Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In the present paper  investigate rational two-parameter families of spheres and their envelope surfaces in Euclidean R^3. The four dimensional cyclographic model of the set of spheres in R^3 is an appropriate framework to show that a quadratic triangular Bezier patch in R^4 corresponds to a two-parameter family of spheres with rational envelope surface. The construction shows also that the envelope has rational offsets. Further  outline how to generalize the construction to obtain a much larger class of surfaces with similar properties.
['Martin Peternell', 'Boris Odehnal', 'Maria Lucia Sampoli']
I am writing a research paper on a idea On quadratic two-parameter families of spheres and their envelopes
[{"from": "human", "value": "I am writing a research paper on a idea On quadratic two-parameter families of spheres and their envelopes"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In the present paper  investigate rational two-parameter families of spheres and their envelope surfaces in Euclidean R^3. The four dimensional cyclographic model of the set of spheres in R^3 is an appropriate framework to show that a quadratic triangular Bezier patch in R^4 corresponds to a two-parameter family of spheres with rational envelope surface. The construction shows also that the envelope has rational offsets. Further  outline how to generalize the construction to obtain a much larger class of surfaces with similar properties."}]