A fresh look at surface modeling

Solid modelers still need surface modeling to form complex surfaces. The surface model of a racing ski helmet was generated in Cadkey Workshop V21 by Louis Garneau Sports Inc., Quebec, Canada, ( ). Surfaces can be used to design structural elements which conform to the shape of aerodynamic and ergonomic surfaces. An equation defines the shape of every curve and curves define a surface. Foundation curve geometry is used to create surfaces which are trimmed and filleted to produce a finished part. With so much buzz surrounding solid modeling, why should anyone bother with surface modeling? Because even with the best of today's capable solid modelers, there are times only surface-modeling functions can properly shape a part. A little history, a little math, and a little comparison between surface and solid modeling can help explain the role of modern surface modelers. Surface modeling was developed in the automotive and aerospace industries in the late 1970s to design and manufacture complex shapes. Nurbs -- nonuniform rational B-splines -- and cubic-surface formats appeared early and remain the primary spline and surface formats used throughout the CAD industry. Nurbs and cubics are supported by IGES (Initial Graphics Exchange Specification), a neutral file format for exchanging data between CAD systems. Nurbs and cubic formats are represented in a computer by polynomial equations generated by a CAD system, and onscreen through the location and shape of curves and surfaces. For example, the equation of a line, a first-degree polynomial, has this form Y = ax + b The equation for a parabola, a second-degree polynomial, has the form Y = ax2 + bx + c And the equation of a cubic spline, a third-degree polynomial, looks like Y = ax3 + bx2 + cx + d The more terms in the polynomial equation, the more "shape"