% cubicstructures.mp
% L. Nobre G. 
% 2011

input featpost3Dplus2D;

prologues := 1;

f := 2*(5,3,3.5);
Spread := 20;

beginfig(1);
    numeric csr, ind;
    color xv, yv, zv, Ve[];
    path p[];
    csr := sqrt(3)*0.5;
    xv := (csr,0,0);
    yv := (0,csr,0);
    zv := (0,0,csr);
    Ve1 := (-1,-1,-1);
    Ve2 := (-1,1,-1);
    Ve3 := (1,-1,-1);
    Ve4 := (1,1,-1);
    Ve5 := (-1,-1,1);
    Ve6 := (-1,1,1);
    Ve7 := (1,-1,1);
    Ve8 := (1,1,1);
    Ve9 := (0,0,0);
    for ind=1 upto 9:
	p[ind] := rigorousfearpath( Ve[ind], csr );
    endfor;
    unfill p1;
    draw p1;
    draw rp(Ve1+yv)--rp(Ve2-yv);
    draw rp(Ve1+xv)--rp(Ve3-xv);
    unfill p2;
    draw p2;
    draw rp(Ve1+zv)--rp(Ve5-zv);
    unfill p5;
    draw p5;
    draw rp(Ve5+yv)--rp(Ve6-yv);
    draw rp(Ve5+xv)--rp(Ve7-xv);
    unfill p9;
    draw p9;
    unfill p3;
    draw p3;
    draw rp(Ve4-yv)--rp(Ve3+yv);
    draw rp(Ve4-xv)--rp(Ve2+xv);
    unfill p4;
    draw p4;
    draw rp(Ve2+zv)--rp(Ve6-zv);
    draw rp(Ve3+zv)--rp(Ve7-zv);
    draw rp(Ve4+zv)--rp(Ve8-zv);
    unfill p6;
    draw p6;
    unfill p7;
    draw p7;
    draw rp(Ve8-yv)--rp(Ve7+yv);
    draw rp(Ve8-xv)--rp(Ve6+xv);
    unfill p8;
    draw p8;
endfig;

beginfig(2);
    numeric csr, ind;
    color xv, yv, zv, Ve[];
    path p[];
    csr := 1;
    xv := (csr,0,0);
    yv := (0,csr,0);
    zv := (0,0,csr);
    Ve1 := (-1,-1,-1);
    Ve2 := (-1,1,-1);
    Ve3 := (1,-1,-1);
    Ve4 := (1,1,-1);
    Ve5 := (-1,-1,1);
    Ve6 := (-1,1,1);
    Ve7 := (1,-1,1);
    Ve8 := (1,1,1);
    for ind=1 upto 8:
	p[ind] := rigorousfearpath( Ve[ind], csr );
    endfor;
    unfill p1;
    draw p1;
    draw rp(Ve1+yv)--rp(Ve2-yv);
    draw rp(Ve1+xv)--rp(Ve3-xv);
    unfill p2;
    draw p2;
    draw rp(Ve1+zv)--rp(Ve5-zv);
    unfill p5;
    draw p5;
    draw rp(Ve5+yv)--rp(Ve6-yv);
    draw rp(Ve5+xv)--rp(Ve7-xv);
    unfill p3;
    draw p3;
    draw rp(Ve4-yv)--rp(Ve3+yv);
    draw rp(Ve4-xv)--rp(Ve2+xv);
    unfill p4;
    draw p4;
    draw rp(Ve2+zv)--rp(Ve6-zv);
    draw rp(Ve3+zv)--rp(Ve7-zv);
    draw rp(Ve4+zv)--rp(Ve8-zv);
    unfill p6;
    draw p6;
    unfill p7;
    draw p7;
    draw rp(Ve8-yv)--rp(Ve7+yv);
    draw rp(Ve8-xv)--rp(Ve6+xv);
    unfill p8;
    draw p8;
endfig;

beginfig(3);
    numeric csr, ind;
    color xv, yv, zv, Ve[];
    path p[];
    csr := sqrt(2)*0.5;
    xv := (csr,0,0);
    yv := (0,csr,0);
    zv := (0,0,csr);
    Ve1 := (-1,-1,-1);
    Ve2 := (-1,1,-1);
    Ve3 := (1,-1,-1);
    Ve4 := (1,1,-1);
    Ve5 := (-1,-1,1);
    Ve6 := (-1,1,1);
    Ve7 := (1,-1,1);
    Ve8 := (1,1,1);
    Ve9 := (-1,0,0);
    Ve10 := (0,0,-1);
    Ve11 := (0,0,1);
    Ve12 := (0,1,0);
    Ve13 := (0,-1,0);
    Ve14 := (1,0,0);
    for ind=1 upto 14:
	p[ind] := rigorousfearpath( Ve[ind], csr );
    endfor;
    unfill p1;
    draw p1;
    draw rp(Ve1+yv)--rp(Ve2-yv);
    draw rp(Ve1+xv)--rp(Ve3-xv);
    unfill p2;
    draw p2;
    draw rp(Ve1+zv)--rp(Ve5-zv);
    unfill p9;
    draw p9;
    unfill p5;
    draw p5;
    draw rp(Ve2+zv)--rp(Ve6-zv);
    draw rp(Ve5+yv)--rp(Ve6-yv);
    unfill p6;
    draw p6;
    unfill p10;
    draw p10;
    draw rp(Ve5+xv)--rp(Ve7-xv);
    unfill p13;
    draw p13;
    unfill p3;
    draw p3;
    draw rp(Ve4-yv)--rp(Ve3+yv);
    draw rp(Ve4-xv)--rp(Ve2+xv);
    unfill p4;
    draw p4;
    unfill p11;
    draw p11;
    draw rp(Ve3+zv)--rp(Ve7-zv);
    unfill p12;
    draw p12;
    unfill p14;
    draw p14;
    unfill p7;
    draw p7;
    draw rp(Ve8-yv)--rp(Ve7+yv);
    draw rp(Ve8-xv)--rp(Ve6+xv);
    draw rp(Ve4+zv)--rp(Ve8-zv);
    unfill p8;
    draw p8;
endfig;

beginfig(4);
    numeric csr, ind;
    color xv, yv, zv, Ve[];
    path p[];
    csr := 0.21;
    xv := (csr,0,0);
    yv := (0,csr,0);
    zv := (0,0,csr);
    Ve1 := (-1,-1,-1);
    Ve2 := (-1,1,-1);
    Ve3 := (1,-1,-1);
    Ve4 := (1,1,-1);
    Ve5 := (-1,-1,1);
    Ve6 := (-1,1,1);
    Ve7 := (1,-1,1);
    Ve8 := (1,1,1);
    Ve21:= (0,0,0);
    Ve9 := (-1,-0.5,0); Ve15 := (-1,0.5,0); 
    Ve10 := (-0.5,0,-1);Ve16 := (0.5,0,-1);
    Ve11 := (-0.5,0,1); Ve17 := (0.5,0,1); 
    Ve12 := (0,1,-0.5); Ve18 := (0,1,0.5); 
    Ve13 := (0,-1,-0.5);Ve19 := (0,-1,0.5);
    Ve14 := (1,-0.5,0); Ve20 := (1,0.5,0); 
    for ind=1 upto 21:
	p[ind] := rigorousfearpath( Ve[ind], csr );
    endfor;
    unfill p1;
    draw p1;
    draw rp(Ve1+yv)--rp(Ve2-yv);
    draw rp(Ve1+xv)--rp(Ve3-xv);
    unfill p2;
    draw p2;
    draw rp(Ve1+zv)--rp(Ve5-zv);
    unfill p9;
    draw p9;
    draw rp(Ve9+yv)--rp(Ve15-yv);
    unfill p15;
    draw p15;
    unfill p5;
    draw p5;
    draw rp(Ve2+zv)--rp(Ve6-zv);
    draw rp(Ve5+yv)--rp(Ve6-yv);
    unfill p6;
    draw p6;
    unfill p10;
    draw p10;
    draw rp(Ve10+xv)--rp(Ve16-xv);
    unfill p16;
    draw p16;
    draw rp(Ve5+xv)--rp(Ve7-xv);
    unfill p13;
    draw p13;
    draw rp(Ve13+zv)--rp(Ve19-zv);
    unfill p19;
    draw p19;
    unfill p21;
    draw p21;
    unfill p3;
    draw p3;
    draw rp(Ve4-yv)--rp(Ve3+yv);
    draw rp(Ve4-xv)--rp(Ve2+xv);
    unfill p4;
    draw p4;
    unfill p11;
    draw p11;
    draw rp(Ve11+xv)--rp(Ve17-xv);
    unfill p17;
    draw p17;
    draw rp(Ve3+zv)--rp(Ve7-zv);
    unfill p12;
    draw p12;
    draw rp(Ve12+zv)--rp(Ve18-zv);
    unfill p18;
    draw p18;
    unfill p14;
    draw p14;
    draw rp(Ve14+yv)--rp(Ve20-yv);
    unfill p20;
    draw p20;
    unfill p7;
    draw p7;
    draw rp(Ve8-yv)--rp(Ve7+yv);
    draw rp(Ve8-xv)--rp(Ve6+xv);
    draw rp(Ve4+zv)--rp(Ve8-zv);
    unfill p8;
    draw p8;
endfig;

beginfig(5);
  color Ve[], violet, va, vb, vc, vu;
  numeric i, j, k, e[]p[];
  string comm, comn, como, a, b, col[];
  violet = red+blue;
  col1 = "violet";
  col2 = "red";
  col3 = "green";
  col4 = "blue";
  Ve1  = (2,1,-1);
  Ve2  = (0,1,-1);
  Ve3  = (-2,1,-1);
  Ve4  = (-2,-1,-1);
  Ve5  = (0,-1,-1);
  Ve6  = (2,-1,-1);
  Ve7  = (1,1,0);
  Ve8  = (-1,1,0);
  Ve9  = (-2,0,0);
  Ve10 = (-1,-1,0);
  Ve11 = (1,-1,0);
  Ve12 = (2,0,0);
  Ve13 = (2,1,1);
  Ve14 = (0,1,1);
  Ve15 = (-2,1,1);
  Ve16 = (-2,-1,1);
  Ve17 = (0,-1,1);
  Ve18 = (2,-1,1);
  Ve19 = (1,0,1);
  Ve20 = (0,0,0);
  Ve21 = (-1,0,1);
  Ve22 = (1,0,-1);
  Ve23 = (-1,0,-1);
  for i=1 upto 23:
    comm := "unfill rigorousfearpath(" & cstr(Ve[i]) & ",0.08);";
    comn := "draw rigorousfearpath(" & cstr(Ve[i]) & ",0.08);";
    getready( comm & comn, Ve[i] );
  endfor; 
  e1p1 = 1; e2p1 = 2; e3p1 = 3; e4p1 = 4; e5p1 = 5; e6p1 = 6;
  e1p2 = 2; e2p2 = 3; e3p2 = 4; e4p2 = 5; e5p2 = 6; e6p2 = 1;
  e7p1 = 13; e8p1 = 14; e9p1 = 15; e10p1 = 16; e11p1 = 17; e12p1 = 18;
  e7p2 = 14; e8p2 = 15; e9p2 = 16; e10p2 = 17; e11p2 = 18; e12p2 = 13;
  e13p1 = 1; e14p1 = 2; e15p1 = 3; e16p1 = 4; e17p1 = 5; e18p1 = 6;
  e13p2 = 13; e14p2 = 14; e15p2 = 15; e16p2 = 16; e17p2 = 17; e18p2 = 18;
  e19p1 = 2; e19p2 = 5; e20p1 = 14; e20p2 = 17;
  e101p1 = 22; e201p1 = 10; e301p1 = 5;  e401p1 = 5; 
  e101p2 = 2;  e201p2 = 17; e301p2 = 23; e401p2 = 22; 
  e102p1 = 2;  e202p1 = 17; e302p1 = 23; e402p1 = 22; 
  e102p2 = 8;  e202p2 = 19; e302p2 = 8;  e402p2 = 7; 
  e103p1 = 8;  e203p1 = 19; e303p1 = 8;  e403p1 = 7; 
  e103p2 = 21; e203p2 = 7;  e303p2 = 14; e403p2 = 14;
  e104p1 = 21; e204p1 = 7;  e304p1 = 14; e404p1 = 14;
  e104p2 = 17; e204p2 = 2;  e304p2 = 19; e404p2 = 21;
  e105p1 = 17; e205p1 = 2;  e305p1 = 19; e405p1 = 21;
  e105p2 = 11; e205p2 = 23; e305p2 = 11; e405p2 = 10;
  e106p1 = 11; e206p1 = 23; e306p1 = 11; e406p1 = 10;
  e106p2 = 22; e206p2 = 10; e306p2 = 5;  e406p2 = 5;  
  for i=1 upto 20:
    vc := Ve[e[i]p2]-Ve[e[i]p1];
    vu := N(vc);
    va := Ve[e[i]p1]+0.2*vu;
    vb := Ve[e[i]p2]-0.2*vu;
    a := cstr( va );
    b := cstr( vb-va );
    comm := "rigorousdisc( 0, true," & a & ",0.08," & b & ");";
    getready( comm, 0.5[va,vb] );
  endfor;
  for j=1 upto 4:
    for i=1 upto 6:
      k := 100*j+i;
      vc := Ve[e[k]p2]-Ve[e[k]p1];
      vu := N(vc);
      va := Ve[e[k]p1]+0.2*vu;
      vb := Ve[e[k]p2]-0.2*vu;
      a := cstr( va );
      b := cstr( vb-va );
      comm := "rigorousdisc( 0, true," & a & ",0.08," & b & ");";
      comn := "drawoptions( withcolor " & col[j] & " );";
      como := "drawoptions();";
      getready( comn & comm & como, 0.5[va,vb] );
    endfor;
  endfor;
  doitnow;
endfig;

Nobjects := 0; 

beginfig(6);
  numeric i, j, k, c, Mx, My, Mz, is;
  string comm, comn, this;
  boolean jisodd, kisodd;
  color there, ref, aux, Ve[];
  path pa, pb, pc, pd;
  Mx = 3;
  My = 3;
  Mz = 3;
  kisodd = false;
  c = 0.5*sqrt(2);
  ref = -0.5*c*(Mx,My,Mz);
  aux = ref-0.5*(1,1,1);
  Ve0 = aux;
  Ve1 = (-X(aux),Y(aux),Z(aux));
  Ve2 = (X(aux),-Y(aux),Z(aux));
  Ve3 = (X(aux),Y(aux),-Z(aux));
  Ve4 = (X(aux),-Y(aux),-Z(aux));
  Ve5 = (-X(aux),Y(aux),-Z(aux));
  Ve6 = (-X(aux),-Y(aux),Z(aux));
  Ve7 = (-X(aux),-Y(aux),-Z(aux));
  pa = rp(Ve0)--rp(Ve1)--rp(Ve6)--rp(Ve2)--cycle;
  pb = rp(Ve0)--rp(Ve2)--rp(Ve4)--rp(Ve3)--cycle;
  pc = rp(Ve0)--rp(Ve3)--rp(Ve5)--rp(Ve1)--cycle;
  pd = rp(Ve7)--rp(Ve4)--rp(Ve2)--rp(Ve6)--cycle;
  unfill pa; draw pa;
  unfill pb; draw pb;
  unfill pc; draw pc;
  for k=0 upto Mz:
    if kisodd:
      jisodd := true;
    else:
      jisodd := false;
    fi;
    for j=0 upto My:
      if jisodd:
	is := 1;
      else:
	is := 0;
      fi;
      for i=is step 2 until Mx:
	there := c*(i,j,k)+ref;
	this := "rigorousfearpath(" & cstr(there);
	comm := "unfill " & this & ",0.5);";
	comn := "draw " & this & ",0.5);";
	getready( comm & comn, there );
      endfor; 
      jisodd := not jisodd;
    endfor;
    kisodd := not kisodd;
  endfor; 
  doitnow;
  unfill pd; draw pd;
endfig;

end;