CAGD 2002 Course Notes: Notation

In general, lower case letters are used to denote scalars (reals), and upper case letters to denote more complicated entities. Round brackets are used for grouping scalars in expressions, and square ones for grouping more complicated entities.

However, round brackets are used for n-tuples, square ones for intervals, and curly ones to denote sets, following standard notation. There should not be any confusion arising.

Some specific letters have connotations. I have tried to avoid using these letters in other contexts:-

• P is almost always a generic point, usually of a curve or surface
• but occasionally it is used to denote the set of all points
• D is occasionally used to denote the set of all displacements
• Q,R,S are given points
• but R also denotes the set of reals
• and occasionally the rotation matrix of a coordinate system
• N is a vector normal to a surface
• T is a displacement tangent to a curve or surface
• U and V are displacements tangent to a surface
• u,v are surface parameters
• t is a curve parameter
• u,v,w are homogeneous surface parameters
• s,t are homogeneous curve parameters
• X,Y,Z are axis vectors of a coordinate system
• O is the origin of a coordinate system
• x,y,z are coordinates within a coordinate system
• for want of a separate symbol in the standard font, x is also used between two upper case letters denoting displacements to denote the vector cross product
• . is used to denote the vector dot product
• * is used to denote multiplication by a scalar
• + and - are used with their normal meaning, but are also overloaded to denote vector addition and subtraction
• := is used to denote assignment in a computation
• f( ) and F( ) denote generic functions returning scalar and more complex results respectively