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**Polyhedral subdivision methods for free-form surfaces.**
*(English)*
Zbl 0637.65144

Polyhedral subdivision is a powerful technique for designing free-form surfaces. It is not only a recipe method for handling n-sided regions for all values of n, but also a good candidate to be employed in a geometric modeling context. A surface or solid object can be designed by a polyhedral mesh of point that no longer needs to be topologically rectangular. Initially, the generated surface maintains all the features of the B-spline scheme such as variation diminishing and convex hull properties, etc. Additionally, it is shown that the boundary curves of such a surface can be controlled by the shape of the boundary polygons of the defining polyhedron. This is important since it is, sometimes, desirable to achieve discontinuity of slope or sharp edges on the surface. Furthermore, the user has the choice of interpolating some or all of the points of the network and thus increasing local control capability. A scheme for representing surfaces passing through data points on irregular networks, can, therefore, be devised.

Reviewer: T.Rapesák

### MSC:

65S05 | Graphical methods in numerical analysis |

65D15 | Algorithms for approximation of functions |

65D07 | Numerical computation using splines |

53A05 | Surfaces in Euclidean and related spaces |

68U99 | Computing methodologies and applications |

51N05 | Descriptive geometry |