NURBS曲面与隐式曲面求交的计算机实现及应用

阐述了参数曲面与隐式曲面求交的算法原理，给出计算机实现方法及交点可能的分布示意图，将其应用于基于NURBS的船体曲面与任意平面的求交中，并针对船体曲面的特点指出应用过程中应注意的问题。

Implementation and Application of Intersection between NURBS-based Surface and Implicit Surface

The paper applies the algorithm for intersection of parametric surface and implicit surface to ship hull surface based on UNRBS. The parametric formula are substi tuted into the implicit surface equation and then the nonlinear two dimensional equation on parametric domain is obtained the theory of extracting isocurve in two dimension scalar field is used to solve the equation instead of iterative algorithm. The parametric domain is devided along u and v direction equidistantly or non equidistantly respectively, forming rectangle meshes to overcome possible divergent connection of intersection points. Every rectangular cell is divided into four triangular parts by its two diagonals. Isocurve extraction is performed directly in the triangulars. The intersection curve is the mapping of the isocurves on the parametric surface. The 3D display of intersection curve of a ship hull and an arbitrary plane is given, as well as the frame plans of bulbous bow and stern. Meshes of the parametric domain should be more dense on the regions where the cure crrvature is lange such as bulbous bow, and vice versa. The method is simple and practical compared with iterative process.