A flexible and adaptable design method for the tooth crown is presented based on the direct manipulation of free-form deformation （FFD）. The correct shape of the tooth crown can be obtained by adding, modifying, and...A flexible and adaptable design method for the tooth crown is presented based on the direct manipulation of free-form deformation （FFD）. The correct shape of the tooth crown can be obtained by adding, modifying, and deleting constraint points or load points based on stretching and compressing operation. Finally, an example is given to illustrate the method to be efficient.展开更多
Let x:M → Rn be an umbilical free hypersurface with non-zero principal curvatures.Then x is associated with a Laguerre metric g,a Laguerre tensor L,a Laguerre form C,and a Laguerre second fundamental form B,which are...Let x:M → Rn be an umbilical free hypersurface with non-zero principal curvatures.Then x is associated with a Laguerre metric g,a Laguerre tensor L,a Laguerre form C,and a Laguerre second fundamental form B,which are invariants of x under Laguerre transformation group.An eigenvalue of Laguerre tensor L of x is called a Laguerre eigenvalue of x.In this paper,we classify all oriented hypersurfaces with constant Laguerre eigenvalues and vanishing Laguerre form.展开更多
文摘A flexible and adaptable design method for the tooth crown is presented based on the direct manipulation of free-form deformation （FFD）. The correct shape of the tooth crown can be obtained by adding, modifying, and deleting constraint points or load points based on stretching and compressing operation. Finally, an example is given to illustrate the method to be efficient.
基金supported by National Natural Science Foundation of China (Grant Nos.10801006,10971110,10771005)
文摘Let x:M → Rn be an umbilical free hypersurface with non-zero principal curvatures.Then x is associated with a Laguerre metric g,a Laguerre tensor L,a Laguerre form C,and a Laguerre second fundamental form B,which are invariants of x under Laguerre transformation group.An eigenvalue of Laguerre tensor L of x is called a Laguerre eigenvalue of x.In this paper,we classify all oriented hypersurfaces with constant Laguerre eigenvalues and vanishing Laguerre form.
