This paper presents a method for constructing composite surfaces based on a collection of quadrilateral patches. A global parameterization using bilinear quadrilateral meshes and FEM like minimization procedure are introduced. Smoothing conditions such as C1 and G1 are handled by constraint equation and a related duality argument is implemented. The surfaces that can be constructed in this way include conforming and non‐conforming connections (3 n 6, T‐nodes) between elementary patches. Non‐manifold surfaces are automatically treated also by this data structure. The underlying quadratic programming with linear constraints is solved by duality methods. Hierarchical data structure with bordering matrices methods are implemented to deal with local refinement (subdivision). The present work details the actual implementation for the case of Bézier patches.

A new method for surface reconstruction from an initial triangular mesh is introduced. The method transforms the mesh to a quadrilateral one and then builds a smooth surface on top of it. This approach is efficient for large collections of triangular patches, including difficult situations such as sharp junctions and n-patch vertices. During the reconstruction process, the number of mesh elements is considerably reduced. The possibility of parallel computation makes the method efficient in practice. The method is illustrated by building several free-form surfaces from a triangular mesh.

In this work, a new method for mesh simplification and surface reconstruction specifically designed for the needs of CAD/CAM engineering design and analysis is introduced. The method simplifies the original free-form face model by first constructing restricted curvature deviation regions, generating a boundary conforming finite element quadrilateral mesh of the regions, and then fitting a smooth surface over the quadrilateral mesh using the plate energy method. It is more general in scope than existing methods because it handles models with free-form faces and non-manifold geometry, not just triangular or polygonal faces. It produces a high-quality quadrilateral mesh which is suited for both finite element analysis and CAD/CAM. The smooth surface obtained by energy functional stabilization over limited curvature regions preserves the number of quadrilateral elements, and is best suited for surface modeling. The method is illustrated by building of several free-form surfaces from an arbitrary topology mesh.

Abstract Piecewise Bézier Curves are constructed using a minimization principle. Ck and GCk continuity is imposed by linear constraints. The corresponding quadratic programming with linear constraints problem is introduced and solved by duality methods. Bordering matrices methods are implemented to deal with local refinement (subdivision). The result is a versatile tool for defining/editing contours made of piecewise Bézier curves.