# Spline Curves and Surfaces for Data Modeling

• André Guéziec
Chapter
Part of the NATO ASI Series book series (NSSA, volume 284)

## Abstract

We provide a brief introduction to spline functions. In modeling data, splines are associated with the notion of smoothness. They really are the analog to the draftsman’s wooden spline. They are useful for curve and surface interpolation or approximation.

Our goal is to give a simple and original development of the basic material needed for understanding spline curves and the notion of curvature associated with them. The advantages of using splines for analyzing data are that splines are computationally simple and they satisfy the minimum curvature property. A review of algorithms involving splines as well as a comprehensive theory can be found elsewhere.

We begin by quickly tracing the ancestry of splines, which dates back to the eighteenth century. Then, we consider a quadratic Bézier curve, defined with only three points. In order to construct complex curves, we piece together Bézier curves, and, when specific continuity conditions are satisfied, we obtain B-spline curves. We provide a general definition of spline curves, comprising both Bézier and B-spline curves. We finish by combining B-spline curves to form tensor product B-spline surface patches.

## Keywords

Spline Function Spline Curve Bezier Curve Computer Assist Surgery Control Vertex
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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