A vector valued interpolation scheme for a pentagon is described which is compatible with surface patches which have a rectangular domain of definition. Such a scheme could be useful in computeraided geometric design problems, where a pentagonal patch occurs within a rectangular patch framework.

Compared to single-hole orifices (SOs), multi-hole orifices (MOs) have smaller orifice sizes and various patterns of orifice distribution. The geometric description of MOs is more complex, increasing the difficulty of MO structural design. Therefore, it is worthwhile to investigate the key factors affecting MO throttle or flow control characteristics and to develop a general MO design method. T...

We present techniques needed for editing generative designs. When a feature is edited, all features attached later must be reevaluated to satisfy the required constraints and shape references in the initial design. We describe name matching techniques that support the design reevaluation procedure. The algorithms account for failed or multiple matches. The matching uses a naming schema based on...

The effects of computer-assisted and distance learning of geometric modeling and computer aided geometric design are studied. It was shown that computer algebra systems and dynamic geometric environments can be considered as excellent tools for teaching mathematical concepts of mentioned areas, and distance education technologies would be indispensable for consolidation of successfully passed t...

Some recent methods of Computer Aided Geometric Design are related to the apolar bilinear form, an inner product on the space of homogeneous multivariate polynomials of a fixed degree, already known in 19th century invariant theory. Using a generalized version of this inner product, we derive in a straightforward way some of the recent results in CAGD, like Marsden’s identity, the expression fo...

A solution to get the problem off, have you found it? Really? What kind of solution do you resolve the problem? From what sources? Well, there are so many questions that we utter every day. No matter how you will get the solution, it will mean better. You can take the reference from some books. And the fundamentals of computer aided geometric design is one book that we really recommend you to r...

We give an overview of resultant theory and some of its applications in computer aided geometric design. First, we mention different formulations of resultants, including the projective resultant, the toric resultant, and the residual resultants. In the second part we illustrate these tools, and others projection operators, on typical problems as surface implicitization, inversion, intersection...

An algebra for geometric reasoning is developed that is amenable to software implementation. The features of the algebra are chosen to support geometric programming of the variety found in computer graphics and computer aided geometric design applications. The implementation of the algebra in C++ is described, and several examples illustrating the use of this software are given.

In this paper, we introduce and study a new implicit representation of parametric curves and parametric surfaces . We show how these representations which we will call the matrix implied, establish a bridge between geometry and linear algebra, thus opening the possibility of a more robust digital processing. The contribution of this approach is discussed and illustrated on important issues of g...