inverse function of transformation, length dependence of the width?

Replies to This Discussion

Permalink Reply by Hannes Löschke on January 28, 2012 at 3:54pm

Depends on how you create the cylinders. You will usually have independent inputs for diameter and height.

You need a mathematical description of how height will vary with diameter (or the other way around). Then use math components or expression component to solve the other value for a given diameter or height and input both results into your cylinder creation.

Permalink Reply by spiral on January 28, 2012 at 9:57pm

You are right, the two parameters I need to synchronize the diameter increases, the height decreases, or vice versa, what it looks like math component? or components of an expression or a simple example of its use. Thank you for your reply.

Permalink Reply by Hannes Löschke on January 29, 2012 at 4:32am

It's really easy once you know where to look.

Given your answer I strongly recommend reading at least one of the primers in the "getting started" section if this site. > see here /a>

Permalink Reply by spiral on January 29, 2012 at 9:21am

Thank you very much

Permalink Reply by spiral on January 29, 2012 at 10:00am

Works great and so easy, you genius, and I'm a microbiologist and mathematics uncomprehending. Thank you.

Permalink Reply by spiral on February 3, 2012 at 2:31am

can `t solve the problem, file with the curves, the length of the curve should be constant

http://www.grasshopper3d.com/forum/topics/2d-3d-spiral-frames-defin...

Permalink Reply by Hannes Löschke on February 3, 2012 at 3:02pm

Sorry, I can't see any relation of this thread and the link?

What file?

Permalink Reply by spiral on February 3, 2012 at 11:49pm

file reference-helix increases depending on the height (h) and diameter (r), is it possible to link the sliders (h) with a slider (r) that would be the length of the spiral was constant during the deformation?

Thank you for your support

Permalink Reply by Hannes Löschke on February 4, 2012 at 11:29am

If you want to constrain one parameter to another one, you need to know its mathematical relationship. For the cylinder I used the volume as a given constant and calculated the radius from volume and height.

In case of the spirals you were linking to, this relationship isn't trivial. Actually there are three radii and heights involved.

If you only want a simple helix with constant radius r and given height h, the arclength calculates to L = T*SQRT(r^2+h^2), where T depends on the number of wraps your helix has. (see here) You can use this equation to relate radius to height.

If your spiral is spline as in the example through multiple points, the length is way harder to calculate. You could fake it by lets say using the inverse of height as a radius. That way, the height will decrease with radius but the length will not remain constant.

Permalink Reply by spiral on February 5, 2012 at 1:02am

Yes you're right, it requires a new algorithm, I need to find a model video, (r) curves are able to change the length, if there are options please send to my mail. Regards, Yuri