Injectivity of NURBS curves

Injectivity of NURBS curves

The injectivity of NURBS curve implies the curve has no self-intersection. In this paper, we propose a geometric condition on the control polygon which guarantees the NURBS curve to be injective for all possible choices of positive weights. The proof is based on the degree elevation algorithm and to...

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Veröffentlicht in:Journal of computational and applied mathematics 2016-08, Vol.302, p.129-138
Hauptverfasser: Zhao, Xuan-Yi, Zhu, Chun-Gang
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Computation
Control polygon
Curves (geometry)
Degeneration
Degree elevation
Injectivity
Mathematical models
NURBS curve
Polygons
Proving
Self-intersection
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Zusammenfassung:The injectivity of NURBS curve implies the curve has no self-intersection. In this paper, we propose a geometric condition on the control polygon which guarantees the NURBS curve to be injective for all possible choices of positive weights. The proof is based on the degree elevation algorithm and toric degeneration theory of NURBS curve.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2016.01.046