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% nulldefectanglexample.mp
% L. Nobre G.
% 2012
input featpost3Dplus2D;
prologues := 1;
beginfig(1);
color po[];
numeric ta, tb;
pen stroke;
stroke = pencircle scaled 3pt;
ta = sind(36)/cosd(36);
tb = sind(18)/cosd(18);
po1 = (1,ta,0);
po2 = (-1,ta,0);
po3 = (-1,tb,0);
po4 = (-1,-ta,0);
po5 = (0,-ta,0);
po6 = (1,-ta,0);
po7 = (1,0,0);
path frame;
frame = rp(po1)--rp(po2)--rp(po4)--rp(po6)--cycle;
unfill frame;
drawoptions( withpen stroke );
draw frame;
drawoptions( dashed evenly );
draw rp(black)--rp(po1);
draw rp(black)--rp(po3);
draw rp(black)--rp(po5);
draw rp(black)--rp(po7);
endfig;
beginfig(2);
numeric parang, refdista, refdistb, auxa, auxb;
parang = 55;
refdista = conorm(po1-po3);
refdistb = 1 ++ ta;
auxa = (ta-tb)*sind(18);
auxb = (ta-tb)*cosd(18);
po7 := (cosd(parang),0,-sind(parang));
po6 := po7+po5;
po1 := improvertex( black, refdistb, po7, ta, po3, refdista, po1 );
po8 = po3+N(po3)*auxa;
po2 := po8+auxb*ncrossprod(po3,ccrossprod(po1,po3));
drawoptions( withpen stroke );
path a, b, c, d;
a = rp(black)--rp(po3)--rp(po4)--rp(po5)--cycle;
b = rp(black)--rp(po5)--rp(po6)--rp(po7)--cycle;
c = rp(black)--rp(po7)--rp(po1)--cycle;
d = rp(black)--rp(po1)--rp(po2)--rp(po3)--cycle;
unfill a; draw a;
unfill b; draw b;
unfill c; draw c;
unfill d; draw d;
endfig;
beginfig(3);
numeric a, b, c, i, j;
a = 0.5;
b = 0.5*sqrt(3);
V1 := (b,-a,a);
V2 := (2*b,-a,0);
V3 := (b,a,a);
V4 := (2*b,a,0);
V5 := (b,a,0);
V6 := (0,1,0);
c = 6;
for j=1 upto 2:
for i=1 upto 6:
c := incr(c);
V[c] := rotvecaroundanother( j*120, V[i], blue );
endfor;
endfor;
makeface1(1,3,7,9,13,15);
makeface2(1,2,4,3);
makeface3(3,4,5);
makeface4(3,5,6,7);
makeface5(7,6,8);
makeface6(7,8,10,9);
makeface7(9,10,11);
makeface8(9,11,12,13);
makeface9(13,12,14);
makeface10(13,14,16,15);
makeface11(15,16,17);
makeface12(15,17,18,1);
makeface13(1,18,2);
f := (5,0.9,9);
draw_invisible( false, false, white, black );
endfig;
beginfig(4);
numeric bsang, dista, distb, distc, distd, verdi, hordi, si, co;
color cauxa, cauxb, cauxd;
bsang = 15;
cauxa = (-1-sind(22),-1-cosd(22),1);
cauxb = (-1-cosd(22),-1-sind(22),1);
cauxd = (1+cosd(15),sind(15)-1,1);
V1 := (-1,1,1);
V2 := (-1,-1,1);
distc = conorm(V2-cauxb);
V3 := (1,-1,1);
dista = conorm(cauxa-V3);
V4 := (1,1,1);
distd = conorm(V4-cauxd);
V6 := (-1-cosd(bsang)*cosd(22),1+sind(22),1-sind(bsang)*cosd(22));
V7 := (-1-cosd(bsang)*cosd(22),-1-sind(22),1-sind(bsang)*cosd(22));
distb = conorm(cauxa-cauxb);
V8 := improvertex( V3, dista, V7, distb, V2, distc, cauxb-(0,0,0.5) );
V5 := (X(V8),-Y(V8),Z(V8));
verdi = 1-Z(V8);
hordi = Y(V8)+1;
si = verdi/(verdi++hordi);
co = hordi/(verdi++hordi);
V9 := (1+0.5*sqrt(2),-1+0.5*sqrt(2)*co,1-0.5*sqrt(2)*si);
V10 := improvertex( V9, 1, V3, 1, V4, distd, (1,-1,0) );
V11 := (X(V10),-Y(V10),Z(V10));
V12 := (X(V9),-Y(V9),Z(V9));
NF := 0;
makeface1(1,2,3,4);
makeface2(1,5,6);
makeface3(1,2,7,6);
makeface4(2,7,8);
makeface5(2,3,9,8);
makeface6(3,9,10);
makeface7(3,4,11,10);
makeface8(4,11,12);
makeface9(1,5,12,4);
f := (9,2,5);
draw_invisible( false, false, white, black );
endfig;
end.
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