Mathematical Equation to generate curve

Hello all,

As I was looking around to find ways to generate a coiling/looping curve, I stumbled upon a definition by Grasshopper3dvn. These 2 equations were used:

I tried Wolfram alpha to find out what does u, v and a mean but there was little explanation. I would appreciate it if you guys can point me to where I can learn more about these 2 equations and their parameters. Thanks!

Replies to This Discussion

Permalink Reply by Birk Binnard on January 26, 2017 at 11:17pm

Usually u and v refer to the X and Y dimensions of a 2D rectangle. The typical values for both u and v are from 0 to 1. The variable a is probably a constant that can have any value, but the 2nd equation looks like it should not be 0. My guess is the first equation will give you the X value of a point on the curve, and the second one the corresponding Y value.

Permalink Reply by Hien Nguyen on January 29, 2017 at 1:35pm

Thanks Binnard! I tried to use a slider to test what each component will do to the shape but was not able to figure it out.

Permalink Reply by Hyungsoo Kim on January 26, 2017 at 11:44pm

Hi.

You'll be able to try like this and play more.

Attachments:

MathCurveByEquation.gh, 21 KB

Permalink Reply by Hien Nguyen on January 29, 2017 at 1:22pm

Thank you Hyungsoo, I'm messing around with the definition to get a clearer sense of the equations' parameters. Really appreciate your input!

Permalink Reply by Hien Nguyen on January 29, 2017 at 1:25pm

Hi Tom,

I'm actually testing out drawing circles and use bi-arcs to connect and split them so that in the end I will end up with a semi-coiling curve. The math seems way over my head after reading and testing the parameters repeatedly. I will read more into this in the future. But for now, I guess I will have to improvise haha! Thank you for your input, I really appreciate it!

Permalink Reply by MEGHANA PATIL on January 30, 2017 at 12:47am

HI,

you can use mathForV4 plugin in rhino for generating curves from equation or you may use evaluate component in grasshopper for equation and give input as U and V such As X and Y in grasshopper

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