Appendix B: Notation

Here is the notation used in this book:

		cross product
		curve derivatives with respect to the current parameter
a, b, ?, ?		real numbers or real-valued functions
0		short for or
e ₁, e ₂, e ₃		directions of a coordinate system
a, b		points or vectors
a _x, a _y, a _z		x, y, z components of the point a.
x		homogeneous coordinates of the point x
A, B		matrices
A, B		matrices whose elements are points ("hypermatrices")
b ^r _i		intermediate points in the de Casteljau algorithm
B ⁿ _i		Bernstein polynomial of degree n
H ³ _i		cubic Hermite polynomials
L ⁿ _i		Lagrange polynomial of degree n
N ⁿ _i		B-spline basis function of degree n
IE ^d		d dimensional Euclidean or affine space
IR ^d		d dimensional linear or real space
? _i		difference in parameter intervals (i.e., ? _i = u _i+1 u _i)
? ^r		iterated forward difference
P		control polygon
v		(Euclidean) length of the vector v
x _u		u-partial of x( u, v)
a ? (1, 0, 0)		barycentric coordinates of a are (1, 0, 0)
? _i		Greville abscissa

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The Essentials of CAGD