Conic function (similar to graph mapper)

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?

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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).

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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?

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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!