Computer graphics and animation experts have been using the Catmull-Rom smooth curve interpolation equations since 1974, but the vector and matrix equations can be derived and simplified using basic algebra, resulting in a simple set of linear equations with constant coefficients. A variety of uses of Catmull-Rom interpolation are demonstrated,…

Presents computer programs (Applesoft Basic) for: (1) 2-D rotation about any point through any angle; (2) matrix transformation for 2-D rotation; (3) 3-D translation; (4) 3-D rotation; and (5) hyperboloid rotated in 2-D space. Includes background information and sample output for the matrix transformation subroutines. (JN)

One requirement often stressed by the author's Japanese business English students in sales and marketing positions is the need to talk about the product, or make presentations, in terms of its market growth and market share over time with the use of a visual representation. These requests have linguistic and conceptual elements that demand a lot…