A Generalized Quasi Cubic Trigonometric Bernstein Basis Functions and Its B-Spline Form

In this paper, under the framework of Extended Chebyshev space, four new generalized quasi cubic trigonometric Bernstein basis functions with two shape α(t) and β(t) are constructed in a space span{1,sin2t,(1−sint)2α(t),(1−cost)2β(t)}, which includes lots previous work as special cases. Sufficient conditions concerning to guarantee construction given, three specific examples related applications shown. The corresponding Bézier curves corner cutting algorithm also given. Based on functions, kind B-spline local αi(t) βi(t) is detail. Some important properties proven, including partition unity, nonnegativity, linear independence, total positivity C2 continuity. parametric generated by proposed can be adjusted flexibly.