Recently, it was shown that a bi-cubic patch complex with n-sided holes can be completed into a curvature-continuous () surface by n-sided caps of degree bi-5 that offer good and flexible shape (Karciauskas and Peters, 2013). This paper further explores the space of n-sided caps of degree bi-5 but focuses on functionals to set degrees of freedom and to optimally propagate and average out curvature from the bi-cubic complex. 
Biquintic G 2 surfaces via functionals