问题:

Does the method for computing the cross-product change for left handed coordinates?

回答1:

The formula for the cross product of the vectors (x1, x2, x3) and (y1, y2, y3) is

z1 = x2 * y3 - x3 * y2
z2 = x3 * y1 - x1 * y3
z3 = x1 * y2 - x2 * y1

It is designed in a way that the three vectors x, y and z in the given order have the same handedness as the coordinate system itself. This property does not depend on the handedness of the coordinate system -- for a left-handed coordinate system the vectors fulfil the left-hand rule. You don't need to change anything about the formula.

Useful links:

Righthanded and Lefthanded Systems of Coordinates and the Cross Product
Relevant section from the Wikipedia article

回答2:

In left-handed coordinates, the cross product is the same magnitude simply pointed the other way. The easiest way then that I know of to convert from a right-handed coordinate system's cross-product, and a left-handed coordinate system's cross-product, is to take the components of the right-handed cross-product and reverse the signs.