##
5.1 INTRODUCTION

• When we have a basic shape we can use equations to describe the shape,

- circle

- sphere

- oval

- plane

- line

- conic

- etc.

• When the shape is not common, splines enable curved surfaces to be defined easily, with good control of the shape

• The source of control points for the splines are experimental data or design parameters or artistic judgement, etc.

• A spline uses end points, and some internal control points to adjust the shape which could not be defined with known primitive geometries.

• Common spline types are,

- Polynomial

- B-Spline

- Bezier Splines

- Hermite Splines

- Catmull-Ron

- etc.

• A spline can be used as a face in a B-Rep (solid) model.

• Some splines allow variable tension, such as the Catmull-Ron, and some B-Splines. This allows a skin which is stretched, tightly, or loose.

• Mathematical functions for curves and surfaces may be explicit or parametric.

Explicit - The values are directly related

Parametric - The curve is described by varying other numbers