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Pavages…

Pavages triangulaires

pavagesequiexemples.mp
%%D'apres 'Pour la science' n272 Avril 2000 - p106
 
input geometriesyr12;
 
vardef pavagesequi(expr chemin,tour,coul,coull)=
  save $;
  picture $;
  pair A,B,C;
  A=u*(0,0);
  B=u*(1,0);
  C=rotation(B,A,60);
  path especes;
  especes = chemin
	    -- rotation(chemin,symetrie(iso(A,B,C),A,B),-120)
	    -- rotation(chemin,symetrie(iso(A,B,C),A,B),120)
	    -- cycle;
  if tour=0:
    $=image(
      trace chemin;
      );
  elseif tour=1:
    $=image(
      fill especes withcolor coul;
      fill (chemin--symetrie(chemin,iso(A,B))--cycle) withcolor coull;
      trace especes;
      trace symetrie(chemin,iso(A,B));
      A:=symetrie(C,A);
      B:=symetrie(C,B);
      );
  elseif tour>=2:
    $=pavagesequi(chemin,1,coul,coull);
    for k=2 upto tour:
      $:=image(
	trace $;
	trace rotation($,symetrie(iso(A,B,C),A,B),-120);
	trace rotation($,symetrie(iso(A,B,C),A,B),120);
	trace symetrie($,iso(A,B));
	A:=symetrie(C,A);
	B:=symetrie(C,B)
	);
    endfor;
  fi;
  $
enddef;
 
vardef pavagesequiqui(expr chemin,tour,coul,coull)=
  save $;
  picture $;
  pair A,B,C;
  A=u*(0,0);
  B=u*(1,0);
  C=rotation(B,A,60);
  path especes;
    especes = chemin 
	      -- rotation(chemin,symetrie(iso(A,B,C),A,B),-120)
	      -- rotation(chemin,symetrie(iso(A,B,C),A,B),120)
	      -- cycle;
  if tour=0:
    $=image(
      trace chemin;
      );
  elseif tour=1:
    $=image(
      trace chemin;
      drawoptions(dashed evenly);
      trace rotation(chemin,symetrie(iso(A,B,C),A,B),-120);
      trace rotation(chemin,symetrie(iso(A,B,C),A,B),120);
      trace symetrie(chemin,iso(A,B));
      drawoptions();
      A:=symetrie(C,A);
      B:=symetrie(C,B);
      );
  elseif tour=2:
    $=image(
      fill especes withcolor coul;
      fill (chemin--symetrie(chemin,iso(A,B))--cycle) withcolor coull;
      trace especes;
      trace symetrie(chemin,iso(A,B));
      A:=symetrie(C,A);
      B:=symetrie(C,B);
      );
    $:=image(
      trace $;
      drawoptions(dashed evenly);
      trace rotation(pavagesequi(chemin,1,coul+0.5blanc,coull+0.5blanc),
        symetrie(iso(A,B,C),A,B),-120);
      trace rotation(pavagesequi(chemin,1,coul+0.5blanc,coull+0.5blanc),
        symetrie(iso(A,B,C),A,B),120);
      trace symetrie(pavagesequi(chemin,1,coul+0.5blanc,coull+0.5blanc),
        iso(A,B));
      drawoptions();
      A:=symetrie(C,A);
      B:=symetrie(C,B);
      );
  elseif tour>=3:
    $=pavagesequi(chemin,1,coul,coull);
    for k=2 upto tour-1:
      $:=image(
	trace $;
	trace rotation($,symetrie(iso(A,B,C),A,B),-120);
	trace rotation($,symetrie(iso(A,B,C),A,B),120);
	trace symetrie($,iso(A,B));
	A:=symetrie(C,A);
	B:=symetrie(C,B);
	);
    endfor;
    $:=image(
      trace $;
      drawoptions(dashed evenly);
      trace rotation(pavagesequi(chemin,tour-1,coul+0.5blanc,coull+0.5blanc),
        symetrie(iso(A,B,C),A,B),-120);
      trace rotation(pavagesequi(chemin,tour-1,coul+0.5blanc,coull+0.5blanc),
        symetrie(iso(A,B,C),A,B),120);
      trace symetrie(pavagesequi(chemin,tour-1,coul+0.5blanc,coull+0.5blanc),
        iso(A,B));
      drawoptions();
      A:=symetrie(C,A);
      B:=symetrie(C,B);
      );
  fi;
  $:=image(
    trace $;
    trace A--B--C--cycle 
	dashed dashpattern(on12bp off6bp on3bp off6bp) withcolor gris;
    trace iso(A,B)--iso(B,C)--iso(C,A)--cycle 
	dashed dashpattern(on12bp off6bp on3bp off6bp) withcolor gris;
    );
  $
enddef;
 
pavagesequiexemples (figure 1)
beginfig(1);
  path MM;
  MM=(0,0)--u*(0.25,0)--u*(0.25,0.4)--u*(0.75,0.2)--u*(1,0);
  trace pavagesequiqui(MM,0,orange,vert);
endfig;
pavagesequiexemples (figure 2)
beginfig(2);
  trace pavagesequiqui(MM,1,orange,vert);
endfig;
pavagesequiexemples (figure 3)
beginfig(3);
  trace pavagesequiqui(MM,2,orange,vert);
endfig;
pavagesequiexemples (figure 4)
beginfig(4);
  trace pavagesequiqui(MM,3,orange,vert);
endfig;
pavagesequiexemples (figure 5)
beginfig(5);
  trace pavagesequiqui(MM,4,orange,vert);
endfig;
 
end