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-% Maxime Chupin, Alexander Grahn
-% 2013/10/15
-
-filenametemplate "%j_%c.mps";
-
-verbatimtex
-\documentclass{article}
-\usepackage[latin1]{inputenc}
-\usepackage[T1]{fontenc}
-\usepackage{lmodern}
-\usepackage{amsmath}
-\begin{document}
-etex
-
-u:=4cm;
-
-vardef proj(expr P,M,N)=
- save H;
- pair H;
- H=whatever [M,N];
- H-P=whatever * (M - N) rotated 90;
- H
-enddef;
-
-path dr,cercle,drb,scara;
-pair A,B,C,D,Q,T,O',P,O,M;
-O:=(0,0);
-O':=(-u/3,0);
-A:=(u/sqrt(2),u/sqrt(2)) shifted O';
-B:=(u/sqrt(2),-u/sqrt(2)) shifted O';
-C:=(-u/sqrt(2),-u/sqrt(2))shifted O';
-D:=(-u/sqrt(2),u/sqrt(2)) shifted O';
-dr:=A--C;
-drb:=B--D;
-
-%scarabaeus construction
-for i:=0 upto 100:
- if i=0:
- P:=A;
- Q:=O';
- M:=proj(O,P,Q);
- scara:=M;
- else:
- scara:=M;
- for j:=1 upto 4:
- k:=4*(i-1)+j;
- if (k<200) or (k=200):
- P:=point (k*0.005) of dr;
- cercle:=halfcircle
- scaled 2u rotated 45 shifted P;
- if k=0:
- Q:=O';
- fi;
- if (k<>0) and (k<>200):
- Q:=cercle intersectionpoint drb;
- fi;
- if k=200:
- Q:=O';
- fi;
- else:
- P:= point (2-k*0.005) of dr;
- cercle:=halfcircle
- scaled 2u rotated (-135) shifted P;
- if k<400:
- Q:=cercle intersectionpoint drb;
- fi;
- if k=400:
- Q:=O';
- fi;
- fi;
- M:=proj(O,P,Q);
- scara:=scara--M;
- endfor;
- fi;
- beginfig(i) %red scarabaeus segments
- setbounds currentpicture to
- (u,1.2u)--(u,-1.2u)--(-1.5u,-1.2u)--(-1.5u,1.2u)--cycle;
- pickup pencircle scaled 1pt;
- draw scara withcolor red;
- clip currentpicture to
- (u,1.2u)--(u,-1.2u)--(-1.5u,-1.2u)--(-1.5u,1.2u)--cycle;
- endfig;
- beginfig(i+101) %moving construction lines and labels
- setbounds currentpicture to
- (u,1.2u)--(u,-1.2u)--(-1.5u,-1.2u)--(-1.5u,1.2u)--cycle;
- draw 12[P,Q]--12[Q,P] dashed evenly;
- draw O--M dashed evenly;
- pickup pencircle scaled 1.4pt;
- draw P--Q withcolor blue;
- label.rt(btex $2l$ etex, 0.5[P,Q]);
- dotlabel.urt(btex $P$ etex, P);
- dotlabel.llft(btex $Q$ etex,Q);
- dotlabel.top(btex $M$ etex,M);
- clip currentpicture to
- (u,1.2u)--(u,-1.2u)--(-1.5u,-1.2u)--(-1.5u,1.2u)--cycle;
- endfig;
- if (i/2.-floor(i/2.))=0: %gray lines every second image
- beginfig(i/2+202)
- setbounds currentpicture to
- (u,1.2u)--(u,-1.2u)--(-1.5u,-1.2u)--(-1.5u,1.2u)--cycle;
- draw P--Q withcolor 0.8 white;
- clip currentpicture to
- (u,1.2u)--(u,-1.2u)--(-1.5u,-1.2u)--(-1.5u,1.2u)--cycle;
- endfig;
- fi;
-endfor;
-
-%coordinate axes and stationary stuff
-beginfig(253);
- setbounds currentpicture to
- (u,1.2u)--(u,-1.2u)--(-1.5u,-1.2u)--(-1.5u,1.2u)--cycle;
- path ida,mida;
- drawarrow(-1.5u,0)--(1u,0);
- drawarrow(0,-1.2u)--(0,1.2u);
- ida:=12[A,C]--12[C,A];
- mida:=(12[D,B]--12[B,D]);
- draw ida dashed evenly;
- draw mida dashed evenly;
- label.top(btex $a$ etex, 0.5[O,O']);
- label.top(btex $x$ etex, (0.8u,0));
- label.rt(btex $y$ etex, (0,u));
- label.bot(btex\itshape{\underline{scarabaeus}} etex,(-1.1u,1.1u));
- label.bot(btex $r=l\cos 2t-a\cos t$ etex, (-u/2,1.1u));
- dotlabel.urt(btex $O'$ etex, O');
- dotlabel.urt(btex $O$ etex, O);
- dotlabel.rt(btex $A$ etex,A);
- dotlabel.rt(btex $B$ etex,B);
- dotlabel.lft(btex $C$ etex,C);
- dotlabel.lft(btex $D$ etex,D);
- clip currentpicture to
- (u,1.2u)--(u,-1.2u)--(-1.5u,-1.2u)--(-1.5u,1.2u)--cycle;
-endfig;
-
-end.