Modelling
When defining a form, an important factor is the continuity between surfaces - how smoothly they connect to one another.
One example of where surfacing excels is automotive body panels. Just blending two curved areas of the panel with different radii of curvature together, maintaining tangential continuity (meaning that the blended surface doesn't change direction suddenly, but smoothly) won't be enough. They need to have a continuous rate of curvature change between the two sections, or else their reflections will appear disconnected.
The continuity is defined using the terms
- G0 – position (touching)
- G1 – tangent (angle)
- G2 – curvature (radius)
- G3 – acceleration (rate of change of curvature)
To achieve a high quality NURBS or Bézier surface, degrees of 5 or greater are generally used. Depending on the product and production process, different levels of accuracy are used but tolerances usually range from 0.02 mm to .001 mm (for example, in the fairing of BIW concept surfaces to production surface). For ship building, this need not be so tight, but for precision gears and medical devices it is much finer.
Read more about this topic: Freeform Surface Modelling
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