This paper elaborates the implementation of boundary evaluation of interval-based manifold and non-manifold solid models, based on the interval geometric representation and graph-based data structure for interval geometries. Boundary evaluation of 2D interval objects is introduced first. The paper then focuses on boundary evaluation of 3D interval objects based on the refinement of vertex, edge, face and shell nodes. Examples are given to illustrate the method. Copyright

This paper introduces and develops an interval geometric representation for curved objects. The representation is based on rounded interval arithmetic and addresses robustness problems in current boundary representation solid modelers operating in floating point arithmetic. These problems include topology violation (such as gaps and inappropriate intersections), incidence asymmetry, and incidence intransitivity. The concepts of interval polynomial spline curves and surface patches are employed in this context. A graph-based data structure incorporating the special features of interval geometries is developed and extended to represent nonmanifold objects. Copyright

The design of geometric shapes with physical constraints, such as hydrodynamic and aerodynamic constraints reflecting the functionality of the shapes, remains an important problem in CAGD. This paper presents a method to design surfaces by incorporating physical constraints involving surface normal vectors. The design of functional surfaces is formulated as a linear problem using vector calculus. The final surface is an integral non-uniform B-spline surface, which is the solution of the linear equation system resulting from the least-squares fitting of the given grid points and the normal vectors at these points. The geometric design of propeller blade surfaces in conjunction with hydrodynamic analysis illustrates the method. Copyright

In this paper, the necessary and sufficient conditions for two adjacent BEzier surface patches of arbitrary degrees joining Gn-continuously along a common boundary curve are presented. These conditions are represented directly by the two surface patches, or via an intermediate surface patch. Configurations of the coefficient functions attached to the adjacent B

The problem of ensuring compatibility of mixed partial derivative vectors of surface patches joining G2-continuously around a common nodepoint is essential in modelling G2-continuous nsided surfaces. Although the compatibility constraints can be removed by using C2 Gregory patches, these patches have singularities at their comer points. This paper presents conditions for ensuring the compatibility of the mixed partial derivative vectors of surface patches joining GZ-continuously around a common nodepoint. After investigating the solvability of these compatibility conditions, a new solution method exploiting G3-continuity of surface patches at a common nodepoint is given. Example surfaces based on this solution method are also provided.