Sometimes we draw ambiguous curves and wish we knew the circle and its center that creates the curve.

Grasshopper’s OSC_CIRCLES button mathematically calculates the circle to a curve, given a surface and a point in Rhino.

The proper definition of an osculating circle of a curve at a given point P is the tangent circle
at point P that approaches the curve most tightly.  The center of the
osculating circle then lies on the inner normal line and its curvature is the same
as that of the given curve at the same point.

These geometries can then be lofted together to create a form; however, sometimes,
it’s just nice to know where the center of the tangent circle is to the curve that
we want to justify in our design.

-Diana Chan


  1. 1. I would “reparameterize” the “s” input.
    2. UV input should between 0-1. so I will use a point component, its x, y values controlled by a slide bar between 0-1. The feed the point component into UV input.