Added centroid method

[seangrate]

Added a method to compute the centroid of a polyhedron. This implements the feature requested in #4172.

[mahrud]

Thanks! This is great, I left a few comments ranging from typos to just some FYIs in case you're interested.

[mahrud]

Sidenote: this way next time someone adds a function they don't edit two lines, which can sometimes avoid merge conflicts.

Suggested change

	"centroid"
	"centroid",

[mahrud]

Following the convention in the rest of the package:

Suggested change

	Computes the centroid or barycenter of a polyhedron.
	computes the centroid or barycenter of a polyhedron

[seangrate]

At least in Polyhedra/documentation/documentation.m2, it looks like the main convention is a capitalized first letter and the phrase ends with a period.

[mahrud]

Huh, that's definitely not the suggestion of the style guide, but from the toc it seems only a few nodes are like that.

[mahrud]

Suggested change

	The centroid a polyhedron is the center of mass of the polyhedron.
	The centroid of a polyhedron is the center of mass of the polyhedron.

[mahrud]

Others can correct me if I'm mistaken, but I believe this is meant for the caveats of the algorithm or implementation, not assumptions of the definition. You could mention in the Inputs section that P must be compact.

[mahrud]

This is totally fine as as, but FYI, this also works:

Suggested change

	sum for delta in barycentricTriangulation P list (
	barycenter := (sum delta) / #delta;
	(volume convexHull delta / totalVolume) * barycenter
	)
	sum(barycentricTriangulation P, delta -> (
	barycenter := (sum delta) / #delta;
	(volume convexHull delta / totalVolume) * barycenter
	)
	)

The advantage (which is negligible here) is that unlike this way we don't need to construct a list and then sum it, we just sum as we go.

[seangrate]

Didn't realize sum could do this, thanks!