Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  give a precise mathematical formulation for the notions of a parametric patch and linear precision, and establish their elementary properties.  relate linear precision to the geometry of a particular linear projection, giving necessary (and quite restrictive) conditions for a patch to possess linear precision. A main focus is on linear precision for Krasauskas’ toric patches, which  show is equivalent to a certain rational map on \({\mathbb C}{\mathbb P}^d\) being a birational isomorphism. Lastly,  establish the connection beten linear precision for toric surface patches and maximum likelihood degree for discrete exponential families in algebraic statistics, and show how iterative proportional fitting may be used to compute toric patches.
['Luis David García-Puente', 'Frank Sottile']
I am writing a research paper on a idea Linear precision for parametric patches
[{"from": "human", "value": "I am writing a research paper on a idea Linear precision for parametric patches"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  give a precise mathematical formulation for the notions of a parametric patch and linear precision, and establish their elementary properties.  relate linear precision to the geometry of a particular linear projection, giving necessary (and quite restrictive) conditions for a patch to possess linear precision. A main focus is on linear precision for Krasauskas\u2019 toric patches, which  show is equivalent to a certain rational map on \\({\\mathbb C}{\\mathbb P}^d\\) being a birational isomorphism. Lastly,  establish the connection beten linear precision for toric surface patches and maximum likelihood degree for discrete exponential families in algebraic statistics, and show how iterative proportional fitting may be used to compute toric patches."}]