BLIDIA , Ahmed

In CAD systems, a piecewise polynomial function is behind any curve, surface or scalar field representation. Thus, it is important to analyse the properties of the spaces of piecewise polynomial functions. In this thesis, we study commutative algebra tools that can be used to analyze the dimension of piecewise polynomial spaces, and to...

We analyze the space of differentiable functions on a quad-mesh $\cM$, which are composed of 4-split spline macro-patch elements on each quadrangular face. We describe explicit transition maps across shared edges, that satisfy conditions which ensure that the space of differentiable functions is ample on a quad-mesh of arbitrary topology....

Given a topological complex $M$ with glueing data along edges shared by adjacent faces, we study the associated space of geometrically smooth spline functions that satisfy differentiability properties across shared edges. We present new and efficient constructions of basis functions of the space of $G^{1}$-spline functions on quadrangular...