Nurbs Technical Analysis And Its Behavior In The Hull Form Expression

NURBS(Nonniform Rational Bpline) is the most popular technology in modern surface modeling. By studying the technology of NURBS, the paper proposes some new algorithms and applies them in ship surface modeling. Chapter one briefly reviews the developing history of surface modeling, and introduces the main work of the paper. Chapter two discusses the basic theory of Bpline in detail, which is the basis of NIJRBS. The equation of k degree Bpline curve is n p(u) = ZdINj,k(u). From this equation, it can be easily seen that Bpline is composed of three parts: the control points d, (i=O,1,晻昻), the normalized B梥pline basic function NEk(u), and the points of the curve p(u). Several basic algorithms concentrate on the three parts. When the control points d1 (i=O,1,.~n) have been given, to get the points of the curve p(u) is called 搊bverse calculatIon? contrarily, it is called N S reverse calculation . Both 搊bverse calculation and 搑everse calculation?need to decide the knot vector firstly, then B梥pline basic function can be gotten from the knot vector. While the knot vector is usually calculated according to the given d, or p,. In 搑everse calculation? the first step is to parametrize the data points p,. After discussing four widely梪sed parametrization methods, combining centripetal parametrization with Forley parametrization, the paper proposes centripetal Forley arametrization. Application proves that the new method inherits its parents?merits. In 搊bverse calculation? the paper first discusses Riesenfeld method and Hartley ?Judd method, therefore, proposes a new method to calculate i~i ABSTRACT the knot vector according to the control points, which borrows the thought of global interpolation. Chapter two also introduces some other basic theories of B梥pline, such as the definition and the property of B梥pline basic function, the property of B梥pline curve and the deBoor algorithm. Since 憆everse calculation?is very complicated, the thesis specially deals with it in a whole chapter, chapter three. This chapter discusses the traditional reverse calculation method in detail firstly, and by extending a simple reverse calculation method, gives out a reverse calculation method that can be used in a more wide scope. Besides the two methods, this chapter also introduces the global interpolation method. Chapter four, discusses some theories of the B梥pline surface, and applies them to a twin skeg ship hull expressing and the presentation of general ship抯 surface. Chapter five discusses some basic theories of NURBS, compares the three expressions of NURBS curve and surface, explains the geometric meaning of weight and the concept of rational interpolation. In addition, chapter five recommends some methods on how to modify the shape of the NIJRBS curve and surface. The last chapter summarizes the whole paper...