Freeform surface modelling

The first begins with construction curves (splines) from which the 3D surface is then swept (section along guide rail) or meshed (lofted) through.

They are used to describe forms such as turbine blades, car bodies and boat hulls.

Initially developed for the automotive and aerospace industries, freeform surfacing is now widely used in all engineering design disciplines from consumer goods products to ships.

The order of a polynomial is one greater than the degree, and gives the number of coefficients rather than the greatest exponent.

The number of knots will determine the influence of the poles on either side and how smooth the transition is.

The smoothness between patches, known as continuity, is often referred to in terms of a C value: Two more important aspects are the U and V parameters.

The continuity is defined using the terms: To achieve a high quality NURBS or Bézier surface, degrees of 5 or greater are generally used.