Signed distance functions

[kai-qu]

Style writers and implementers need abstractions for optimizing the relationships between any pair of objects, rather then having to write special-purpose graphics code for every new objective/constraint function and every n-ary combination of graphical primitives.

Therefore, to improve the generality of our optimizer and the user experience for Style implementers, do the following:

For any object and any point in the plane, add the ability to compute a signed distance function from that point to the object (positive if outside, negative if inside). Additionally, compute level sets of distances for use in margins.

Test how well your implementation works with the existing optimizer and how well it works with the existing Styles. Specifically, test the following two important applications of signed distance:

• Improve our label layout (and any objective functions that act on text), now that you can calculate the signed distance to the outline of the text, rather than just a bounding box.
• Optimize objects composed of Bezier curves by writing new objective functions that use the signed distance to Bezier curves.

This issue depends on issue #75.

[wodeni]

I had some early attempts on this and I do plan to take this on as a part of my goals this semester(at least have a framework that works on simple primitives). Some related materials here:

http://jamie-wong.com/2016/07/15/ray-marching-signed-distance-functions/#signed-distance-functions
http://iquilezles.org/www/articles/distfunctions/distfunctions.htm