Reference work entry
Freeform is where the surface shape has no continuous translational or rotational symmetry about axes. Freeform surfaces belongs to the class of complex invariant surfaces (ISO 17450-1 2011).
Theory and Application
Freeform surface is becoming ubiquitous in industrial products, either for functional or aesthetical reasons. The geometry of freeform surfaces cannot be described by a single universal equation and it has a great influence on the performances of a product (Jiang and Whitehouse 2012). Many types of surfaces are defined as freeform by industry: e.g., off-centred rotational optics, toroidal, etc. These are mathematically not true freeform surfaces but they do have an axis, however this axis does not pass through the functional surface. What follows is also applicable to these quasi-freeform surfaces. Here there are described two types of freeform applications: freeform optics (see Fig. 1)...
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