Abstract
The construction of quadratic $C^1 $ surfaces from B-spline control points is generalized to a wider class of control meshes capable of outlining arbitrary free-form surfaces in space. Irregular meshes with nonquadrilateral cells and more or less than four cells meeting at a point are allowed so that arbitrary free-form surfaces with or without boundary can be modeled in the same conceptual frame work as tensor-product B-splines. That is, the mesh points serve as control points of a smooth piecewise polynomial surface representation that is local, evaluates by averaging, and obeys the convex hull property. For a regular region of the input mesh, the representation reduces to the standard quadratic spline. In general, a surface spline is represented by Bernstein–Bezier patches of degree two and three with derivatives matching across boundaries after local reparametrization. According to the user’s choice, these patches can be polynomial or rational, and three-sided, four-sided, or a combination thereof.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
