Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  studies triangulations obtained from Poisson disc sampling. The Poisson disc sampling strategy with radius parameter α can be used to obtain a set of points in the interior or on the boundary of a given solid object in the plane. Using this sampling,  study a certain triangulation from its α-complex which results in two contributions. First, if  choose the same parameter α for the Poisson disc sampling and for the solid α-complex,  prove that all the triangles in the complex have aspect ratio less or equal than , which is only three times the aspect ratio of an equilateral triangle. Moreover,  prove that this bound is tight. Second,  establish a condition on the parameter α that allows to recover, with topological guarantees, the original solid object from the α-complex representation.
['Esdras Medeiros', 'Luiz Velho', 'Hélio Lopes', 'Thomas Lewiner']
I am writing a research paper on a idea ON 2D SOLID α-COMPLEXES OF POISSON DISC SAMPLINGS
[{"from": "human", "value": "I am writing a research paper on a idea ON 2D SOLID \u03b1-COMPLEXES OF POISSON DISC SAMPLINGS"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  studies triangulations obtained from Poisson disc sampling. The Poisson disc sampling strategy with radius parameter \u03b1 can be used to obtain a set of points in the interior or on the boundary of a given solid object in the plane. Using this sampling,  study a certain triangulation from its \u03b1-complex which results in two contributions. First, if  choose the same parameter \u03b1 for the Poisson disc sampling and for the solid \u03b1-complex,  prove that all the triangles in the complex have aspect ratio less or equal than , which is only three times the aspect ratio of an equilateral triangle. Moreover,  prove that this bound is tight. Second,  establish a condition on the parameter \u03b1 that allows to recover, with topological guarantees, the original solid object from the \u03b1-complex representation."}]