Surface modeling technique
Each surface modeling software offers unique methods for creating and working with surface models, depending on the application, such as engineering, illustration, or animation. Polygonal modelling is the basic form of surface modelling that produces lower-quality surfaces without precise curvature control. Polygonal modeling creates surfaces that are quick and easy to modify, and this is common for applications such as character design for games. Most CAD systems use non-uniform rational basis spline (NURBS) or non-uniform rational B-spline (NURBS) mathematics to produce accurate curves and surfaces for surface modelling.
Curves and surfaces are the principal elements of surface models created using NURBS technology. Curves provide the basic form and geometry necessary for constructing surfaces. A NURB curve is a complex mathematical spline representation that includes control points. A spline is a curve that uses a series of control points and other mathematical principles to define the location and form of the curve. The term spline comes from the flexible spline devices used by shipbuilders and drafters to draw smooth shapes. Spline control points typically lie some distance from the curve and are used to define the curve shape and change the curve design (see Figure). Typically, adding control points to a spline increases the complexity of the curve. Surface modeling uses splines because of their ease and accuracy of construction and evaluation and their ability to approximate complex shapes through curve design.
A surface model usually includes multiple NURB surfaces known as patches. Patches fit together using different levels of mathematical formulas to create what is known as geometric continuity. In the simplest terms, geometric continuity is the combining of features into a smooth curve. In actual practice, geometric continuity is a complex mathematical analysis of the shapes used to create a smooth curve. The figure shows NURBS used to design a surface. NURB geometry offers the ability to represent any necessary shape, from lines to planes to complex free-form surfaces. Examples of applications for freeform shapes include automobile and ship design and ergonomic consumer products. The figure shows a surface model of a sailboat with standard and freeform geometric shapes.
Creating Surfaces
Common methods for creating surfaces include direct and procedural modeling and surface editing. Different surface modeling techniques can often be applied to achieve the same objective. Usually, a combination of methods is required to develop a complete surface model. Surface modeling, like other forms of CADD, requires detailed knowledge of software tools and processes and knowing when each tool and process is best suited for a specific task.
Surface modeling typically involves creating a series of curves that form the spans for defining a surface. Transition surfaces are added as needed to fill gaps within the model. Direct surface modelling is a basic method for developing existing surfaces created using multiple curves by adjusting the position of the surface control points or poles (see Figure). Another approach to surface construction is the use of procedural modeling tools to create surfaces from curves. Common options include extruding a curve, sweeping a profile curve along a path curve, lofting through multiple curves, and using curves to define a boundary (see Figure).
Most surface modeling software provides tools that allow you to construct additional surfaces from initial surface geometry. Examples of these techniques are offsetting, extending, and blending surfaces. Tools are also available for trimming intersecting surfaces. The figure shows basic examples of constructing additional surfaces from initial surface shapes. Many other advanced surface modeling tools are also available. Some surface modelling packages provide the ability to manage the structure of surface objects and maintain a modelling history. For high-quality surfaces, analytical tools such as comb curves and zebra analysis are used to check the continuity of curvature so that reflections and highlights can be managed for the best aesthetic quality.
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