Quadratic Non-uniform hyperbolic B-spline curves with a local parameter are presented in this paper. The changes of a local shape parameter will only affect one curve segment. With the increase or decrease of the value of a shape parameter, the given curves can move locally toward the corresponding control points or the quadratic B-spline curves, respectively. The introduced curves can be used to interpolate the control points locally. Thus, the curves unify the representation of the curves for interpolating and approximating the control polygon. The hyperbola can be represented with the introduced curves exactly.
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