Research On NURBS Curves And Its Application In Ship Lines

Ship lines design has been playing the important role in ship design. It is the main goal of the shipbuilder that how to improve the level of ship lines design to a high grade. Since the ship lines, including straight line, conic curve and free one, are very complex, it seems to be impossible to present them by an uniform formula without NURBS. So it is significant to study the principle and key techniques of NURBS and apply them to the practice of ship lines design.NURBS curve equation has three kinds of the equivalence form, i.e. rational fraction, rational base function and homogeneous coordinate. Each of them plays a different role respectively. NURBS curve equation contains two shape parameters, i.e. control convex and the weight factor. Moving control convex will change the shape of NURBS curve, while altering the weight factor will also vary the shape of NURBS. The great modification of shape of NURBS curve can be got by moving the control convex adaptably, while the less diversification is made when the weight factor changed.Conic is indispensable in geometric modeling and CAD/CAM system. Typically, arc and circle are the most widely used contents of the conic. They should be presented by NURBS curve reasonably and correctly.In the use of the recurrence definition and the matrix presentation of NURBS curve, the algorithm of curve is outlined from the correspondent algorithm of B-Spline, concerning on the evaluating, derivative, integral, knots inserting and degree elevating. Especially, a deep research is paid to integral. An algorithm for computing area of regions bounded by quadratic NURBS curves is presented.According to the matrix presentation of NURBS curve, ordinary interpolating algorithm on cubic NURBS curve is shown. And boundary condition and parametrization of offset data points influencing on interpolating curve is discussed.A manner is presented with which complex curves including straight line, conic or free curves can be represented precisely, and corresponding algorithm isdesigned. The curve can be C1 or C0 continuous. So all type of curves and their composites can be represented in NURBS.Although ship lines are quite complex, they are divided into some simple form, e.g. the line, the conic and the free curve. By making use of NURBS presentation of the complex curve, ship lines are uniquely presented by NURBS curve. So new method is provided for ship lines design.There will be much work worth to the continued research on NURBS curve and its application in ship lines design.