Curved splicing of copulas

First, we recall the properties of the curved section of a copula that is specified by an automorphism of the unit interval. Then, inspired by the operation of diagonal splicing of two copulas, we develop the curved splicing operation, which essentially glues together different restrictions of two copulas that share the same curved section. In order to exploit this operation in practice, we propose two new classes of semilinear copulas. Applying the curved splicing operation to members of these two classes leads to two other classes of semilinear copulas.