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

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.

We present algorithms for computing the differential geometry properties of intersection curves of two surfaces where the combination of two surfaces can be parametric-parametric, implicit-implicit and parametric-implicit. We derive unit tangent vector, curvature vector, binormal vector, curvature, torsion, and algorithms to evaluate the higher-order derivatives for transversal as well as tangential intersections for all three types of intersection problems.

Today, they are students in colleges and universities. Tomorrow, they will be engineers in various industrial sectors. One of the primary goals of education is to prepare people for successful careers in the real world. As in every course, students want to obtain the maximum value of a CAD related course for their future careers. They want to obtain knowledge and skills that are most practical and useful to them when they become engineers. College professors and teachers also want to provide the maximum value for students in their CAD courses. The question is: what should be included in such a CAD curriculum. This paper tries to answer some critical questions related to developing such a curriculum, from an industrial perspective, based on the authors' survey results and the first author's own (rather limited) experiences as a R&D staff for a CAD vendor. It focuses on issues related to teaching and training students on CAD systems. These include, for different roles, how much underlying mathematical foundations in CAD systems should be taught, how much computer skills and engineering knowledge the students should know, how much design methodologies related to CAD systems should be taught, and how much ability the students should develop in order to specify their CAD needs and to evaluate and choose the CAD systems most suitable for their specific applications. The paper then shares some personal experiences and suggestions from long-term CAD veterans on the essential topics of CAD education. Based on the survey results, last section concludes the paper by authors' suggestions on what should be included in CAD curriculums for different levels of students.

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