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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"

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Rapid Prototyping Services
Rapid prototyping automates the fabrication of a prototype part from a three-dimensional (3-D) CAD drawing. These physical models convey more complete information about the product earlier in the development cycle.
CNC Machining Services
CNC machining services use fast, repeatable, and programmable machines which can function while unattended in order to manufacture parts quickly and efficiently.
Coordinate Measuring Machines (CMM)
Coordinate measuring machines (CMMs) are mechanical systems designed to move a measuring probe to determine the coordinates of points on a work piece surface.
Surface Plates
Surface plates provide a precision reference surface for layout, checking, machining and gaging work.
Linear Guides and Rails
Linear guides and rails provide a smooth, precision, guiding surface on which the rolling element of a linear bearing rides.

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##### Topics of Interest

Figure 10.1: A B-spline spiral. Compared with composite B zier curves, a more complete theory of splines is found in B-spline curves. These days, B-spline curves are often referred to as NURBS...

Figure 13.1: Conics in the circular model of the projective plane. We shall now describe the main geometric features of this curve and surface representation. Much of the discussion of B-spline...

A free-form-modeling technology based on N-sided surfaces eliminates the tedious task of laying out square patch networks. A car object is being designed with Nurbs. Such models contain curves that...

The equation of a B-spline surface follows directly from the equation of a B-spline curve. This relationship is analogous to that between B zier curves and surfaces. Furthermore, we define the...

Overview NURBS is short for " Non- Uniform Rational B-splines. This is a somewhat unlucky naming convention, since B-splines are non-uniform to begin with. We give an outline of B-spline curves in...

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