船体曲面的NURBS表达与设计

在AutoCAD的ObjectARX开发环境中，以VC^ 为编程语言，建立了AutoCAD图形数据库与外部数据库的数据链接，采用非均匀有理B样条技术，对综合定型值点的船体曲面插值及边界条件处理进行了研究， 构造出以NURBS为统一数学表达式的船体曲面。根据投影原理，对船体曲面与任意平面的求交问题给出数值算法。首先用直线段逼近曲面的单参数曲线，在投影坐标系内求出直线段与平面的交点，再将交点映射到实际坐标系中得到真实的交点，这些点的集合即为平面与曲面的交线。

Ship hull surface′s NURBS representation and design

Using the object oriented technique, authors define the customer classes for ship hull form modeling in the ObjectARX programming environment. Through DAO database API of MFC, the connection between AutoCAD and outside database (MS Access, MS SQL Server etc.) is established. According to the points net of offset, authors give the boundary conditions, interpolate the ship hull shape with NURBS surface, and represent the ship hull form. At last, an algorithm for surface plane intersection based on projection principle is proposed. Firstly isoparametric curves are divided into line segments respectively. Then a new auxiliary space, i.e. projection coordinate system, is established. Projecting intersections between plane and line segments in auxiliary space, mapping intersections form auxiliary space into object space, intersections between NURBS surface patches and an arbitrary plane are implemented finally.