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Diffstat (limited to 'Master/texmf-dist/doc/asymptote/examples/Klein.asy')
-rw-r--r-- | Master/texmf-dist/doc/asymptote/examples/Klein.asy | 51 |
1 files changed, 51 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/asymptote/examples/Klein.asy b/Master/texmf-dist/doc/asymptote/examples/Klein.asy new file mode 100644 index 00000000000..99914d90432 --- /dev/null +++ b/Master/texmf-dist/doc/asymptote/examples/Klein.asy @@ -0,0 +1,51 @@ +import graph3; + +size(469pt); + +viewportmargin=0; + +currentprojection=perspective( +camera=(25.0851928432063,-30.3337528952473,19.3728775115443), +up=Z, +target=(-0.590622314050054,0.692357205025578,-0.627122488455679), +zoom=1, +autoadjust=false); + +triple f(pair t) { + real u=t.x; + real v=t.y; + real r=2-cos(u); + real x=3*cos(u)*(1+sin(u))+r*cos(v)*(u < pi ? cos(u) : -1); + real y=8*sin(u)+(u < pi ? r*sin(u)*cos(v) : 0); + real z=r*sin(v); + return (x,y,z); +} + +surface s=surface(f,(0,0),(2pi,2pi),8,8,Spline); +draw(s,lightolive+white,"bottle",render(merge=true)); + +string lo="$\displaystyle u\in[0,\pi]: \cases{x=3\cos u(1+\sin u)+(2-\cos u)\cos u\cos v,\cr +y=8\sin u+(2-\cos u)\sin u\cos v,\cr +z=(2-\cos u)\sin v.\cr}$"; + +string hi="$\displaystyle u\in[\pi,2\pi]:\\\cases{x=3\cos u(1+\sin u)-(2-\cos u)\cos v,\cr +y=8\sin u,\cr +z=(2-\cos u)\sin v.\cr}$"; + +real h=0.0125; + +begingroup3("parametrization"); +draw(surface(xscale(-0.38)*yscale(-0.18)*lo,s,0,1.7,h,bottom=false), + "[0,pi]"); +draw(surface(xscale(0.26)*yscale(0.1)*rotate(90)*hi,s,4.9,1.4,h,bottom=false), + "[pi,2pi]"); +endgroup3(); + +begingroup3("boundary"); +draw(s.uequals(0),blue+dashed); +draw(s.uequals(pi),blue+dashed); +endgroup3(); + +add(new void(frame f, transform3 t, picture pic, projection P) { + draw(f,invert(box(min(f,P),max(f,P)),P),"frame"); + }); |