VARKON Version 1.15 1997-10-16

### Basic surface representations

VARKON supports several basic types of parametric surfaces. The first is the common bicubic parametric surface CUB_SUR. This surface can be used to interpolate positions and tangents or it can be used to approximate other surfaces. Due to the fact that many other systems also support the bicubic it is also well suited for import and export of surface data. VARKON also supports the rational form of the bicubic, RAT_SUR.

The second type of surface is a special type of conic lofting surface implemented in Varkon by G. Liden for SAAB Military Aircraft. LFT_SUR is based on the idea of a varying conic section moving along some curves while generating or sweeping the surface. 5 curves of any type are used to control the shape of each conic in the section and a 6:th curve called the spine is used to control how the section moves.

LFT_SUR is a surface of extremely high quality with a lot of built in smoothness. It is also very flexible since its mathematical formulation is totally independent of the mathematical representation of the defining curves. Any curves can be used, splines, conics, offsets or UV-curves.

Next surface type is the NURBS surface. NURBS surfaces can be created in MBS by specifying the control polygon or imported from external files or created by approximation of a surface of other type.

VARKON also includes a faceted surface. FAC_SUR is used to approximate other surfaces. Each patch in the surface is a planar triangle with the same property as a B-plane. This means that faceted surfaces can be used to produce images with hidden lines automatically removed. FAC_SUR can also be used to produce approximations suited for export to other systems.

An offset surface sur_offs is implemented in much the same way as the offset curve cur_offs. An offset surface is not a surface type of its own but rather an ordinary extension to any other surface. As for curves this means that no approximation is involved in the evaluation of an offset surface. VARKON does it the hard way by first evaluating the original surface and then "add" the offset.

The default graphical representation of a surface is based on four solid boundary curves and two dashed mid curves. The SDASHL attribute can be used to control the dashlength for the 2 mid curves. The VARKON shading functions based on OpenGL can be used to produce more realistic images of surfaces when required.

VARKON is a system based on a true parametric evaluator. This is important for the quality of different algorithms and also for the possibility of adding new curve and surface representations in the future. This has already been done at SAAB Military Aircraft with very good results. A new surface type was implemented in only a few days with practically no changes to existing code. A new evaluation routine was added of course but old routines for intersects, closest point, graphics and so on did not need any changes.

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