Grasshopper

algorithmic modeling for Rhino

# Derivative graph on a rolled up toroidal space.

Hi everybody!

I'm here opening this discussion to explain to who are interested, how I managed my last gh user object :P

Probably there are better method to achieve the same or better results, like scripting or such...

This is just my approach...

Basic math: the derivative is a graph where y is the angle of the curve/function at parameter x.

We can interpolate a curve trough all evaluated point (with x=a simple series and y= angle) of the curve.

Is useful to intersect derivative graph with an offset of x axis.

Intersection points will tell us which parameter (X) have the wanted angle (Y).

But here's the problem "I've found"...

Derivative graph limit angles to 0<angle<360...

The interpolate curve point will give out wrong results, obviously.

(this can be solved by "partitioning" or splitting the derivative graph in more

sub-graphs i think, but I don't like that way XD )

To solve that problem I've bent the graph in a cylindrical shape where previous

"error" doesn't happen :D

For a periodic curve a similiar problem would happen when "intersecting" near end-start of the graph curve.

Again to solve this, I've bended again the whole graph!

Toroidal then.

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And here is what happen while the user object is working:

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thank you for taking the time to explain the steps and how/why you solved the problems that led to the working user object. The solutions were far from intuitive for me... so your explanations were very helpful. thanks

Great stuff Riccardo!!

thank you for sharing this.

cheers

alex

Like it! Thank you for taking the time to explain this Riccardo, this is clever stuff:)

by June Lee

by June Lee

by June Lee

by June Lee

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