a) A type of mathematical model used to represent curves. They are usually displayed as polylines with a large number of very small sides.

The importance of splines is that they give very smooth curves for a relatively small number of points. b) In wooden ships, the curved skeleton of a hull is built by attaching bendable strips of wood to small, fixed, and angled blocks of wood. The strips are splines. In computer graphic splines, the blocks of wood are called control points. In computer graphics, curved lines are always visualized by drawing many short vectors. However, since each vector requires a fair amount of storage, curves are often stored in terms of their control points; whenever the curve is needed, the spline is recreated. Another advantage of storing splines as curves is the ease with which a spline curve is manipulated by moving its control points. Instead of moving the curve’s vectors one at a time, a large section of the curve is moved by dragging its control point. Splines convert discontinuity into smoothness. These properties make splines very useful in animation. When we create a keyframe for path animation, the object’s position becomes a control point for a spline that defines the entire path for all the in-between frames as well. This allows us to get smooth motion between all the keyframes, and avoid instantaneous (single frame) changes of direction.

Such changes would be highly unrealistic and could never yield satisfying animation. Another tremendous advantage of splines is that they are resolution independent. Magnifying and then redrawing a shape that is represented by a spline does not reveal the short vectors that represent the curve on the screen, because these vectors are recalculated to take into account the new magnification. Spline represented objects can also be easily rotated or skewed in 3D, again with no loss in clarity. So called “vector- based” systems make use of these features by representing fonts and shapes with splines, rather than the traditional bitmap. Bitmap systems, on the other hand, cannot represent or manipulate shapes nearly as handily.