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An interpolating 4-point \(C^{2}\) ternary non-stationary subdivision scheme with tension control. (English) Zbl 1171.65326

Summary: 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 \(C^{2}\)-continuous limit curves showing considerable variations of shape.As a generalization we additionally propose a locally-controlled \(C^{2}\)-continuous subdivision scheme, which allows a different tension value to be assigned to every edge of the original control polygon.

MSC:

65D17 Computer-aided design (modeling of curves and surfaces)
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