We present some new methods for parameterizing the triangle mesh surface （TMS） which result from the Marching Cubes （MC） algorithm. The methods apply to surfaces of genus zero and the parameter domain is a unit sp...We present some new methods for parameterizing the triangle mesh surface （TMS） which result from the Marching Cubes （MC） algorithm. The methods apply to surfaces of genus zero and the parameter domain is a unit sphere. We take advantage of some special properties of the TMS resulting from the MC algorithm to obtain simple, computational efficient representations of the nearest neighbor coordinates and utilize these coordinates in the characterization of the parameterization by means of systems of equations which are solved iteratively. Examples and comparisons are presented.展开更多
In this paper,we introduce the Minkowski measure of asymmetry for the spherical bodies of constant width.Then we prove that the spherical balls are the most symmetric bodies among all spherical bodies of constant widt...In this paper,we introduce the Minkowski measure of asymmetry for the spherical bodies of constant width.Then we prove that the spherical balls are the most symmetric bodies among all spherical bodies of constant width,and the completion of the spherical regular simplexes are the most asymmetric bodies.展开更多
基金supported by the US Army Research Office under contract W911NF-05-1-0301the US National Science Foundation.
文摘We present some new methods for parameterizing the triangle mesh surface （TMS） which result from the Marching Cubes （MC） algorithm. The methods apply to surfaces of genus zero and the parameter domain is a unit sphere. We take advantage of some special properties of the TMS resulting from the MC algorithm to obtain simple, computational efficient representations of the nearest neighbor coordinates and utilize these coordinates in the characterization of the parameterization by means of systems of equations which are solved iteratively. Examples and comparisons are presented.
基金Supported by the National Natural Science Foundation of China(12071334,12071277)。
文摘In this paper,we introduce the Minkowski measure of asymmetry for the spherical bodies of constant width.Then we prove that the spherical balls are the most symmetric bodies among all spherical bodies of constant width,and the completion of the spherical regular simplexes are the most asymmetric bodies.
