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Area-Preserving Geometric Hermite Interpolation. (arXiv:1810.01285v1 [math.NA])
来源于:arXiv
In this paper we establish a framework for geometric interpolation with exact
area preservation using B\'ezier cubic polynomials. We show there exists a
family of such curves which are $5^{th}$ order accurate, one order higher than
standard geometric Hermite interpolation. We prove this result is valid when
the curvature at the endpoints does not vanish, and in the case of vanishing
curvature, the interpolation is $4^{th}$ order accurate. The method is
computationally efficient and prescribes the parametrization speed at endpoints
through an explicit formula based on the given data. Additional accuracy (i.e.
same order but lower error constant) may be obtained through an iterative
process to find optimal parametrization speeds which further reduces the error
while still preserving the prescribed area exactly. 查看全文>>