Documentation is a bit unclear

[oisyn]

The documentation for incircle, orient2d and orient3d all speak of "counterclockwise order", but without specifying the assumed handedness of the coordinate system, this is fairly meaningless.

The documentation for insphere speaks of the points needing to be in a "positive orientation". It is unclear what is meant by this. I'm also not sure if this is in any way intuitively quantifyable? Perhaps something along the lines of: a positive orientation is where point d is on the left or right (whichever is applicable, handedness applies here as well) of the plane defined by the triangle abc. I'm not sure whether this definition always holds, though.

[urschrei]

The documentation for incircle, orient2d and orient3d all speak of "counterclockwise order", but without specifying the assumed handedness of the coordinate system, this is fairly meaningless.

The meanings of clockwise, counterclockwise, and positive are assumed to be in keeping with the original paper and documentation coordinate system (section 4.1):

These definitions extend to arbitrary dimensions. For instance, ORIENT3D returns a positive value if d lies below the oriented plane passing through a, b , and c. By oriented plane, I mean that a, b, and c appear in counter- clockwise order when viewed from above the plane.

[oisyn]

Well, yes, but the paper doesn't seem to be very clear about that either.

[urschrei]

In that case I suggest you direct your questions to Jonathan Shewchuk.

[oisyn]

Suppose I found out, would you be open to change the documentation? Because that's what this is ultimately about.

[urschrei]

Yes, we're always open to clearer documentation.

[hugoledoux]

It's actually clear in the paper:

This is consistent with the left-hand rule: when the ordering of $a$, $b$ and $c$ follows the direction of rotation of the curled fingers of the left hand, then the thumb points towards the positive side (the above side of the plane).