Hi everybody !
Hereby, three ways to define-and-draw the O centered torus in plan x-y (R=3?; r=1/2) and three concerns. Cheers !
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1? with implicit cartesian equation?:
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load(draw)$
draw3d(implicit(x^2+y^2+z^2+8.75=6*sqrt(x^2+y^2),x,-3,3,y,-3,3,z,-.5,.5));
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inconvenience?: no smooth appearence. Which options can improve that??
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2? with cartesian parametric coordinates?:
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draw3d(parametric_surface((3+.5*cos(a))*cos(t), (3+.5*cos(a))*sin(t), .5*sin(a), a, 0, 2*%pi, t, 0, 2*%pi) );
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inconvenience?: smooth surface but z-axis strechted and finally distorted appearance. Same question??
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3? with cylindrical coordinates?:
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draw3d(cylindrical(3+sqrt(0.25-z^2),z,-.5,.5,az,0,2*%pi),cylindrical(3-sqrt(0.25-z^2),z,-.5,.5,az,0,2*%pi));
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inconvenience : the same as 2?