g(macro)e(is)i(lik)o(e)f(a)h(v)n(ariable)e(of)i(t)o(yp)q(e)g (\\macro.")137 1023 y(Instead)h(of)e Fo(def)g Fk(h)p Ft(sym)o(b)q(olic)g(tok) o(en)p Fk(i)p Ft(,)g(a)h(v)n(ardef)g(macro)e(b)q(egins)749 1114 y Fo(vardef)5 b Fk(h)p Ft(generic)15 b(v)n(ariable)o Fk(i)75 1206 y Ft(where)h(a)f Fk(h)p Ft(generic)h(v)n(ariable)p Fk(i)e 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y(p)q(ossibilities)c(is)345 2660 y Fk(h)p Ft(lab)q(el)g(su\016x)p Fk(i)f(!)f(h)p Ft(empt)o(y)o Fk(i)h(j)f Fo(lft)g Fk(j)g Fo(rt)g Fk(j)g Fo(top)g Fk(j)g Fo(bot)g Fk(j)g Fo(ulft)g Fk(j)g Fo(urt)g Fk(j)g Fo(llft)g Fk(j)g Fo(lrt)p eop %%Page: 17 71 bop 75 -54 a Fq(A)14 b(User's)h(Man)o(ual)e(for)g(MetaP)o(ost)1203 b Ft(17)397 89 y Fo(ABCDEFGHIJKLMNOPQRST)o(UVWXY)o(Z_ab)o(cdefg)o(hijkl)o (mnopq)o(rstuv)o(wxyz)921 139 y(:<=>|)931 188 y(#&@$)942 238 y(/*\\)953 288 y(+-)953 338 y(!?)953 388 y('`)953 438 y(^~)953 487 y({})964 537 y([)964 587 y(])587 701 y Ft(T)m(able)13 b(1:)18 b(Character)d(classes)g(for)f(tok)o(enization)75 826 y(consecutiv)o(ely)m(.)k (Th)o(us)c Fo(\(\(\)\))f Ft(is)g(four)h(tok)o(ens,)f(not)h(one)g(or)f(t)o(w)o (o.)18 b(The)c(p)q(ercen)o(t)h(sign)f(is)f(v)o(ery)h(sp)q(ecial)g(b)q(ecause) h(it)75 876 y(in)o(tro)q(duces)e(commen)o(ts.)j(The)d(p)q(ercen)o(t)h(sign)d (and)h(ev)o(erything)h(after)f(it)g(up)g(to)g(the)h(end)g(of)f(the)g(line)g (are)h(ignored.)137 950 y(Another)k(sp)q(ecial)e(c)o(haracter)i(is)f(the)g(p) q(erio)q(d.)23 b(Tw)o(o)16 b(or)f(more)g(p)q(erio)q(ds)h(together)g(form)e(a) i(sym)o(b)q(olic)d(tok)o(en,)75 1000 y(but)g(a)g(single)g(p)q(erio)q(d)h(is)f (ignored,)g(and)g(a)g(p)q(erio)q(d)g(preceded)j(or)d(follo)o(w)o(ed)f(b)o(y)h (digits)f(is)h(part)h(of)e(a)h(n)o(um)o(b)q(er)g(Th)o(us)75 1050 y Fo(..)18 b Ft(and)12 b Fo(...)17 b Ft(are)c(sym)o(b)q(olic)e(tok)o (ens)i(while)f Fo(a.b)g Ft(is)g(just)h(t)o(w)o(o)f(tok)o(ens)h Fo(a)f Ft(and)g Fo(b)p Ft(.)18 b(It)12 b(con)o(v)o(en)o(tional)g(to)g(use)h (p)q(erio)q(ds)75 1100 y(to)h(separate)h(tok)o(ens)f(in)g(this)g(fashion)f (when)h(naming)e(a)h(v)n(ariable)g(that)h(is)g(more)f(than)g(one)i(tok)o(en)f (long.)75 1241 y Fg(6.2)56 b(V)-5 b(ariable)18 b(Declarations)75 1342 y Ft(A)e(v)n(ariable)g(name)f(is)h(a)g(sym)o(b)q(olic)e(tok)o(en)i(or)h (a)f(sequence)i(of)e(sym)o(b)q(olic)e(tok)o(ens.)26 b(Most)16 b(sym)o(b)q(olic)f(tok)o(ens)i(are)75 1392 y(legitimate)10 b(v)n(ariable)i(names,)f(but)i(an)o(ything)e(with)h(a)h(prede\014ned)h (meaning)c(lik)o(e)i Fo(draw)p Ft(,)f Fo(+)p Ft(,)h(or)h Fo(..)k Ft(is)c(disallo)o(w)o(ed;)75 1442 y(i.e.,)19 b(v)n(ariable)e(names)h(cannot)h (b)q(e)h(macros)e(or)h(MetaP)o(ost)g(primitiv)o(es.)31 b(This)19 b(minor)e(restriction)j(allo)o(ws)d(an)75 1492 y(amazingly)f(broad)j(class)h (of)e(v)n(ariable)g(names:)28 b Fo(alpha)p Ft(,)18 b Fo(==>)p Ft(,)i Fo(@&#$&)p Ft(,)e(and)h Fo(~~)g Ft(are)g(all)f(legitimate)f(v)n (ariable)75 1542 y(names.)g(Suc)o(h)e(sym)o(b)q(olic)d(tok)o(ens)i(without)f (sp)q(ecial)i(meanings)d(are)i(called)g Fu(tags)p Ft(.)137 1616 y(A)h(v)n(ariable)e(name)h(can)g(b)q(e)h(a)g(sequence)h(of)e(tags)g(lik) o(e)g Fo(f.bot)g Ft(or)g Fo(f.top)p Ft(.)19 b(The)c(idea)f(is)g(to)h(pro)o (vide)f(some)g(of)75 1666 y(the)j(functionalit)o(y)d(of)i(P)o(ascal)g (records)i(or)e(C)g(structures.)27 b(It)17 b(is)f(also)f(p)q(ossible)i(to)f (sim)o(ulate)e(arra)o(ys)i(b)o(y)g(using)75 1716 y(v)n(ariable)f(names)g (that)i(con)o(tain)e(n)o(um)o(b)q(ers)h(as)g(w)o(ell)g(as)g(sym)o(b)q(olic)e (tok)o(ens.)26 b(F)m(or)15 b(example,)g(the)i(v)n(ariable)e(name)75 1766 y Fo(x2r)e Ft(consists)i(of)e(the)i(tag)e Fo(x)p Ft(,)g(the)h(n)o(um)o (b)q(er)f(2,)h(and)f(the)i(tag)e Fo(r)p Ft(.)18 b(There)d(can)f(also)f(b)q(e) h(v)n(ariables)f(named)g Fo(x3r)g Ft(and)75 1816 y(ev)o(en)i Fo(x3.14r)p Ft(.)k(These)c(v)n(ariables)f(can)h(b)q(e)g(treated)h(as)e(an)g (arra)o(y)h(via)e(constructions)j(lik)o(e)e Fo(x[i]r)p Ft(,)f(where)j Fo(i)e Ft(has)75 1865 y(an)g(appropriate)g(n)o(umeric)f(v)n(alue.)k(The)d(o)o (v)o(erall)f(syn)o(tax)h(for)f(v)n(ariable)g(names)g(is)h(sho)o(wn)g(in)f (Figure)h(16.)500 2000 y Fk(h)p Ft(v)n(ariable)o Fk(i)e(!)f(h)p Ft(tag)o Fk(i)q(h)p Ft(su\016x)p Fk(i)500 2050 y(h)p Ft(su\016x)p Fk(i)h(!)f(h)p Ft(empt)o(y)o Fk(i)g(j)h(h)p Ft(su\016x)p Fk(ih)p Ft(subscript)q Fk(i)g(j)f(h)p Ft(su\016x)p Fk(ih)p Ft(tag)p Fk(i)500 2099 y(h)p Ft(subscript)q Fk(i)h(!)f(h)p Ft(n)o(um)o(b)q(er)p Fk(i)g(j)g Fo([)p Fk(h)p Ft(n)o(umeric)i(expression)r Fk(i)p Fo(])593 2232 y Ft(Figure)h(16:)j(The)d(syn)o(tax)g(for)g(v)n(ariable)f (names.)137 2332 y(V)m(ariables)g(lik)o(e)g Fo(x2)g Ft(and)h Fo(y2)f Ft(tak)o(e)g(on)h(n)o(umeric)e(v)n(alues)i(b)o(y)f(default,)g(so)h(w) o(e)f(can)h(use)h(the)f(fact)f(that)h Fo(z)p Fk(h)p Ft(su\016x)p Fk(i)75 2382 y Ft(is)g(an)f(abbreviation)h(for)795 2431 y(\()p Fp(x)p Fk(h)p Ft(su\016x)p Fk(i)p Fp(;)g(y)q Fk(h)p Ft(su\016x)q Fk(i)p Ft(\))75 2506 y(to)j(generate)i(pair-v)n(alued)d(v)n(ariables)h(when)h (needed.)30 b(It)17 b(turns)i(out)e(that)g(the)h Fo(beginfig)e Ft(macro)g(wip)q(es)i(out)75 2556 y(pre-existing)c(v)n(alues)e(v)n(ariables)h (that)g(b)q(egin)g(with)g(the)h(tags)f Fo(x)g Ft(or)g Fo(y)g Ft(so)h(that)f Fo(beginfig)e Fp(:)c(:)g(:)19 b Fo(endfig)12 b Ft(blo)q(c)o(ks)h(do)75 2606 y(not)g(in)o(terfere)i(with)e(eac)o(h)h(other) h(when)f(this)f(naming)f(sc)o(heme)h(is)h(used.)19 b(In)13 b(other)h(w)o(ords,)g(v)n(ariables)f(that)g(start)p eop %%Page: 16 72 bop 75 -54 a Fq(A)14 b(User's)h(Man)o(ual)e(for)g(MetaP)o(ost)1203 b Ft(16)137 91 y(There)15 b(is)e(a)h(whole)f(class)h(of)f(other)h(op)q (erators)h(that)e(classify)g(expressions)i(and)f(return)h(b)q(o)q(olean)e (results.)19 b(A)75 141 y(t)o(yp)q(e)12 b(name)f(suc)o(h)i(as)f Fo(pair)f Ft(can)h(op)q(erate)h(on)e(an)o(y)h(t)o(yp)q(e)g(of)f Fk(h)p Ft(primary)p Fk(i)g Ft(and)g(return)i(a)f(b)q(o)q(olean)f(result)i (indicating)75 191 y(whether)j(the)g(argumen)o(t)e(is)h(a)f Fo(pair)p Ft(.)21 b(Similarly)l(,)12 b(eac)o(h)j(of)g(the)g(follo)o(wing)d (can)k(b)q(e)f(used)h(as)f(a)g(unary)g(op)q(erator:)75 241 y Fo(numeric)p Ft(,)g Fo(boolean)p Ft(,)h Fo(color)p Ft(,)f Fo(string)p Ft(,)h Fo(transform)p Ft(,)f Fo(path)p Ft(,)g Fo(pen)p Ft(,)h(and)h Fo(picture)p Ft(.)24 b(Besides)19 b(just)d(testing)h(the)75 291 y(t)o(yp)q(e)g(of)g(a)g Fk(h)p Ft(primary)p Fk(i)p Ft(,)e(y)o(ou)i(can)g (use)h(the)g Fo(known)d Ft(and)i Fo(unknown)f Ft(op)q(erators)i(to)f(test)h (if)e(it)g(has)h(a)g(completely)75 340 y(kno)o(wn)c(v)n(alue.)137 415 y(Ev)o(en)g(a)f(n)o(um)o(b)q(er)f(can)i(b)q(eha)o(v)o(e)g(lik)o(e)e(an)h (op)q(erator)h(in)f(some)f(con)o(texts.)19 b(This)12 b(refers)i(to)e(the)h (tric)o(k)f(that)g(allo)o(ws)75 465 y Fo(3x)17 b Ft(and)f Fo(3cm)h Ft(as)g(alternativ)o(es)g(to)g Fo(3*x)f Ft(and)h Fo(3*cm)p Ft(.)27 b(The)17 b(rule)g(is)g(that)g(a)g Fk(h)p Ft(n)o(um)o(b)q(er)f(or)h (fraction)p Fk(i)g Ft(that)g(is)g(not)75 515 y(follo)o(w)o(ed)12 b(b)o(y)i Fo(+)p Ft(,)f Fo(-)p Ft(,)g(or)g(another)h Fk(h)p Ft(n)o(um)o(b)q(er)f(or)h(fraction)p Fk(i)f Ft(can)h(serv)o(e)h(as)f(a)f Fk(h)p Ft(primary)g(binop)p Fk(i)p Ft(.)k(Th)o(us)d Fo(2/3x)f Ft(is)g(t)o(w)o(o)75 565 y(thirds)h(of)g Fo(x)f Ft(but)h Fo(\(2\)/3x)f Ft(is)555 548 y Fn(2)p 546 555 36 2 v 546 579 a(3)p Fh(x)600 565 y Ft(and)h Fo(3)21 b(3)14 b Ft(is)f(illegal.)137 639 y(There)g(are)f (also)f(op)q(erators)i(for)e(extracting)h(n)o(umeric)f(sub\014elds)i(from)d (pairs,)i(colors,)f(and)h(ev)o(en)g(transforms.)75 689 y(If)i Fo(p)f Ft(is)h(a)f Fk(h)p Ft(pair)h(primary)p Fk(i)p Ft(,)e Fo(xpart)21 b(p)13 b Ft(and)h Fo(ypart)21 b(p)13 b Ft(extract)i(its)f(comp)q (onen)o(ts)g(so)g(that)779 780 y Fo(\(xpart)20 b(p,)i(ypart)f(p\))75 872 y Ft(is)14 b(equiv)n(alen)o(t)g(to)h Fo(p)f Ft(ev)o(en)h(if)f Fo(p)h Ft(is)f(an)h(unkno)o(wn)f(pair)g(that)h(is)f(b)q(eing)h(used)g(in)f(a) h(linear)f(equation.)20 b(Similarly)l(,)11 b(a)75 922 y(color)j Fo(c)f Ft(is)h(equiv)n(alen)o(t)f(to)583 971 y Fo(\(redpart)20 b(c,)h(greenpart)f(c,)i(bluepart)e(c\))75 1046 y Ft(The)14 b(part)g(sp)q(eci\014ers)i(for)e(transforms)f(will)f(b)q(e)j(discussed)g (later.)75 1208 y Fv(6)69 b(V)-6 b(ariables)75 1324 y Ft(MetaP)o(ost)22 b(allo)o(ws)e(comp)q(ound)h(v)n(ariable)f(names)h(suc)o(h)h(as)g(x.a,)g Fo(x2r)p Ft(,)g Fo(y2r)p Ft(,)h(and)e Fo(z2r)p Ft(,)h(where)h Fo(z2r)e Ft(means)75 1374 y Fo(\(x2r,y2r\))16 b Ft(and)h Fo(z.a)g Ft(means)g Fo(\(x.a,y.a\))p Ft(.)27 b(In)17 b(fact)h(there)h(is)e(a)h(broad)f (class)h(of)f(su\016xes)h(suc)o(h)g(that)g Fo(z)p Fk(h)p Ft(suf-)75 1424 y(\014x)p Fk(i)c Ft(means)789 1474 y(\()p Fp(x)p Fk(h)p Ft(su\016x)p Fk(i)p Fp(;)g(y)q Fk(h)p Ft(su\016x)q Fk(i)p Ft(\))p Fp(:)75 1548 y Ft(Since)g(a)g Fk(h)p Ft(su\016x)p Fk(i)g Ft(is)g(comp)q(osed) f(of)h(tok)o(ens,)f(it)h(is)g(b)q(est)h(to)e(b)q(egin)h(with)g(a)f(few)h (commen)o(ts)f(ab)q(out)g(tok)o(ens.)75 1689 y Fg(6.1)56 b(T)-5 b(ok)n(ens)75 1791 y Ft(A)13 b(MetaP)o(ost)g(input)f(\014le)g(is)h(treated)g (as)g(a)f(sequence)j(of)c(n)o(um)o(b)q(ers,)h(string)h(constan)o(ts,)g(and)f (sym)o(b)q(olic)f(tok)o(ens.)18 b(A)75 1841 y(n)o(um)o(b)q(er)13 b(consists)j(of)d(a)h(sequence)i(of)e(digits)f(p)q(ossibly)h(con)o(taining)f (a)h(decimal)e(p)q(oin)o(t.)19 b(T)m(ec)o(hnically)m(,)12 b(the)j(min)o(us)75 1891 y(sign)f(in)g(fron)o(t)g(of)f(a)h(negativ)o(e)g(n)o(um)o(b)q(er)g(is)g (a)g(separate)i(tok)o(en.)j(Since)c(MetaP)o(ost)g(uses)g(\014xed)g(p)q(oin)o (t)f(arithmetic,)75 1940 y(it)f(do)q(es)g(not)g(understand)h(exp)q(onen)o 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b(constan)o(ts)i(are)e(giv)o (en)g(in)g(double)g(quotes)75 362 y Fo("like)f(this")o Ft(.)30 b(String)18 b(constan)o(ts)h(cannot)f(con)o(tain)f(double)h(quotes)h(or)f (newlines,)h(but)f(there)h(is)f(a)g(w)o(a)o(y)f(to)75 412 y(construct)f(a)d (string)h(con)o(taining)f(an)o(y)g(sequence)j(of)e(eigh)o(t-bit)f(c)o (haracters.)137 484 y(The)e(b)q(o)q(olean)e(t)o(yp)q(e)h(has)g(the)h(constan) o(ts)f Fo(true)f Ft(and)h Fo(false)f Ft(and)g(the)i(op)q(erators)g Fo(and)p Ft(,)e Fo(or)p Ft(,)h Fo(not)p Ft(.)16 b(The)10 b(relations)75 534 y Fo(=)16 b Ft(and)g Fo(<>)f Ft(test)j(ob)r(jects)f(of)e(an)o(y)h(t)o(yp) q(e)g(for)g(equalit)o(y)f(and)h(inequalit)o(y.)24 b(Comparison)14 b(relations)i Fo(<)p Ft(,)g Fo(<=)p Ft(,)f Fo(>)p Ft(,)h(and)75 583 y Fo(>=)d Ft(are)h(de\014ned)h(lexicographically)d(for)h(strings)h(and)g (in)f(the)h(ob)o(vious)f(w)o(a)o(y)g(for)g(n)o(umerics.)18 b(Ordering)c(relations)75 633 y(are)g(also)g(de\014ned)h(for)e(b)q(o)q (oleans,)h(pairs,)g(colors,)f(and)h(transforms,)f(but)h(the)h(comparison)d (rules)j(are)f(not)g(w)o(orth)75 683 y(discussing)g(here.)137 755 y(The)h(picture)g(data)e(t)o(yp)q(e)i(is)f(just)g(what)g(the)h(name)e (implies.)j(An)o(ything)e(that)g(can)g(b)q(e)h(dra)o(wn)f(in)f(MetaP)o(ost)75 804 y(can)f(b)q(e)h(stored)f(in)g(a)g(picture)g(v)n(ariable.)17 b(In)11 b(fact,)h(the)h Fo(draw)e Ft(statemen)o(t)h(actually)f(stores)i(its)f (results)h(in)e(a)h(sp)q(ecial)75 854 y(picture)k(v)n(ariable)e(called)h Fo(currentpicture)p Ft(.)20 b(Pictures)c(can)g(b)q(e)g(added)f(to)g(other)h (pictures)h(and)e(op)q(erated)h(on)75 904 y(b)o(y)e(transforms.)137 976 y(Finally)m(,)c(there)j(is)f(a)g(data)f(t)o(yp)q(e)i(called)e(a)h(p)q (en.)18 b(The)13 b(main)c(function)j(of)f(p)q(ens)i(in)f(MetaP)o(ost)g(is)g (to)g(determine)75 1026 y(line)h(thic)o(kness,)i(but)f(they)g(can)h(also)e(b) q(e)h(used)h(to)f(ac)o(hiev)o(e)g(calligraphic)f(e\013ects.)20 b(The)14 b(statemen)o(t)750 1109 y Fo(pickup)20 b Fk(h)p Ft(p)q(en)15 b(expression)q Fk(i)75 1193 y Ft(causes)h(the)f(giv)o(en)e(p)q(en)i(to)f(b)q (e)h(used)h(in)d(subsequen)o(t)j Fo(draw)e Ft(statemen)o(ts.)19 b(Normally)m(,)11 b(the)k(p)q(en)g(expression)g(is)g(of)75 1243 y(the)f(form)617 1293 y Fo(pencircle)20 b(scaled)g Fk(h)p Ft(n)o(umeric)13 b(primary)o Fk(i)p Fp(:)75 1363 y Ft(This)20 b(de\014nes)h(a)e(circular)h(p)q(en)g(that)g(pro)q(duces)h(lines)f(of)f (constan)o(t)h(thic)o(kness.)36 b(If)20 b(calligraphic)e(e\013ects)k(are)75 1413 y(desired,)15 b(the)f(p)q(en)h(expression)g(can)f(b)q(e)g(adjusted)h(to) e(giv)o(e)h(an)f(elliptical)g(p)q(en)h(or)g(a)g(p)q(olygonal)e(p)q(en.)75 1549 y Fg(5.2)56 b(Op)r(erators)75 1648 y Ft(There)11 b(are)g(man)o(y)d (di\013eren)o(t)k(w)o(a)o(ys)e(to)g(mak)o(e)e(expressions)k(of)e(the)h(nine)f (basic)g(t)o(yp)q(es,)i(but)e(most)f(of)h(the)h(op)q(erations)75 1698 y(\014t)20 b(in)o(to)e(a)h(fairly)f(simple)g(syn)o(tax)i(with)f(four)g (lev)o(els)g(of)g(precedence)k(as)c(sho)o(wn)g(in)g(Figure)h(14.)34 b(There)21 b(are)75 1747 y(primaries,)d(secondaries,)i(tertiaries,)g(and)e (expressions)i(of)e(eac)o(h)h(of)e(the)i(basic)g(t)o(yp)q(es,)h(so)e(the)h (syn)o(tax)f(rules)75 1797 y(could)g(b)q(e)g(sp)q(ecialized)g(to)g(deal)g (with)f(items)g(suc)o(h)h(as)g Fk(h)p Ft(n)o(umeric)f(primary)p Fk(i)p Ft(,)g Fk(h)p Ft(b)q(o)q(olean)h(tertiary)p Fk(i)p Ft(,)g(etc.)31 b(This)75 1847 y(allo)o(ws)17 b(the)h(result)h(t)o(yp)q(e)f(for)g(an)g(op)q (eration)g(to)g(dep)q(end)h(on)e(the)i(c)o(hoice)f(of)g(op)q(erator)g(and)g (the)h(t)o(yp)q(es)g(of)e(its)75 1897 y(op)q(erands.)35 b(F)m(or)18 b(example,)h(the)h Fo(<)e Ft(relation)h(is)g(a)g Fk(h)p Ft(tertiary)g(binary) p Fk(i)g Ft(that)g(can)h(b)q(e)f(applied)g(to)g(a)g Fk(h)p Ft(n)o(umeric)75 1947 y(expression)p Fk(i)d Ft(and)e(a)f Fk(h)p Ft(n)o(umeric)h(tertiary)p Fk(i)h Ft(to)f(giv)o(e)f(a)h Fk(h)p Ft(b)q(o)q(olean)g(expression)p Fk(i)p Ft(.)21 b(The)14 b(same)g(op)q(erator) g(can)h(accept)75 1996 y(other)h(op)q(erand)g(t)o(yp)q(es)g(suc)o(h)g(as)f Fk(h)p Ft(string)g(expression)p Fk(i)i Ft(and)e Fk(h)p Ft(string)h(tertiary)p Fk(i)p Ft(,)f(but)h(an)f(error)h(message)f(results)75 2046 y(if)e(the)i(op)q(erand)f(t)o(yp)q(es)h(do)e(not)h(matc)o(h.)137 2118 y(The)d(m)o(ultiplicatio)o(n)d(and)i(division)f(op)q(erators)i Fo(*)f Ft(and)g Fo(/)g Ft(are)h(examples)f(of)f(what)h(Figure)h(14)f(calls)f (a)h Fk(h)p Ft(primary)75 2168 y(binop)p Fk(i)p Ft(.)17 b(Eac)o(h)11 b(can)g(accept)h(t)o(w)o(o)f(n)o(umeric)f(op)q(erands)i(or)f(one)g(n)o (umeric)f(op)q(erand)i(and)f(one)g(op)q(erand)g(of)g(t)o(yp)q(e)g(pair)75 2218 y(or)j(color.)k(The)c(exp)q(onen)o(tiation)f(op)q(erator)i Fo(**)e Ft(is)h(a)f Fk(h)p Ft(primary)g(binop)p Fk(i)g Ft(that)h(requires)h (t)o(w)o(o)e(n)o(umeric)h(op)q(erands.)75 2267 y(Placing)19 b(this)h(at)f(the)i(same)e(lev)o(el)g(of)g(precedence)k(as)d(m)o (ultiplicatio)o(n)d(and)j(division)e(has)i(the)h(unfortunate)75 2317 y(consequence)15 b(that)d Fo(3*a**2)f Ft(means)h(\(3)p Fp(a)p Ft(\))740 2302 y Fn(2)759 2317 y Ft(,)g(not)g(3\()p Fp(a)914 2302 y Fn(2)933 2317 y Ft(\).)17 b(Since)c(unary)g(negation)f (applies)g(at)g(the)h(primary)e(lev)o(el,)75 2367 y(it)16 b(also)g(turns)i (out)e(that)h Fo(-a**2)f Ft(means)g(\()p Fk(\000)p Fp(a)p Ft(\))828 2352 y Fn(2)847 2367 y Ft(.)26 b(F)m(ortunately)m(,)16 b(subtraction)h(has)g (lo)o(w)o(er)f(precedence)k(so)d(that)75 2417 y Fo(a-b**2)c Ft(do)q(es)h(mean)f Fp(a)c Fk(\000)h Ft(\()p Fp(b)531 2402 y Fn(2)549 2417 y Ft(\))k(instead)g(of)g(\()p Fp(a)9 b Fk(\000)g Fp(b)p Ft(\))892 2402 y Fn(2)911 2417 y Ft(.)137 2489 y(Another)16 b Fk(h)p Ft(primary)d(binop)p Fk(i)h Ft(is)g(the)i Fo(dotprod)d Ft(op)q(erator)i(that)f(computes)h(the)g(v)o(ector)g(dot)g(pro)q(duct)g(of)f (t)o(w)o(o)75 2538 y(pairs.)k(F)m(or)13 b(example,)g Fo(z1)21 b(dotprod)f(z2)14 b Ft(is)f(equiv)n(alen)o(t)h(to)f Fo(x1*y1)21 b(+)h(x2*y2)p Ft(.)137 2610 y(The)13 b(additiv)o(e)f(op)q(erators)i Fo(+)e Ft(and)g Fo(-)h Ft(are)f Fk(h)p Ft(secondary)i(binops)p Fk(i)f Ft(that)f(op)q(erate)i(on)e(n)o(umerics,)g(pairs,)g(or)h(colors)75 2660 y(and)i(pro)q(duce)h(results)g(of)e(the)h(same)f(t)o(yp)q(e.)22 b(Other)15 b(op)q(erators)h(that)f(fall)e(in)i(this)g(category)g(are)g (\\Pythagorean)p eop %%Page: 12 76 bop 75 -54 a Fq(A)14 b(User's)h(Man)o(ual)e(for)g(MetaP)o(ost)1203 b Ft(12)75 91 y Fv(5)69 b(Expressions)75 207 y Ft(It)19 b(is)g(no)o(w)f(time) g(for)g(a)h(more)f(systematic)g(view)h(of)f(the)i(MetaP)o(ost)f(language.)32 b(W)m(e)19 b(ha)o(v)o(e)g(seen)h(that)f(there)75 257 y(are)e(n)o(umeric)e (quan)o(tities)h(and)g(co)q(ordinate)h(pairs,)f(and)g(that)h(these)g(can)g(b) q(e)g(com)o(bined)e(to)h(sp)q(ecify)h(paths)f(for)75 307 y Fo(draw)d Ft(statemen)o(ts.)18 b(W)m(e)13 b(ha)o(v)o(e)g(also)g(seen)i(ho)o (w)e(v)n(ariables)f(can)i(b)q(e)g(used)g(in)f(linear)g(equations,)g(but)h(w)o (e)g(ha)o(v)o(e)f(not)75 357 y(discussed)j(all)c(the)j(op)q(erations)f(and)g (data)f(t)o(yp)q(es)i(that)f(can)g(b)q(e)g(used)h(in)f(equations.)137 431 y(It)j(is)f(p)q(ossible)g(to)g(exp)q(erimen)o(t)g(with)g(expressions)i (in)o(v)o(olving)c(an)o(y)i(of)f(the)i(data)f(t)o(yp)q(es)h(men)o(tioned)e(b) q(elo)o(w)75 481 y(b)o(y)f(using)f(the)i(statemen)o(t)819 531 y Fo(show)6 b Fk(h)p Ft(expression)q Fk(i)75 606 y Ft(to)19 b(ask)f(MetaP)o(ost)i(to)e(prin)o(t)h(a)f(sym)o(b)q(olic)f(represen)o(tation) j(of)f(the)g(v)n(alue)f(of)g(eac)o(h)h(expression.)34 b(F)m(or)18 b(kno)o(wn)75 655 y(n)o(umeric)13 b(v)n(alues,)h(eac)o(h)g(is)g(prin)o(ted)g (on)g(a)g(new)g(line)g(preceded)i(b)o(y)e(\\)p Fo(>>)f Ft(".)18 b(Other)e(t)o(yp)q(es)f(of)e(results)i(are)g(prin)o(ted)75 705 y(similarly)m(,)j(except)k(that)f(complicated)e(v)n(alues)h(are)h (sometimes)e(not)i(prin)o(ted)g(on)f(standard)h(output.)38 b(This)75 755 y(pro)q(duces)15 b(a)f(reference)i(to)e(the)h(transcript)g (\014le)e(that)h(lo)q(oks)g(lik)o(e)f(this:)583 846 y Fo(>>)21 b(picture)f(\(see)h(the)h(transcript)d(file\))75 938 y Ft(If)14 b(y)o(ou)h(w)o(an)o(t)f(to)h(the)g(full)e(results)j(of)e Fo(show)g Ft(statemen)o(ts)h(to)g(b)q(e)g(prin)o(ted)g(on)g(y)o(our)f(terminal,)f (assign)i(a)f(p)q(ositiv)o(e)75 988 y(v)n(alue)f(to)h(the)g(in)o(ternal)g(v)n (ariable)f Fo(tracingonline)p Ft(.)75 1129 y Fg(5.1)56 b(Data)19 b(T)n(yp)r(es)75 1230 y Ft(MetaP)o(ost)14 b(actually)f(has)g(nine)g(basic)h (data)f(t)o(yp)q(es:)19 b(n)o(umeric,)12 b(pair,)g(path,)h(transform,)f (color,)h(string,)g(b)q(o)q(olean,)75 1280 y(picture,)h(and)g(p)q(en.)19 b(Let)14 b(us)g(consider)h(these)g(one)g(at)e(a)h(time)e(b)q(eginning)i(with) f(the)i(n)o(umeric)e(t)o(yp)q(e.)137 1355 y(Numeric)g(quan)o(tities)g(in)g (MetaP)o(ost)h(are)g(represen)o(ted)j(in)c(\014xed)g(p)q(oin)o(t)g (arithmetic)g(as)g(in)o(teger)h(m)o(ultiples)e(of)113 1388 y Fn(1)p 80 1395 83 2 v 80 1419 a(65536)168 1405 y Ft(.)17 b(They)12 b(m)o(ust)f(normally)e(ha)o(v)o(e)i(absolute)h(v)n(alues)f(less)i (than)f(4096)e(but)i(in)o(termediate)f(results)i(can)f(b)q(e)g(eigh)o(t)75 1454 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