MetaPost

 transform pagecoords;
 pagecoords:=identity scaled 10mm shifted (100mm,150mm);
 beginfig (1)
     fill ((0,0)--(2,0)--(2,1)--(1,1)--(1,2)--(0,2)--cycle)
         transformed pagecoords withcolor green;
     draw ((2,0)..(2,1)..(1,1)..(1,2)..(0,2))
         transformed pagecoords;
     drawarrow ((0,0)--(2,2)) transformed pagecoords;
 endfig;
 beginfig (2)
     draw (for i=0 up to 7: dir (135i)-- endfor cycle)
         transformed pagecoords;
 endfig;
 pagecoords:=identity scaled 15mm shifted (100mm,150mm);
 beginfig (3);
     % declare paths to be used
     path p[],p[]t;
     % set up points by defining relationships
     z1=(0,0);   z2=z1+2up;
     z3=z1+whatever*dir (60)=z2+whatever*dir (-50);
     z4=z3+(-1.5,-.5);
     z5=z1+dir (135);
     z0=whatever[z1,z2]=whatever[z3,z4];
     % set up paths
     p0=fullcircle yscaled .5 rotated 45 shifted z0 ;
     p1=z2—z4..z0..z3---z1;
     p2=p1 cutbefore p0 cutafter p0;
     p3=p0 cutbefore p1 cutafter p1;
     p4=p2—p3—cycle;
     % define transformed versions of paths and points
     for i=0 up to 4: p[i]t=p[i] transformed pagecoords; endfor
     for i=0 up to 5: z[i]t=z[i] transformed pagecoords; endfor
     % do some drawing
     fill p4t withcolor (1,1,0.2);
     draw z1t—z2t withcolor .5white;
     draw z3t—z4t withcolor .5white;
     pickup pencircle;
     draw p0t dashed withdots scaled .3;
     draw p1t dashed evenly;
     draw p2t withcolor blue;
     draw p3t withcolor red;
     label.lrt (btex $z_0$ etex, z0t);
     label.llft (btex $z_1$ etex, z1t);
     label.top (btex $z_2$ etex, z2t);
     label.rt (btex $z_3$ etex, z3t);
     label.llft (btex $z_4$ etex, z4t);
     for i=0 up to 4:
         drawdot z[i]t withpen pencircle scaled 2;
     endfor
 endfig;
 bye