Abstract: A process for creating from a mesh an isotopologic set of parameterized surfaces includes providing a mesh having a plurality of vertices connected by edges, defining faces, the vertices comprising regular vertices of valence 4 and irregular vertices of valence different from 4. The mesh may have a sharpness value defined on at least one vertex or edge, with a default value, the sharpness being representative of the attractiveness of the vertex or edge on the surface modeled by the mesh. The sharpness may measure the difference between the mesh as it stands at a given subdivision level and the initial mesh.

Abstract: Creating a parametric surface having a required geometrical continuity Gi from a set of parametric elementary surfaces includes providing a set of parametric elementary surfaces, each elementary surface having edges, with vertices joining adjacent edges, each elementary surface having an internal continuity Cj at least equal to the required continuity Gi, the geometrical continuity between at least two elementary surfaces across their common edge being less than the required continuity Gi. For each singular vertex, the process can include defining a system of equations linking the parameters (including control points) of the parametric elementary surfaces across edges joined to the vertex and enforcing the required geometrical continuity across the joined edges and solving the system of equations to obtain the parameters.

Abstract: A process for creating from a mesh an isotopologic set of parameterized surfaces includes providing a mesh having a plurality of vertices connected by edges, defining faces, the vertices comprising regular vertices of valence 4 and irregular vertices of valence different from 4. The mesh may have a sharpness value defined on at least one vertex or edge, with a default value, the sharpness being representative of the attractiveness of the vertex or edge on the surface modeled by the mesh. The sharpness may measure the difference between the mesh as it stands at a given subdivision level and the initial mesh.

Abstract: Creating a parametric surface having a required geometrical continuity Gi from a set of parametric elementary surfaces includes providing a set of parametric elementary surfaces, each elementary surface having edges, with vertices joining adjacent edges, each elementary surface having an internal continuity Cj at least equal to the required continuity Gi, the geometrical continuity between at least two elementary surfaces across their common edge being less than the required continuity Gi. For each singular vertex, the process can include defining a system of equations linking the parameters (including control points) of the parametric elementary surfaces across edges joined to the vertex and enforcing the required geometrical continuity across the joined edges and solving the system of equations to obtain the parameters.