Blending of mesh objects to parametric surface

• A blending technique for heterogeneous surface representations, mesh and parametric surface is introduced.
• The resulting surface from the blending is called Hybrid PN Parametric Surface which is a mixed mesh and parametric surface.
• The generated Hybrid PN Parametric Surface is a watertight B-Rep model.
• The transition between the mesh and the parametric surface is smooth and G1 continuous to both ends.
• Fairing of the transition is conducted by minimizing the Thin Plate Energy with boundary conditions.

This paper proposes a blending scheme to blend a triangular mesh and a NURBS surface together. The product is called a Hybrid PN Parametric Surface which is a watertight B-Rep surface model of a complex object. The hybrid surface is a compact model taking advantages of the simplicity of NURBS representation and detail geometric description of the triangular mesh model for sculptured objects. PN-Triangle is adopted in the mesh modeling scheme to facilitate a parametric representation. The compatibility between parametric represented mesh and NURBS surface boundaries is achieved by knot insertion. The proposed method also provides discussion on the relevant constraints in ensuring continuity across the blending boundaries between the mesh and the parametric surface. A correspondence between these boundaries is designated and an initial blending surface is generated as a transition between the boundaries to form a hybrid surface model. Then an energy minimization scheme subjected to the continuity constraints is employed for smoothing the transition such that the result is a geometrically smooth hybrid surface B-Rep.

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