Small project: simple flows through a vector field

I have a small project that I would like to do over the next few days, and I'm looking for any advice people might have on it. I understanding scripting conceptually but I suck at VB.net.

I would like to create a very simplified algorithm that calculates linear flows through a 2 dimensional field of vectors.

For the vector field, I would use a grid of points, and there would be a vector associated with each point. I already know how to make this.

For the linear flows, I would like to input a set of start points, and end up with a curve corresponding to each start point. Creating the curve is the part I am not sure how to do, but I have some ideas.

To create the curve, I imagine an algorithm that would take the start point, find the closest point in the "field" grid, and then use the vector associated with the closest field point to move the start point in a particular direction. Once moved, the moving point would have a new closest field point with a different associated vector, which would move the point again, and so on, recursively, for each start point for a given number of steps.

So for each point:
-find the index of the nearest field point
-get the vector from a list of vectors using the index of the nearest point
-move the point the value of the vector
-append the point's new coordinates to a list of points for it's start point
repeat

I need to maintain a list of flow point coordinates for each start point, so that I can use use them to construct interpolated curves.

I remember a discussion about making water flow down a surface which seems very relevant, but I had trouble finding it.

Thanks for any advice or help. I'll post more as I make it.

Replies to This Discussion

Permalink Reply by Benjamin Golder on January 12, 2010 at 11:02pm

here is the discussion about recursive descent:
http://www.grasshopper3d.com/forum/topics/gradient-descent

Permalink Reply by Daniel Piker on January 13, 2010 at 12:18am

Take a look at the second definition on this page.

That uses a continuously defined vector field, whereas you describe using a discrete grid, but the principle would be just the same.

To read more about these techniques try searching for Numerical Integration, Euler's Method, or Line Integrals.

Permalink Reply by Benjamin Golder on January 13, 2010 at 11:53am

Thank you so much Daniel. The vb.net component in that definition has the elements I was looking for, and of course much more.

Permalink Reply by Matt Schmid on February 11, 2011 at 9:52pm

Hey Benjamin,

Just wondering how you made out? Were you able to adapt it to 2d?

Cheers,

Matt

Permalink Reply by Benjamin Golder on February 14, 2011 at 4:51pm

Hi Matt,

I did carry this out. I ended up using Python in rhino 5 to do it

I'll post some info and code when I have a moment (I'm pretty busy though so please be patient).

Thanks for your interest.

-Ben

Permalink Reply by Matt Schmid on February 16, 2011 at 5:02pm

Hi Benjamin,

Thanks for the reply, I look forward to seeing how you went about it. I'm trying to do the same thing right now using VB.net. I've managed to get the streamlines working, but now I'm trying to get a nice even distribution of them throughout the field, which seems like its going to be the hardest part. I was hoping to use a similar strategy to the Delaunay Triangulation and largest circle method used in the CGAL 2D Streamline package. Only problem is I'm not sure how to implement Delaunay Triangulation in VB.net... I should start a new thread on this...

Thanks again.

Matt

Permalink Reply by Angela McCrory on November 5, 2011 at 7:12pm

Hi Matt-

I'm working on a similar project involving a 3D vector field and I was wondering what approach you took. I'm a VB.net beginner so any tips would be appreciated.

Thanks!

Angela

Permalink Reply by Jon Mirtschin on November 5, 2011 at 9:54pm

Some of the progress I made on streamlines on vector fields might help, but only for surfaces/mesh in 3d space rather than a true 3d vector field, although it might be possible to extrapolate the same approach if there was sample data and the time was available to spend on it.

Permalink Reply by Ivan on February 6, 2014 at 1:59pm

Hello guys!

I'm working with vectors now

And I found some difficulties during the realization of Daniel Picker's script with vector fields (from here). I need to create curves through vectors.

Could somebody show on any vector field how can it work?

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