We explore the one-to one correspondence between parametric surfaces in 3D and two dimensional color images
in the RGB color space.
For the case of parametric surfaces defined on general parametric domains recently a new approximate
geometric representation has been introduced<sup>1</sup> which also works for manifolds in higher dimensions. This new
representation has a form which is a generalization to the B´ezier representation of parametric curves and tensorproduct
The main purpose of the paper is to discuss how the so generated technique for modeling parametric surfaces can be used for respective modification (re-modeling) of images. We briefly consider also some of the possible applications of this technique.
This article is a survey of the current state of the art in vertex-based marching algorithms for solving systems of
nonlinear equations and solving multidimensional intersection problems. It addresses also ongoing research and
future work on the topic. Among the new topics discussed here for the first time is the problem of characterizing
the type of singularities of piecewise affine manifolds, which are the numerical approximations to the solution
manifolds, as generated by the most advanced of the considered vertex-based algorithms: the Marching-Simplex
algorithm. Several approaches are proposed for solving this problem, all of which are related to modifications,
extensions and generalizations of the Morse lemma in differential topology.
Expo-rational B-splines have been introduced in 2002 and by now have been shown to exhibit certain 'super-properties'
compared to ordinary polynomial B-splines. The Euler Beta-function B-splines, a polynomial version
of the expo-rational B-splines, has been introduced very recently, and has been shown to share some of the
'super-properties' of the expo-rational B-splines. In this paper we discuss several of the ways in which these
'superproperties' can be used to enhance the theory of polynomial spline wavelets and multiwavelets.