We consider the mixed arrangement which is composed of the central hyperplane arrangement and a sphere. We discuss the lattice of its intersection set and the relationship between the Mobius function of the mixed arra...We consider the mixed arrangement which is composed of the central hyperplane arrangement and a sphere. We discuss the lattice of its intersection set and the relationship between the Mobius function of the mixed arrangement and the original hyperplane arangement. The Mobius function of the mixed arrangement is equal to the positive or the negative Mobius function of original hyperplane arrangement. Moreover, we give an equality of the chambers and the characteristic polynomial for the mixed arrangement.展开更多
In many fields of computer science such as computer animation, computergraphics, computer aided geometric design and robotics, it is a common problem to detect thepositional relationships of several entities. Based on...In many fields of computer science such as computer animation, computergraphics, computer aided geometric design and robotics, it is a common problem to detect thepositional relationships of several entities. Based on generalized characteristic polynomials andprojective transformations, algebraic conditions are derived for detecting the various positionalrelationships between two planar conies, namely, outer separation, exterior contact, intersection,interior contact and inclusion. Then the results are applied to detecting the positionalrelationships between a cylinder (or a cone) and a quadric. The criteria is very effective andeasier to use than other known methods.展开更多
基金Supported by the National Natural Science Foundation of China(10471020)
文摘We consider the mixed arrangement which is composed of the central hyperplane arrangement and a sphere. We discuss the lattice of its intersection set and the relationship between the Mobius function of the mixed arrangement and the original hyperplane arangement. The Mobius function of the mixed arrangement is equal to the positive or the negative Mobius function of original hyperplane arrangement. Moreover, we give an equality of the chambers and the characteristic polynomial for the mixed arrangement.
文摘In many fields of computer science such as computer animation, computergraphics, computer aided geometric design and robotics, it is a common problem to detect thepositional relationships of several entities. Based on generalized characteristic polynomials andprojective transformations, algebraic conditions are derived for detecting the various positionalrelationships between two planar conies, namely, outer separation, exterior contact, intersection,interior contact and inclusion. Then the results are applied to detecting the positionalrelationships between a cylinder (or a cone) and a quadric. The criteria is very effective andeasier to use than other known methods.
