Abstract
Algebraic curve plays an important role in geometric modelling. In order to improve algebraic curve’s flexibility, we construct point-tangent interpolating piecewise algebraic curve with shape parameters. We first construct degree three and degree four point-tangent interpolating algebraic curves when the number of the given points is three or four. The continuity of the curve is also provided. We then discuss the issue of smooth joint between curve segments. Finally, some practical examples are given to show the effectiveness of this new method.
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