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

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

This paper presents a method for local construction of a curvature continuous (GC2) piecewise polynomial surface which interpolates a given rectangular curvature continuous quintic curve mesh. First, we create a G'2 quintic basic curve mesh, which interpolates the same grid points, preserves the tangent slopes and curvatures but not derivative vectors at the grid points. After estimating twist and higher order mixed partial derivatives for each grid point, we generate locally the so-called C2 biquintic basic patches, which serve to compute the first and second order cross-derivative functions of the final interpolation surface. In order to match the tangents and second order derivative vectors of the original boundary curves at the grid points, these basic patches are reparametrized by 5

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.

In this paper, multiresolution models are employed in the context of reverse engineering for feature line extraction. Starting with a proper triangulation of the cloud point data as a priori, our feature line extraction algorithm has three steps: (1) establishing a Gauss normal sphere and creating multiresolution models for the Gauss sphere based on different levels of subdivisions for the sphere regions; (2) mapping the unit normal vectors of triangular faces in the multiresolution Gauss sphere and merging those connected triangular faces whose unit normal vectors fallen on the same Gauss sphere region with a given resolution to form super-faces (the collection of triangular facets with similar normal); and (3) extracting the boundaries from the super-faces and generating the feature lines from the extracted boundaries. We then use these feature lines as a base for tracing boundary curves for B-spline surface construction. Since feature lines maintain the characteristics of the original product models, in this way, we have a good chance to reconstruct B-spline surfaces with high quality. Examples are given in the paper to show the feature line extraction, the influence of the feature lines extracted under different resolutions, and the final reconstructed B-spline surfaces based on these feature lines.