Vector Field Integration

Here's a component that finds the integral lines of 2d or 3d vector fields...

The way it works is very simple: you give it a list of sample points and associated vectors (1 vector for each sample point) and a start point, and it flows that start point along the vector field up to a specified iteration limit and step size. The advantage to having a generalized component like this is that along with things like principal curvature lines, it can also compute paths guided by isovists and visibility algorithms, principal stresses, etc. As long as the vector field is properly defined, it will do something...

Replies to This Discussion

Permalink Reply by Danny Boyes on April 19, 2011 at 11:21am

Very nice indeed! Bobbing along:

Permalink Reply by Danny Boyes on April 19, 2011 at 11:26am

How about for future development you introduce a Vector component for the object in the field. Such as a vessel under power, you could also vary it along the length at different steps to simulate altering course.

Permalink Reply by Daniel Hambleton on April 19, 2011 at 11:45am

Not sure I follow...do you mean outputting the current direction of travel of the moving point?

Permalink Reply by Danny Boyes on April 19, 2011 at 12:59pm

No. In the image above the vectors are the current in a river. The Blue line shows the path of the object when released in the stream at that point. The path is a result of the vector field only, like releasing a rubber duck. No imagine that the object released was a power boat with a constant vector of its own, or as described the direction changed as it went along from some predefined way points.

I was just curious really.

Permalink Reply by Daniel Hambleton on April 19, 2011 at 1:34pm

I think with the updated version you could do this....just add the vector you want to act on the moving point to every sample vector. In the dynamic simulation, you could change this at different time steps....haven't tried it yet, though.

Permalink Reply by Danny Boyes on April 21, 2011 at 7:45am

Brilliant! I've just played with your dynamic vector field example and added an MD slider as a joystick and was able to get the Ball off track and back on.

Thank You very much for this.

Permalink Reply by Danny Boyes on April 21, 2011 at 8:04am

It gets even better. If you hook up the dynamic VFI component to the static VFI you get the predicted course of the Object at that instance.

Permalink Reply by Giulio Piacentino on April 21, 2011 at 11:35am

Awesome!

We could try connecting it with stock exchange information and gain some well-deserved money* :)

- Giulio
____________

giulio@mcneel.com
McNeel Europe

* [insert some guarantee-avoiding wording here]

Permalink Reply by Daniel Hambleton on April 19, 2011 at 1:32pm

K. Here's an updated version:

Dynamic Simulation component added (just attach a timer and reset toggle...)
Step size has been absorbed into the vector field definition (the point will move in the direction and magnitude of the sample vector)
Principal Curvature component should work now...although it's debatable whether this special case should merit it's own component...

Permalink Reply by Luis Fraguada on April 19, 2011 at 2:19pm