# Splines: Representations of 2D and 3D Curved Surfaces

## Introduction

There are two general problems with curved surfaces:

1. May have a curve ( or surface ) with a few known points and want to interpolate between them. For example an energy surface in Physics or Chemistry or measured data in business. Each computed point is very expensive, or else it might be a face, car, etc. witha few digitized points. We could do straight line interpolation, but a better method is curve interpolation.

2. We may want to synthesize a curve or a surface, for example in designing an automobile. Then let designer specify a set of control points (Knots) which define the curve/surface. The computer then computes and displays the curve. As the designer modifies the control points the curve changes.

Splines: General Discussion

1. Hermite (Ferguson) - defines positions and tangents at end points

2. Bezier - defines the positions of the curves' end points and uses 2 other points (usually not on the curve) to indirectly define the tangents at the end points

3. B-Spline - approximates end points rather than matching them