An interpolating 4-point C² ternary non-stationary subdivision scheme with tension control

In this paper we present a non-stationary 4-point ternary interpolatory subdivision scheme which provides the user with a tension parameter that, when increased within its range of definition, can generate C²-continuous limit curves showing considerable variations of shape. As a generalization we additionally propose a locally-controlled C²-continuous subdivision scheme, which allows a different tension value to be assigned to every edge of the original control polygon.