It is frequently necessary to complete the design of a surface from a specification of its boundary. Many techniques have been developed to solve this problem if the boundary is topologically a triangle or rectangle, and the curves are specified as NURBS. More complex boundaries generally require manual efforts to decompose the perimeter into topologically rectangular or triangular regions and ...

Energies of curves and surfaces together with their discrete variants play a prominent role as fairness functionals in geometric modeling and computer aided geometric design. This paper deals with a particular discrete surface energy which is expressible in terms of curve energies, and which occurs naturally in the problem of smoothing digital elevation data with tolerance zone constraints. We ...

The Bernstein-Bézier representation of polynomials is a very useful tool in computer aided geometric design. In this paper we make use of (multilinear) tensors to describe and manipulate multivariate polynomials in their Bernstein-Bézier form. As application we consider Hermite interpolation with polynomials and splines.

Commonly used boundary-based solid and surface modeling methods in traditional computer aided design are not capable of constructing configurations with large numbers of particles or complex topology. In this paper, we propose a new geometric modeling scheme, periodic surface, for material design at atomic, molecular, and meso scales. At molecular scale, periodicity of the model allows thousand...

Dupin cyclides are canal surfaces defined as envelopes of a family of oriented spheres which touch three given oriented spheres. With respect to their attractive geometric properties they are often used in Computer Aided Geometric Design and in many engineering applications. In this paper, we study these surfaces from the point of view of Lie sphere geometry. This representation enables to solv...

Fast and efficient methods of evaluation of the connection coefficients between shifted Jacobi and Bernstein polynomials are proposed. The complexity of the algorithms is O(n), where n denotes the degree of the Bernstein basis. Given results can be helpful in a computer aided geometric design, e.g., in the optimization of some methods of the degree reduction of Bézier curves.

The use of blending and filleting operations in solid modeling and computer-aided geometric design is well established. The question of filling a gap between two (or more) surface boundaries or rounding a sharp edge has been extensively investigated. The vast majority of the prior work on blending and filleting concentrated on a wide variety of fitting schemes as well as attempts to establish a...

Biographical notes: Nickolas Sapidis is an Associate Professor with the Department of Product and Systems Design Engineering of the University of the Aegean, in Greece. He received his PhD in Mechanical and Aerospace Science from the University of Rochester in 1993. N. Sapidis’ research focuses on Computer-Aided Design and Engineering and Geometric Modeling. He is the author of more than 40 pap...

Curves on surfaces play an important role in computer-aided geometric design. Because of the considerably high degree of exact curves on surfaces, approximation algorithms are preferred in CAD systems. To approximate the exact curve with a reasonably low degree curve which also lies completely on the B-spline surface, an algorithm is presented in this paper. The Hausdorff distance between the a...