draw elliptic curves using the EXPRESSION tool

Hey guys,

any useful video tutorials on how to use Expression and other commands where one can write a formula, and enter multiple variables ( not just x and y ) and plot the curves out of these expressions, I am trying to do some experimentation with elliptic curves were y² = x³ + ax + b

thnx in advance :)

Cheers,

Replies to This Discussion

Permalink Reply by David Rutten on March 18, 2016 at 5:15am

You can't draw a curve associated with an implicit equation, because the potential topologies of implicit curves are far more complex than those of Rhino curves. Rhino curves must consist of a single stretch, no gaps, no internal loop, no disjoint pieces.

So unless you can rewrite your implicit equation in parametric form (ie. x = f(t), y = g(t) [, z = h(t)]) you must take another approach.

It is possible to generate an approximation of a 2D implicit function by modifying the equation to have both x and y on the same side and using that to generate an elevation (in your case z = x³ + ax + b - y²). You then intersect this elevated landscape at z=0 and the intersection between the plane and the landscape gives you the curves you're after (or rather, an approximation of the curves you're after).

See my responses in this thread for examples on how to draw implicit, explicit and parametric curves.

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