2013-12-15 20:05:46 +01:00
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\documentclass[margin=1cm]{standalone}
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\usepackage{asymptote}
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\begin{document}
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\begin{asy}
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2013-12-17 16:33:14 +01:00
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settings.render = 0;
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2013-12-15 20:05:46 +01:00
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settings.prc = false;
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import graph3;
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import contour;
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size3(8cm);
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currentprojection = orthographic(10,1,4);
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defaultrender = render(merge = true);
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// create torus as surface of rotation
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int umax = 40;
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int vmax = 40;
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surface torus = surface(Circle(c=2Y, r=0.6, normal=X, n=vmax), c=O, axis=Z, n=umax);
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torus.ucyclic(true);
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torus.vcyclic(true);
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pen meshpen = 0.3pt + gray;
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draw(torus, surfacepen=material(diffusepen=white+opacity(0.6), emissivepen=white));
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for (int u = 0; u < umax; ++u)
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draw(torus.uequals(u), p=meshpen);
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for (int v = 0; v < vmax; ++v)
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draw(graph(new triple(real u) {return torus.point(u,v); }, 0, umax, operator ..),
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p=meshpen);
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pair a = (floor(umax/2) + 2, 3);
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dot(torus.point(a.x, a.y), L="$a$", align=W);
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pair b = (5, floor(vmax/2));
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dot(torus.point(b.x, b.y), L="$b$", align=2Z + X);
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path3 abpath(int ucycles, int vcycles) {
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pair bshift = (ucycles*umax, vcycles*vmax);
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triple f(real t) {
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pair uv = (1-t)*a + t*(b+bshift);
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return torus.point(uv.x, uv.y);
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}
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return graph(f, 0, 1, operator ..);
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}
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real linewidth = 0.8pt;
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draw(abpath(0,0), p=linewidth + orange);
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draw(abpath(1,0), p=linewidth + red);
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draw(abpath(1,-1), p=linewidth + darkgreen);
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\end{asy}
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\end{document}
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