Introduction to Nonimaging Optics, 2nd Edition

21

Plane Curves

21.1 General Considerations

This chapter presents some plane curves¹ that are useful in designing non-imaging optics.

The magnitude of a vector v is given by

||v||=v⋅v⁢(21.1)

A normalized vector with the same direction as v, but with unit magnitude, can be obtained from

The distance [A,B] between two points A and B is given by the magnitude of the vector B − A, that is, ||B − A|| or

[A,B]=(B-A)⋅(B-A)⁢(21.3)

The angle between two vectors u and v is given by

This angle, however, is 0 ≤ θ ≤ π. Consider then that vectors u and ...