Bicubic splines and biquartic polynomials
The paper proposes a new efficient approach to computation of interpolating spline surfaces. The generalization of an unexpected property, noticed while approximating polynomials of degree four by cubic ones, confirmed that a similar interrelation property exists between biquartic and bicubic polyno...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2016-02-01
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| Series: | Open Computer Science |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/comp-2016-0001 |
| Summary: | The paper proposes a new efficient approach
to computation of interpolating spline surfaces. The generalization
of an unexpected property, noticed while approximating
polynomials of degree four by cubic ones,
confirmed that a similar interrelation property exists between
biquartic and bicubic polynomial surfaces as well.
We prove that a 2×2-component C1 -class bicubic Hermite
spline will be of class C2 if an equispaced grid is used and
the coefficients of the spline components are computed
from a corresponding biquartic polynomial. It implies that
a 2×2 uniform clamped spline surface can be constructed
without solving any equation. The applicability of this biquartic
polynomials based approach to reducing dimensionalitywhile
computing spline surfaces is demonstrated
on an example. |
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| ISSN: | 2299-1093 |