In this article an explicit method (relying on representation theory) to construct packings in Grassmannian space is presented. Infinite families of configurations having only one non-trivial set of principal angles are found using 2-transitive groups. These packings are proved to reach the simplex bound and are therefore optimal w.r.t. the chordal distance. The construction is illustrated by a...

Article history: Received 9 July 2014 Accepted 19 August 2014 Available online xxxx

In this paper we define a new linearity measure which can be applied to open planar curve segments. We have considered the sum of the distances between the curve end points and the curve centroid. We have shown that this sum is bounded from above by the length of the curve segment considered. In addition, we have proven that this sum equals the length of the curve segment only in the case of st...

This paper proposes a new approach for surface modeling. Considering that a surface is described by an atlas of overlapping disk-like patches, this model creates a joining set of implicit surfaces in order to obtain the resulting whole surface. Topological constraints linked to classical models decrease and the geometry of complex surfaces can be easily and naturally described.

Curvature formulas for implicit curves and surfaces are derived from the classical curvature formulas in Differential Geometry for parametric curves and surfaces. These closed formulas include curvature for implicit planar curves, curvature and torsion for implicit space curves, and mean and Gaussian curvature for implicit surfaces. Some extensions of these curvature formulas to higher dimensio...

This paper presents a framework for modeling, animating and morphing textured implicit models. Our hierarchical skeletal implicit surface model incorporates key-frame animation and procedural solid texturing in a unified and coherent way. Our system enables the designer to create complex special effects by synchronizing shape, animation and texture transformations.

Article history: Received 30 October 2009 Received in revised form 17 October 2010 Accepted 12 November 2010 Available online 19 November 2010

This article proposes an automatic generation method of a relation matrix for Interpretive Structural Modelling (ISM). In ISM, keywords related to the problem are selected. Then the relation between two arbitrary keyword pairs is examined. When there is a relation between these two keywords, a non-zero value such as 1 is assigned to this relation. After examining the relations of all pairs of k...

We use the auxiliary principle technique to suggest and analyze an implicit method for solving the equilibrium problems on Hadamard manifolds. The convergence of this new implicit method requires only the speudomonotonicity, which is a weaker condition than monotonicity. Some special cases are also considered.