Nurbs Surfaces Reverse Modeling Key Algorithms Research And Application

The modeling of NURBS surfaces is one of the hotspots of CAD/CAM research field, this paper makes a further discussion and study on the fundamental theory of NURBS in order to provide some practical design methods to resolve the problems in the application of the modeling of NURBS. The paper includes such contents as:Some basic theories of NURBS curves and surfaces are discussed such as the calculation of the values and derivatives, knot inserting and removing, and simplifications of some specific algorithms.The paper introduces the method of Optimal Design, which includes the non-constrained optimal design and constrained optimal design, then brings this method into the modeling of NURBS surfaces to resolve practical problems.The fitting of NURBS curves and surfaces are discussed in detail. The matrix representations of NURBS are applied in the interpolation of NURBS curves and surfaces. In order to improve the effect of approximation, the paper introduces optimal method and presents a practical optimal algorithm for approximation of NURBS curves and surfaces.The paper studies the smoothness and fairness of NURBS curves and surfaces, gives a practical and efficient global fairing method of NURBS curves, then introduces the criterion of minimum energy to deal with the smoothness of NURBS surfaces.At last the smooth blending between adjacent NURBS surfaces are discussed, which includes the joining of two adjacent NURBS surfaces along the common boundary and the adjustment of more than two NURBS surfaces at corner, also the paper gives the concrete algorithm of surface blending.The main algorithms are applied in the practical system-andreceived sound effects.