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INTRODUCTION The technology encompasses two main fields. Either creating aesthetic ( Class A Surfaces ) that also perform a function; for example, car bodies and consumer product outer forms, or technical surfaces for components such as gas turbine blades and other fluid dynamic engineering components. CAD software packages use two basic methods for the creation of surfaces. The first begins with construction curves ( Splines ) from which the 3D surface is then swept (section along guide rail) or meshed (lofted) through. ]] The second method is direct creation of the surface with manipulation of the surface poles/control points. From these initially created surfaces, other surfaces are constructed using either derived methods such as offset or angled extensions from surfaces; or via bridging and blending between groups of surfaces. ]] SURFACES Freeform surface, or '''freeform surfacing''', is used in CAD and other Computer Graphics software to describe the skin of a 3D geometric element. Freeform surfaces do not have rigid radial dimensions, unlike regular surfaces such as Plane s, Cylinder s and Conic surfaces. They are used to describe forms such as Turbine blades, car bodies and boat Hull s. 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. Most systems today use Nonuniform Rational B-spline (NURBS) mathematics to describe the Surface forms; however, there are other methods such as Gorden Surface s or Coon Surface s . The forms of freeform surfaces (and curves) are not stored or defined in curvature. Some CAD systems use the term ''order'' instead of ''degree''. The order of a polynomial is one greater than the degree, and gives the number of Coefficient s rather than the greatest Exponent . The poles (sometimes known as '' Control Point s'') of a surface define its shape. The natural surface edges are defined by the positions of the first and last poles. (Note that a surface can have trimmed boundaries.) The intermediate poles act like magnets drawing the surface in their direction. The surface does not, however, go through these points. The second and third poles as well as defining shape, respectively determine the start and Tangent angles and the Curvature . In a single patch surface ( Bézier Surface ), there is one more pole than the degree values of the surface. Surface patches can be merged into a single NURBS surface; at these points are knot lines. 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. These are values on the surface ranging from 0 to 1, used in the mathematical definition of the surface and for defining paths on the surface: for example, a trimmed boundary edge. Note that they are not proportionally spaced along the surface. A curve of constant U or constant V is known as an isoperimetric curve, or U (V) line. In CAD systems, surfaces are often displayed with their poles of constant U or constant V values connected together by lines; these are known as ''control polygons''. 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. If two curved areas of the panel have different radii of curvature and are blended 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
To achieve a high quality NURBS or Bezier 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 fairing of BIW concept surfaces to production surface). Obviously for ship building this need not be so tight and for precision gears and medical devices it is much finer. HISTORY OF TERMS The term lofting originally came from the shipbuilding industry where loftsmen worked on "barn loft" type structures to create the keel and bulkhead forms out of wood. This was then passed on to the aircraft then automotive industries who also required streamline shapes. The term spline also has nautical origins coming from East Anglian dialect word for a thin long strip of wood (probably from old English and Germanic word splint). FREEFORM SURFACE MODELLING SOFTWARE
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