Ensuring compatibility of G~2-continuous surface patches around a nodepoint

摘要

The problem of ensuring compatibility of mixed partial derivative vectors of surface patches joining G~2-continuously around a common nodepoint is essential in modelling G~2-continuous n-sided surfaces. Although the compatibility constraints can be removed by using C~2 Gregory patches, these patches have singularities at their corner points. This paper presents conditions for ensuring the compatibility of the mixed partial derivative vectors of surface patches joining G~2-continuously around a common nodepoint. After investigating the solvability of these compatibility conditions, a new solution method exploiting G~3-continuity of surface patches at a common nodepoint is given. Example surfaces based on this solution method are also provided.