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Hermite Interpolation by Pythagorean Hodograph Quintics
| Content Provider | Scilit |
|---|---|
| Author | Farouki, R. T. Neff, C. A. |
| Copyright Year | 1995 |
| Description | The Pythagorean hodograph (PH) curves are polynomial parametric curves whose hodograph (derivative) components satisfy the Pythagorean condition for some polynomial . Thus, unlike polynomial curves in general, PH curves have arc lengths and offset curves that admit exact rational representations. The lowest-order PH curves that are sufficiently flexible for general interpolation/approximation problems are the quintics. While the PH quintics are capable of matching arbitrary first-order Hermite data, the solution procedure is not straightforward and furthermore does not yield a unique result--there are always four distinct interpolants (of which only one, in general, has acceptable "shape" characteristics). We show that formulating PH quintics as complex-valued functions of a real parameter leads to a compact Hermite interpolation algorithm and facilitates an identification of the "good" interpolant (in terms of minimizing the absolute rotation number). This algorithm establishes the PH quintics as a viable medium for the design or approximation of free-form curves, and allows a one-for-one substitution of PH quintics in lieu of the widely-used "ordinary" cubics. |
| Related Links | https://www.ams.org/mcom/1995-64-212/S0025-5718-1995-1308452-6/S0025-5718-1995-1308452-6.pdf |
| Ending Page | 1609 |
| Page Count | 21 |
| Starting Page | 1589 |
| ISSN | 00255718 |
| e-ISSN | 10886842 |
| DOI | 10.2307/2153373 |
| Journal | Mathematics of Computation |
| Issue Number | 212 |
| Volume Number | 64 |
| Language | English |
| Publisher | Duke University Press |
| Publisher Date | 1995-10-01 |
| Access Restriction | Open |
| Subject Keyword | Artificial Intelligence Curves Quintics Hermite Interpolation Hodograph Polynomial Pythagorean Sigma |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Algebra and Number Theory Computational Mathematics |
