Corner-based implicit patches
Multi-sided surfaces are often defined by side interpolants (also called ribbons), i.e. the surface has to connect to the ribbons with a prescribed degree of smoothness. The I-patch is such a family of implicit surfaces capable of interpolating an arbitrary number of ribbons and can be used in desig...
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Zusammenfassung: | Multi-sided surfaces are often defined by side interpolants (also called
ribbons), i.e. the surface has to connect to the ribbons with a prescribed
degree of smoothness. The I-patch is such a family of implicit surfaces capable
of interpolating an arbitrary number of ribbons and can be used in design and
approximation. While in the case of parametric surfaces describing ribbons is a
well-discussed problem, defining implicit ribbons is a different task. This
paper will introduce corner I-patches, a new representation that describes
implicit surfaces based on corner interpolants. Those may be defined with much
simpler surfaces, while the shape of the patch will depend on a handful of
scalar parameters. Continuity between patches will be enforced via constraints
on these parameters. Corner I-patches have several favorable properties that
can be exploited for example in volume rendering or approximation. |
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DOI: | 10.48550/arxiv.2207.00806 |