Managing the shape of planar splines by their control polygons (Q1801864)
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scientific article; zbMATH DE number 218443
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Managing the shape of planar splines by their control polygons |
scientific article; zbMATH DE number 218443 |
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Managing the shape of planar splines by their control polygons (English)
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6 September 1993
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The following shape-preservation theorem is proved for uniform planar quadratic \((C^ 1)\) and cubic \((C^ 2)\) \(B\)-splines and also for beta2- splines: ``Every spline-curve segment has essentially the same shape characterization as the corresponding 4-points control polygon.'' The possible control polygons defined separately on each set of four consecutive control points are of the following types: convex or hyperconvex (concave or hyperconcave), linear, inflected or looped polygons.
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planar \(B\)-splines
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shape-preservation
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interactive design
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control polygon
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0.8913921
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0.87405586
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0.86600286
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0.86568934
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