QUALITY SURFACE CONSTRUCTION

Current surface construction methods in CADCAM use para- metric polynomial equations in the form of a NURBS. This representation is ideal for computer-based implementations, allowing efficient interroga- tion. However, issues exist in constructing and manipulating such sur- faces. When constructing a NURBS surface there are difficulties in de- termining constraints such as parameterisation, tangent magnitudes and twist vectors. Controlling the geometric features like curvature profiles of sectional/longitudinal curves on a NURBS surface is problematical as is joining several such surfaces together. A cause of these difficulties in control is that the control points do not lie on the surface itself. An al- ternative approach to surface construction is to specify the curvature and construct the surface so that it satisfies the curvature constraints. Since NURBS does not directly allow this, a fundamentally different approach is required. The key is to adopt a point-based approach where the surface is defined by a small number of points lying on the surface. Intermediate points are then constructed using a recursive approach which is defined to ensure that the curvature profile between adjacent points is of a very high quality. A case study is presented that illustrates the point-based approac