Module ultraviolet::bivec

Bivectors, i.e. oriented areas.

A bivector is an oriented area, and is equivalent to the result of the exterior (wedge) product of two vectors, i.e. u ∧ v. This means it is the oriented area of the parallelogram created by attaching two vectors and then extending them into a parallelogram.

A normalized bivector can also be thought of as representing a plane and the direction of rotation about that plane such that a positive rotation follows the orientation of the bivector. When you obtain a bivector by taking the exterior product of two vectors, the positive direction of rotation is defined as the one that brings the first vector closer to the second. For example, a bivector created by taking the exterior product x ∧ y of the x and y basis vectors will create a unit bivector that represents the xy plane, with orientation such that a positive rotation of x inside the plane would bring x closer to y. This is why positive rotation is generally defined as "counter clockwise" in 2d, since such a rotation brings x to y.

Structs

Bivec2	A bivector in 2d space.
Bivec3	A bivector in 3d space.
WBivec2	A bivector in 2d space.
WBivec3	A bivector in 3d space.