Generalized Subdivision of Bézier Surfaces

Hu, Shi‐Min; Wang, Guozhao; Jin, Tong-Guang

doi:10.1006/gmip.1996.0018

Cited by 8 publications

(2 citation statements)

References 3 publications

(1 reference statement)

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“…Two types of surfaces are widely used: triangular Bernstein-Bézier surface (TB or TBB surface) and tensor product Bézier surface (TP or TPB surface). For instance, the subdivision of a Bézier surface [3][4][5][6][7] falls into this category and so do the conversions between TB surfaces and TP surfaces. Brueckner [8] represented a TB surface as a trimmed TP surface.…”

Section: Introductionmentioning

confidence: 99%

Triangular Bézier sub-surfaces on a triangular Bézier surface

Chen

Zheng

et al. 2011

Journal of Computational and Applied Mathematics

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a b s t r a c tThis paper considers the problem of computing the Bézier representation for a triangular sub-patch on a triangular Bézier surface. The triangular sub-patch is defined as a composition of the triangular surface and a domain surface that is also a triangular Bézier patch. Based on de Casteljau recursions and shifting operators, previous methods express the control points of the triangular sub-patch as linear combinations of the construction points that are constructed from the control points of the triangular Bézier surface. The construction points contain too many redundancies. This paper derives a simple explicit formula that computes the composite triangular sub-patch in terms of the blossoming points that correspond to distinct construction points and then an efficient algorithm is presented to calculate the control points of the sub-patch.

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Section: Introductionmentioning

confidence: 99%

Triangular Bézier sub-surfaces on a triangular Bézier surface

Chen

Zheng

et al. 2011

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

show abstract

“…Two types of surfaces are wildly used: triangular Bernstein-Bézier surface (TB or TBB surface) and tensor product Bézier surface (PB or TPB surface). For instance, the subdivision of a Bézier surface[98] falls into this category and so are the conversions between TB surfaces and PB surface. Brueckner[99] represented a TB surface as a trimmed PB surface.…”

mentioning

confidence: 99%