DP curves, which possess the shape-preserving property and linear complexity evaluation algorithm, occupy a significantly important place in computer aided geometric design. Thus to do the research on the DP curves algorithms has a positive meaning. Aphirukmatakun et al. presented a degree elevation algorithm of DP curves based on the transformation between the DP basis and power basis. At the ...

Lachance. M.A. and A.J. Schwartz. Four point parabolic interpolation, Computer Aided Geometric Design 8 (1991) 143-149. We show that four points in the plane may be interpolated by one or two parabolas or possibly by no parabola, depending on the configuration of points. We provide methods for distinguishing the cases and constructing the parabolas.

A number of applications in computer-aided manufacturing, CAD, and computer-aided geometric design ask for triangulating pieces of material with defects. These tasks are known collectively as constrained triangulations. Recently, a powerful architecture called the reconng-urable mesh has been proposed: in essence, a reconngurable mesh consists of a mesh-connected architecture augmented by a dyn...

One day, you will discover a new adventure and knowledge by spending more money. But when? Do you think that you need to obtain those all requirements when having much money? Why don't you try to get something simple at first? That's something that will lead you to know more about the world, adventure, some places, history, entertainment, and more? It is your own time to continue reading habit....

This paDer presents the initial results Of our work in using the Computer Aided Geometric Design (CAGD) representations and models as a basis for the visual recognition of 3-D objects for obotic applications. We describe some techniques and algorithms Which allow the generation of computer representations and geometric models of complicated realizable 3-0 objects in a systematic manner. These r...

This paper deals with a kind of design of a ruled surface. It combines concepts from the fields of computer aided geometric design and kinematics. A dual unit spherical Bézierlike curve on the dual unit sphere (DUS) is obtained with respect the control points by a new method. So, with the aid of Study [1] transference principle, a dual unit spherical Bézier-like curve corresponds to a ruled sur...

In this article, optimal properties of the Bernstein basis of polynomials are revisited. In particular, these include optimal shape preserving properties and optimal stability for the evaluation in computer aided geometric design, minimal conditioning of its collocation matrices and fastest convergence rates of the corresponding iteration approximation property. Recent advances on stable evalua...

Geometric problems originating in architecture can lead to interesting research and results in geometry processing, computer aided geometric design, and discrete differential geometry. In this article we survey this development and consider an important problem of this kind: Discrete surfaces (meshes) which admit a multi-layered geometric support structure. It turns out that such meshes can be ...

Ahn, Lee, Park and Yoo proved that the best constrained degree reduction of a polynomial f in L2-norm equals the best weighted Euclidean approximation of the Bernstein–Bézier coefficients of f in a paper, published in the journal, Computer Aided Geometric Design 21 (2) (2004) 181–191. In this note, we point out an error in their paper and give the correct result.  2005 Elsevier B.V. All rights...

Zheng, J., G Wang and Y. Liang, Curvature continuity between adjacent rational B&ier patches, Computer Aided Geometric Design 9 (1992) 321-335. This paper discusses the cutvature continuity between two adjacent rational BCzier surfaces which may be rectangular or triangular patches. The necessary and sufficient conditions are derived, and further, a series of simple sufficient conditions are de...