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Handbook of Computer Aided Geometric Design by M.-S. Kim, J. Hoschek, G. Farin

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Chapter 7

Curve and Surface Constructions

Dianne Hansford and Gerald Farin

This chapter introduces algorithms for the generation of curves and surfaces. The emphasis is on interpolation and approximation using Bézier and B-spline techniques.

7.1 INTRODUCTION

The goal of this chapter is to outline some of the most fundamental interpolation and approximation methods in CAGD. Wherever possible, the developments focus on Bézier and B-spline techniques because of their intuitive geometric definitions. First of all, the focus is on polynomial curve methods, including Lagrange (point) interpolation, point approximation, and Hermite (point and tangent) interpolation. Next, a piecewise polynomial scheme, C2 cubic spline interpolation is presented. ...

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