# Solid sweeps along line segments

## Alec Jacobson

## February 07, 2015

I made a nice realization today that the boolean code I've been working on can also be used to compute "solid sweeps" of meshes along line segments: the Minkowski sum of a polyhedron and a line segment.

Check out `linear_sweep.m`

in gptoolbox. It works in 2D (using Triangle and the winding number to classify the boundary of the swept region):

and in 3D:

~~the 3D version is currently only ~~*robust* if the sweep vector goes outside the bounding box of the input shape. In those cases, I'm using a technique analogous to my robust booleans and it works quite well. But if the sweep vector is small, I'm resorting to using TetGen and computing winding numbers: TetGen will often fail. Hopefully this limitation is not for long, since I have a clear idea how to handle small vectors. Just need to code it up.

**Update:** The 3D version is now robust, too.