The goal of this paper is to propose a mathematical framework to define and analyze a general parametric form of an arbitrary nonsingular Mueller matrix. Starting from previous results about nondepolarizing matrices, we generalize the method to any nonsingular Mueller matrix. We address this problem in a six-dimensional space in order to introduce a transformation group with the same number of ...

A set of modular 2-manifold surface components has been designed that allows the assembly of free-form geometrical sculptures representing single-sided or double-sided surfaces ranging from genus 2 to genus 22. The paper describes the interplay between parameters that define the overall symmetry of the whole structure and other parameters that define the geometry of the individual modular compo...

The ruled surface is a typical modeling surface in computer aided geometric design. It is usually given in the standard parametric form. However, it can also be in the forms than the standard one. For these forms, it is necessary to determine and find the standard form. In this paper, we present algorithms to determine whether a given implicit surface is a rational ruled surface. A parametrizat...