Maharavo Randrianarivony Quadrilateral Removals and Generalized 2-ear Theorems

Quadrilateral Decomposition by Two-Ear Property Resulting in CAD Segmentation

The objective is to split a simply connected polygon into a set of convex quadrilaterals without inserting new boundary nodes. The presented approach consists in repeatedly removing quadrilaterals from the polygon. Theoretical results pertaining to quadrangulation of simply connected polygons are derived from the usual 2-ear theorem. It produces a quadrangulation technique with O(n) number of q...

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

Molecular Surface Decomposition Using Graphical Modeling

We aim at decomposing molecular surfaces which are in the form of Van der Waals model into a structure adapted for mesh-free modeling. We focus on the generation of spherical patches by using rational Bézier surfaces and homogeneous coordinates. We can achieve exact global continuity by using generalized stereographic projection. We support the theoretical descriptions by practical decompositio...

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

We would like to decompose a closed orientable 2-manifold with arbitrary genus g into a set of four-sided tessellants. The input surface is a triangular surface mesh representing a free-form shape. The search for canonical curves is done in two steps: finding initial curves by means of algebraic or geometric methods and improving them by using combinatorial optimization. Afterward, we perform t...