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...

ÐIn this paper, we develop integrated techniques that unify physics-based modeling with geometric subdivision methodology and present a scheme for dynamic manipulation of the smooth limit surface generated by the (modified) butterfly scheme using physics-based aforceo tools. This procedure-based surface model obtained through butterfly subdivision does not have a closed-form analytic formulatio...

Gerald Farin was born on March 20, 1953, and passed away on January 14, 2016. The authors of this note feel that his contributions to CAD and CAGD are so extensive andmultifaceted that they deserve this special ‘‘tribute’’. Correctly, R. Sarraga emphasizes (in Section 1) Gerald Farin’s great contribution to the development of the new scientific field of Computer Aided Geometric Design (CAGD), w...

A monoid hypersurface is an irreducible hypersurface of degree d which has a singular point of multiplicity d−1. Any monoid hypersurface admits a rational parameterization, hence is of potential interest in computer aided geometric design. We study properties of monoids in general and of monoid surfaces in particular. The main results include a description of the possible real forms of the sing...