From B-Spline Curves to Surfaces

 

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Overview

All of the curves and surfaces in this book are based on sets of equations of varying complexity. Most of those equations are polynomial equations. In this first chapter, I will establish a mathematical and conceptual foundation for most of the chapters to follow. For those of you who've had some higher math courses, most of this should be review. For others, this will introduce you to the basics that provide an undercurrent to nearly every other chapter. I'll start off with the following points.

• What is a curve?

• What is a polynomial?

• Lines (first-degree polynomials ) and slopes

• Curves ( higher-degree polynomials) and derivatives

• Joining curves and continuity

• An introduction to a curve application