Computing for Numerical Methods Using Visual C++

Chapter 7. Interpolation and Approximation

• 7.1 Curve Fitting

• 7.2 Lagrange Interpolation

• 7.3 Newton Interpolations

• 7.4 Cubic Spline

• 7.5 Least-Squares Approximation

• 7.6 Visual Solution: Code7

• 7.7 Summary

• Numerical Exercises

• Programming Challenges

CURVE FITTING

The body of a car has been designed in such a way it possesses good aerodynamic features. This is important in order for the car to be comfortable, energy-efficient, cost-effective, and attractive. To achieve these objectives, the body surface of the car is made to be smooth. The normal techniques for designing the body of a car involve computer-aided design tools on the computer. The body is constructed by fitting and blending a set of patches from the B-spline or Bezier surfaces by approximating a set of points. B-spline and Bezier are some two-dimensional curves that are widely used in curve and surface fittings.

In general, curve and surface fitting is useful in many applications, notably in the design of body surfaces such as cars, aircrafts, ships, glasses, pipes, and vases. A patch in the surface is the three-dimensional extension of the B-spline curve which is obtained from a curve fitting technique.

Curve fitting is a generic term for constructing a curve from a given set of points. This objective can be achieved in two ways, through interpolation or approximation. Interpolation refers to a curve that passes through all the given points, whereas approximation is the case when the curve does not pass through one or more of the given ...