constraint-based vector design

[Forrest O.]

I saw the earlier question about CAD drawing. I have a similar question, but thinking about it from a different angle.

(Image text: I’d like to draw this polygon, then attach variables to four of the sides. The angles would solve themselves as the measurement variables change, keeping the general shape. Drawing the shape defines 4 vectors, from which you can find angles and positions. Can the vectors be constrained to keep the angles as similar as possible while changing the distances?)

The distances are static variables input into the system. The constraints would be on the angles. I can see putting this to a physics library, attaching springs to sticks, weighting springs according to the original angles. But would that be linear / applicable with Cassowary?

- Forrest

[Greg Badros]

I think you'd have to write out the parameterizations you're considering and see.  For new application domains, it can be non-intuitive what will work vs. what won't, and once you have something that takes you outside of the system's capabilities, you really end up needing a different approach.  I'm not particularly optimistic about things like this, but would have to spend a bunch of time on the ways to represent the system to convince myself it's applicable or not.

That written, it seems like a simple local propagation solver might be able to do just fine here.  LP is essentially like Excel formulas... you get any computable function, but "simply" have to avoid creating cycles in the computation.  That's sometimes harder than it sounds, but for your application it might be fine.

Good luck!

Greg

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[Forrest O.]

Thanks Greg,

I started reading Ivan Sutherlands 1963 thesis: Sketchpad: A man-machine graphical communication system ... Brilliant stuff. Why aren't these constraints available in drawing programs now?

It seems like a combination of LP (for distances) and a physics-like approach based on energy minimization (for angles) will be the way to go to solve these clothing pattern polygons. We started experimenting here: https://github.com/GabiThume/open-fashion/issues/1

As an aside, http://famo.us/ is touting a physics-based approach to layout constraints. I wonder how that will compare in practice with http://gridstylesheets.org/ 's linear constraints.

- Forrest

[Greg Badros]

The background section of my thesis provides lots of my thoughts on the different approaches including physics-based (and the rest of the thesis argues that Cassowary and its approach is a good addition to the set of techniques available).  See http://www.badros.com/greg/papers/gjbadros-dissertation.pdf .