ABSTRACT

Hurricane Katrina motivates our introduction to points and vectors in 2D. Basic notation for points and vectors in 2D is introduced, which includes describing Euclidean space and real space. We describe the difference between points and vectors in terms of the operations allowed to result in coordinate independent operations. Linear combinations, linear interpolation, and barycentric combinations are defined. The concept of barycentric coordinates is introduced. Vector length is defined and applied to a vector field visualization. Linear independence and basis are introduced. The dot product is defined. A computer graphics lighting model application is described that uses the cosine function as a smooth, natural attenuation factor for producing smoothly lighted 3D models. A section on orthogonal projections provides the foundation for least squares approximation in chapters that will follow. Other important principals are introduced, such as the Pythagorean theorem and Cauchy-Schwartz inequality. Sketches and figures illustrate the concepts.