Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The paper deals with the construction of bivariate quartic splines on Poll–Sabin triangulations. In particular, it provides a spline space that is C2C2 everywhere except across some edges of the refined triangulation. The splines that belong to this space can be described uniquely with interpolation values and derivatives of order at most two. Moreover, they can be represented in a locally supported basis that forms a convex partition of unity. As an application of this result, quasi-interpolants that reproduce polynomials of degree four are derived.
['Jan Grošelj', 'Marjeta Krajnc']
I am writing a research paper on a idea Quartic splines on Powell–Sabin triangulations ☆
[{"from": "human", "value": "I am writing a research paper on a idea Quartic splines on Powell\u2013Sabin triangulations \u2606"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The paper deals with the construction of bivariate quartic splines on Poll\u2013Sabin triangulations. In particular, it provides a spline space that is C2C2 everywhere except across some edges of the refined triangulation. The splines that belong to this space can be described uniquely with interpolation values and derivatives of order at most two. Moreover, they can be represented in a locally supported basis that forms a convex partition of unity. As an application of this result, quasi-interpolants that reproduce polynomials of degree four are derived."}]