A Practical Method for Generating Trigonometric Polynomial Surfaces over Triangular Domains

Han, Xuli; Zhu, Yuanpeng

doi:10.1007/s00009-015-0515-5

Cited by 2 publications

(1 citation statement)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The related patch can be rendered flexible by an adjustment of the values. In [35], Han proposed a patch over a triangular domain, which can construct boundaries that can exactly represent elliptic arcs. A kind of quasi-Bernstein-Bézier polynomials over a triangular domain was proposed in [36].…”

Section: Introductionmentioning

confidence: 99%

New Trigonometric Basis Possessing Denominator Shape Parameters

Kai

Gui-cang

2018

Mathematical Problems in Engineering

View full text Add to dashboard Cite

Four new trigonometric Bernstein-like bases with two denominator shape parameters (DTB-like basis) are constructed, based on which a kind of trigonometric Bézier-like curve with two denominator shape parameters (DTB-like curves) that are analogous to the cubic Bézier curves is proposed. The corner cutting algorithm for computing the DTB-like curves is given. Any arc of an ellipse or a parabola can be exactly represented by using the DTB-like curves. A new class of trigonometric B-spline-like basis function with two local denominator shape parameters (DT B-spline-like basis) is constructed according to the proposed DTB-like basis. The totally positive property of the DT B-spline-like basis is supported. For different shape parameter values, the associated trigonometric B-spline-like curves with two denominator shape parameters (DT B-spline-like curves) can be C2 continuous for a non-uniform knot vector. For a special value, the generated curves can be C(2n-1) (n=1,2,3,…) continuous for a uniform knot vector. A kind of trigonometric B-spline-like surfaces with four denominator shape parameters (DT B-spline-like surface) is shown by using the tensor product method, and the associated DT B-spline-like surfaces can be C2 continuous for a nonuniform knot vector. When given a special value, the related surfaces can be C(2n-1) (n=1,2,3,…) continuous for a uniform knot vector. A new class of trigonometric Bernstein–Bézier-like basis function with three denominator shape parameters (DT BB-like basis) over a triangular domain is also constructed. A de Casteljau-type algorithm is developed for computing the associated trigonometric Bernstein–Bézier-like patch with three denominator shape parameters (DT BB-like patch). The condition for G1 continuous jointing two DT BB-like patches over the triangular domain is deduced.

show abstract

Section: Introductionmentioning

confidence: 99%