?

cross product; L ? M: intersection of two lines;

p ? q: line through two points

?

cross product

, ?

curve derivatives with respect to the current parameter

a, b, ?, ?

real numbers or real-valued functions

0

short for (0, 0, 0)

a, b

points or vectors in affine space

a, b

points in projective space

If b = [ x, y, z, w] ^T, then b = [ x/ w, y/ w, z/ w] ^T.

A, B

matrices

L, M

lines in projective space

,

Bernstein polynomials of degree n

e1, e2, e3

short for [1, 0, 0] ^T, [0, 1, 0] ^T, and[0, 0, 1] ^T

d-dimensional euclidean space

D _d f

directional derivative of f in the direction d

? _i

difference in parameter intervals (i.e., ? _i = u _{i +1} - u _i)

? ^r

iterated forward difference

cubic Hermite polynomials

P

control polygon

?

an affine or projective map

?

an interval in a knot sequence

? v ?

(euclidean) lenght of the vector v

x _u

u-partial of x( u, v)