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% conoscopy.mp
% L. Nobre G.
% 2013
input featpost3Dplus2D;
verbatimtex \documentclass{article}\begin{document} etex
beginfig(1);
f := (6,5,5);
Spread := 125;
numeric maja, raya, angphi, angthe, decl, valy, valz, rectsiz;
color majav, aphiv, aphip, majbv, perpv, perpvl;
maja = 0.72;
raya = 0.5;
angphi = 15;
angthe = 30;
rectsiz = 0.06;
majav = (0,0,maja);
aphiv = raya*(cosd(angphi),sind(angphi),0);
aphip = raya*(sind(angphi),-cosd(angphi),0);
majbv = planarrotation( majav, aphip, angthe );
perpv = ncrossprod(majbv,aphiv);
decl = Z(perpv)/(Y(perpv)++X(perpv));
valy = maja*raya/((decl*raya)++maja);
valz = valy*decl;
if angthe>90: valy:=-valy; fi;
perpv := blue*valz-N(aphip)*valy;
perpvl = maja*N(perpv);
spheroid( black, majav, raya );
drawoptions( dashed (withdots scaled 0.25) );
cartaxes( 1, 1, 1 );
draw rigorouscircle( black, blue, raya );
draw rp(black)--rp(-aphiv);
draw rp(black)--rp(-majbv);
%draw rp(black)--rp(-majav);
%draw rp(black)--rp(-aphip);
%draw rp(black)--rp(-perpv);
draw ellipticpath( black, majbv, aphiv );
drawoptions();
drawarrow rp((raya,0,0))--rp((1,0,0));
drawarrow rp((0,raya,0))--rp((0,1,0));
drawarrow rp(majav)--rp((0,0,1));
drawoptions( withpen pencircle scaled 1.7pt withcolor 0.65blue );
drawarrow rp(black)--rp(aphiv);
drawarrow rp(black)--rp(majbv);
%draw rp(black)--rp(majav);
%drawarrow rp(black)--rp(aphip);
drawarrow rp(black)--rp(perpvl);
drawoptions( withpen pencircle scaled 1.3pt );
draw subpath (-1,15) of ellipticpath( black, majbv, aphiv ) dashed evenly;
%draw ellipticpath( black, aphip, majav ) dashed evenly;
% draw ellipticpath( black, green, 2*blue ) dashed evenly;
drawoptions();
squareangline( perpv, aphiv, black, rectsiz);
squareangline( perpv, majbv, black, rectsiz);
squareangline( majbv, aphiv, black, rectsiz);
angline(majav, perpv, black, maja-raya, btex $\theta$ etex)(rt);
pickup pencircle scaled 3.6pt;
draw rp(-aphiv); %label.bot("aphiv",rp(aphiv));
draw rp(-majbv); %label.lft("majbv",rp(majbv));
%draw rp(majav); label.rt("majav",rp(majav));
%draw rp(-aphip); label.rt("aphip",rp(aphip));
draw rp(perpv); %label.rt("perpv",rp(perpvl));
label.llft(btex $\vec{n}^{\prime\prime}$ etex,rp(aphiv));
label.ulft(btex $\vec{n}^{\prime}$ etex,rp(majbv));
label.top(btex $\vec{p}$ etex,rp(perpvl));
endfig;
beginfig(2);
f := (6,4,3);
Spread := 125;
numeric maja, raya, angphi, angthe, pes;
color majav, aphiv, aphip, majbv;
path ell;
maja = 0.82;
raya = 0.5;
angphi = -15;
angthe = 55;
pes = 1.3pt;
drawoptions( withpen pencircle scaled pes );
majav = (0,0,maja);
aphiv = raya*(cosd(angphi),sind(angphi),0);
aphip = raya*(sind(angphi),-cosd(angphi),0);
majbv = planarrotation( majav, aphip, angthe );
spheroid( black, majav, raya );
ell = ellipticpath( black, majbv, aphiv );
draw subpath (3,20) of ell;
drawoptions( withpen pencircle scaled pes dashed (withdots scaled 0.42) );
draw rigorouscircle( black, blue, raya );
draw rp(aphip)--rp(-aphip);
draw rp(aphiv)--rp(-aphiv);
draw rp(majbv)--rp(-majbv);
draw ell;
endfig;
beginfig(3); %%%%%%%%%%%%%%%% don't change the parameters... %%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%% and forget this (it is wrong). %%%%%%%%%%%%
f := (6,4,7);
Spread := 125;
numeric maja, raya, angphi, angthe, pes, decl;
numeric valy, valz, begp, endp, rectsiz;
color majav, aphiv, aphip, majbv, majcv, perpv, perqv;
path ell, fll, cir;
maja = 0.82;
raya = 0.5;
angphi = 17;
angthe = 82;
pes = 1.3pt;
begp = 14;
endp = 18;
rectsiz = 0.08;
drawoptions( withpen pencircle scaled pes );
majav = (0,0,maja);
aphiv = raya*(cosd(angphi),sind(angphi),0);
aphip = raya*(sind(angphi),-cosd(angphi),0);
majbv = planarrotation( majav, aphip, angthe );
majcv = planarrotation( majav, -aphip, angthe );
perpv = ncrossprod(majbv,aphiv);
decl = Z(perpv)/(Y(perpv)++X(perpv));
valy = maja*raya/((decl*raya)++maja);
valz = valy*decl;
if angthe>90: valy:=-valy; fi;
perpv := blue*valz-N(aphip)*valy;
perqv = (-X(perpv),-Y(perpv),Z(perpv));
spheroid( black, majav, raya );
squareangline( -majbv, perpv, black, rectsiz);
squareangline( -majcv, perqv, black, rectsiz);
drawoptions( withpen pencircle scaled 1.095pes );
cir = spatialhalfcircle(black, majav, raya, true );
undraw subpath (0,0.9*(length cir)) of cir;
ell = ellipticpath( black, majbv, aphiv );
fll = ellipticpath( black, majcv, aphiv );
drawoptions( withpen pencircle scaled pes dashed (withdots scaled 0.42) );
draw ellipticpath( black, majav, aphip );
draw rp(aphiv)--rp(-aphiv);
draw rp(majbv)--rp(-majbv);
draw rp(majcv)--rp(-majcv);
drawoptions( withpen pencircle scaled 2pes );
draw subpath (begp,endp) of fll withcolor blue;
draw ell withcolor red;
draw subpath (endp-36, begp) of fll withcolor blue;
drawarrow rp(black)--rp(perpv) withcolor red;
drawarrow rp(black)--rp(perqv) withcolor blue;
endfig;
beginfig(4);
f := (6,4,7);
Spread := 40;
numeric axa, axb, axc;
color d[];
axa = 2.618;
axb = 1.618;
axc = 1.0;
d1 = (axa,0,0);
d2 = (0,axb,0);
d3 = (0,0,axc);
draw ellipticpath(black,d1,d2);
draw ellipticpath(black,d1,d3);
draw ellipticpath(black,d2,d3);
drawarrow rp(black)--rp(d1);
drawarrow rp(black)--rp(d2);
drawarrow rp(black)--rp(d3);
draw ellipsoid(black,d1,d2,d3) withpen pencircle scaled 2.5pt withcolor blue;
endfig;
beginfig(5);
f := (4,3,6.5);
Spread := 100;
numeric axa, axb, axc, vz, vy;
color va, vb, d[];
axa = 0.505;
axb = 0.495;
axc = 0.82;
d1 = (axa,0,0);
d2 = (0,axb,0);
d3 = (0,0,axc);
vy = axb*(axc+-+axa)/(axc+-+axb);
vz = axa+-+vy;
va = (0,vy,vz);
vb = (0,-vy,vz);
drawarrow rp(black)--rp(d2);
draw ellipticpath(black,d1,va) withcolor red;
draw ellipticpath(black,d1,vb) withcolor green;
draw ellipticpath(black,d2,d3) dashed withdots scaled 0.333;
draw rp(black)--rp(-d1) dashed withdots scaled 0.333;
drawarrow rp(black)--rp(va) withcolor red;
drawarrow rp(black)--rp(vb) withcolor green;
draw rp(black)--rp(-va) dashed withdots scaled 0.333 withcolor red;
draw rp(black)--rp(-vb) dashed withdots scaled 0.333 withcolor green;
draw ellipsoid(black,d1,d2,d3) withpen pencircle scaled 2pt withcolor blue;
drawarrow rp(black)--rp(d3);
drawarrow rp(black)--rp(d1);
draw subpath (0,9) of ellipticpath(black,d1,d2);
draw subpath (0,9) of ellipticpath(black,d1,d3);
draw subpath (0,9) of ellipticpath(black,d2,d3);
labeloffset := 1pt;
label.lrt(btex $n_\alpha$ etex,rp(d2));
label.bot(btex $n_\beta$ etex,rp(d1));
label.top(btex $n_\gamma$ etex,rp(d3));
label.rt(btex $n_\beta$ etex,rp(va));
label.bot(btex $n_\beta$ etex,rp(vb));
color perpv, perqv;
numeric decl, valy, valz, fact;
fact = 1.55;
perpv = ncrossprod(d1,va);
decl = Z(perpv)/Y(perpv);
valy = axc*axb/((decl*axb)++axc);
valz = -valy*decl;
perpv := blue*valz-green*valy;
perqv := blue*valz+green*valy;
drawarrow rp(black)--rp(fact*perpv) withcolor red;
drawarrow rp(black)--rp(fact*perqv) withcolor green;
draw rp(perpv) withpen pencircle scaled 2pt withcolor red;
draw rp(perqv) withpen pencircle scaled 2pt withcolor green;
label.lft(btex OA etex,rp(fact*perpv));
label.rt(btex OA etex,rp(fact*perqv));
endfig;
verbatimtex \end{document} etex
end;
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