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**\(G^ 1\) interpolation of generally unrestricted cubic Bézier curves.**
*(English)*
Zbl 0621.65002

The author gives some mathematical techniques for constructing a \(G^ 1\)-continuous surface of rectangular Bézier patches to interpolate a network of cubic Bézier curves where: 1) three, four or five curves are allowed to meet at an interior network mode, and 2) pairs of adjacent nodes with four tangent curves apiece are not subject to the usual restrictions on ratios of distances between Bézier points.

The curve restrictions that are imposed are minimal. It is shown how to compute the Bézier points of patches forming a \(G^ 1\) interpolating surface over a grid of Bezier curves. In contrast to the usual situation, the grid curves are reasonably unrestricted as to the distance between Bézier points in the vicinity of grid nodes.

The curve restrictions that are imposed are minimal. It is shown how to compute the Bézier points of patches forming a \(G^ 1\) interpolating surface over a grid of Bezier curves. In contrast to the usual situation, the grid curves are reasonably unrestricted as to the distance between Bézier points in the vicinity of grid nodes.

Reviewer: A.López-Carmona

### MSC:

65D05 | Numerical interpolation |

41A05 | Interpolation in approximation theory |

41A63 | Multidimensional problems |

65D10 | Numerical smoothing, curve fitting |

### Keywords:

transfinite interpolation; rectangular Bézier patches; cubic Bézier curves; interpolating surface### Software:

MACSYMA
Full Text:
DOI

### References:

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