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Daniel

Joined: 07 Jun 2010
Posts: 1

 Posted: Mon Jun 07, 2010 8:49 pm    Post subject: Multi-valued functions First of all, Hi everyone, and thanks to Abderrahman for sharing this nice software. I'm wondering about plotting helicoids implicitly in K3dSurf. I've had a long fascination with helicoids and the way the can be combined, as I explored here: http://spacesymmetrystructure.wordpress.com/rheotomic-surfaces/ The helicoid can be described by a height function (Monge form) such as arg(z) where z is a complex number, or : z=tan^-1(x/y) if you want to work only with real numbers. The multivalued nature of the inverse tangent function poses some challenge when plotting this. I did find a way round it, but it was more of a programming than a mathematical solution, and I was thinking about a more general way of doing it that would allow the axes of the helicoids to be non-parallel. I was thinking of an implicit form, such as atan(x/y)+z but want to get multiple turns of the helicoid so need more than just the principal values. (I do know of explicit functions for the helicoid, but I am interested particularly in the implicit form, because of the possibility for combining them) Does anyone have suggestions for how to approach this ?
abdelhamid belaid

Joined: 13 Aug 2009
Posts: 170

 Posted: Tue Jun 08, 2010 10:32 am    Post subject: Hello all, hello Daniel Allow me my friends: Daniel maybe this might help: x*cos(2*z)+y*sin(2*z) =0 Or atan2((y*cos(2*z)-x*sin(2*z)),(x*cos(2*z)+y*sin(2*z)) )=0 You can generally write: f (sqrt (x ^ 2 + y ^ 2)-a, h) = 0 so that h = atan2 (v, u) / n and u = x * cos (n * z) + y * sin (n * z) , v = y * cos (n * z)-x * sin (n * z) Maybe you are looking for this, I hope I'm successful helping you. _________________My YouTube channel
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