This paper presents a unified and mixed interpolatory and approximation subdivision scheme for triangular meshes. It can be used to solve the "popping effect" problem when switching between meshes at different levels of resolution. The scheme generates surfaces coincidence with the Loop subdivision scheme in the limit condition having the coefficient k equal 0. When k equal 1, it will be changed into a new interpolatory subdivision scheme. A new set of rules is designed for computing the newly inserted vertices around extraordinary masks. Eigen-structure analysis demonstrates that subdivision surfaces generated using the new schemes are C1 continuous. The method is a completely simple one without constructing and solving equations. The example of British Museum shell design show the great flexibility advantage of mixed subdivision design method in shell architecture, even in other industry design field.