Maharavo Randrianarivony Topological Transfinite Interpolations in the Multidimensional Simplex and Hypercube

Maharavo Randrianarivony Tetrahedral transfinite interpolation with B-patch faces: construction and regularity

We provide a methodology for efficiently checking whether a tetrahedral transfinite interpolation is regular. From given four triangular surfaces in form of B-patches fulfilling some compatibility conditions, we generate a transfinite interpolation defined on the unit 3D simplex. An efficient subdivision scheme is provided for a B-patch in order to obtain criteria which are verifiable in a disc...

Software pertaining to the preparation of CAD data from IGES interface for mesh-free and mesh-based numerical solvers (IntegralCAD version 0.9.1)

We focus on the programming aspect of the treatment of digitized geometries for subsequent use in mesh-free and mesh-based numerical solvers. That perspective includes the description of our C/C++ implementations which use OpenGL for the visualization and MFC classes for the user interface. We report on our experience about implementing with the IGES interface which serves as input for storage ...

Maharavo Randrianarivony Constructing a Diffeomorphism between a Trimmed Domain and the Unit Square

Implicitization of High Degree Tensor Product Cagd Entities

We focus on the implicitization of parametric CAGD entities which are supposed to be of tensor product type. The presented approach is featured by its ability to treat polynomial or rational splines having a great number of control points. For B-splines, we describe a method of exactly obtaining the Fourier coefficients without using quadrature rules. As for NURBS, a preprocessing step is neces...

Maharavo Randrianarivony Quadrilateral Removals and Generalized 2-ear Theorems

We aim at splitting a given multiply connected polygon into a set of convex quadrilaterals. Our approach consists in repeatedly removing quadrilaterals from the given polygon. We will first derive theoretical results pertaining to quadrangulation of simple polygons from the usual 2-ear theorem. Unfortunately, that theorem holds only for simply connected polygons while we are interested in quadr...