Conic function (similar to graph mapper)

I'm looking for a function that can reproduce the graphical results of the conic graph mapper in GH. At x=-1, i'd have an arc, at x=0 a line, and at x=1 the inverse of the first arc. If necessary, i can use 2 functions for x>0 and x<0. Anyone have an idea?

Replies to This Discussion

Permalink Reply by David Rutten on September 6, 2012 at 5:10am

A conic doesn't consists of lines and arcs at all. I fear there is some confusion somewhere, can you elaborate, in case it's on my end?

David Rutten

david@mcneel.com

Poprad, Slovakia

Permalink Reply by Javier Vizoso on September 6, 2012 at 6:51am

Sorry, it's probably my fault for not explaining well. I'm looking for a mathematical function where i can interpolate from one arc (x=1) through a line (x=0) to a mirror of the first arc (x=-1), similar to the picture. The values -1->1 and the orientation of the arc are arbitrary, I'm just looking to be able to interpolate from one arc to its mirror, so i can use it as a distribution gradient in a component. Thanks!

Attachments:

def.png, 75 KB

Permalink Reply by David Rutten on September 6, 2012 at 7:08am

Ah I see, interpolate that way. Although the conic can indeed represent a line and an arc, most often it is neither. In the attached file, if you set the middle slider to 0, you get a line. If you set it to 0.5 * SquareRoot of 2.0, you get an arc. Other values result in hyperbolas and/or parabolas, I'm not 100% sure which without doing a bunch more research first.

There is no mathematical function of the form y = f(x) that allows the evaluation of a specific x value. I use curve intersections to find the values in the GraphMapper (same for Bezier curve, it also uses curve intersections, all the others do have f(x) functions for quick evaluation).

David Rutten

david@mcneel.com

Poprad, Slovakia

Attachments:

ConicCurve.gh, 2 KB

Permalink Reply by Javier Vizoso on September 6, 2012 at 7:43am

Maybe I'm looking at it the wrong way. My goal is to be able to transition from one gradient distribution to the next, like in the 'circles' image, with a slider. Normally I'd use a graph mapper, but for the current application I cannot.

Attachments:

circles.jpg, 912 KB
def.png, 111 KB

Permalink Reply by David Rutten on September 6, 2012 at 8:08am

What if you use 2 Graphmappers and then blend between the two values using a slider and the [Interpolate] component?

David Rutten

david@mcneel.com

Poprad, Slovakia

Permalink Reply by Javier Vizoso on September 6, 2012 at 8:19am

Problem is I'm translating a def into javascript, so i don't have access to a graph mapper. Thanks again though.

Permalink Reply by Javier Vizoso on September 6, 2012 at 9:04am

However, now that I think of it, I can probably get away with interpolating between two functions (based on sqrt(1-x^2)) in the same way the interpolate component does. Wont be too performant, but it should work. Thanks!

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