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Basis

All objects have a frame of reference: an origin point and an orientation relative to that point. We will represent an object's reference frame with basis vectors and a position vector. The basis vectors control the reference frame orientation. In three dimensional space, three components are needed for the basis vectors. We will use basis vectors and positions to orient the camera and objects in our scenes.

Position

A position vector indicates the location of the object's reference frame in vector space.

Orientation

The orientation of a frame is defined by basis vectors. A basis has one vector for each dimension. Our bases will have orthogonal and have unit length vectors. This is called an orthonormal basis. When describing bases, we will use the symbols \(\mathbf{u}\), \(\mathbf{v}\), and \(\mathbf{w}\). These are the thumb, index, and middle fingers respectively (for right handed systems).