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• W2898096247 abstract "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 <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mrow><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant=normal>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math> continuous for a non-uniform knot vector. For a special value, the generated curves can be <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy=false>(</mml:mo><mml:mn mathvariant=normal>2</mml:mn><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant=normal>1</mml:mn><mml:mo stretchy=false>)</mml:mo></mml:mrow></mml:msup><mml:mo> </mml:mo><mml:mo> </mml:mo><mml:mo stretchy=false>(</mml:mo><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=normal>1,2</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant=normal>3</mml:mn><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo stretchy=false>)</mml:mo></mml:math> 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 <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mrow><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant=normal>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math> continuous for a nonuniform knot vector. When given a special value, the related surfaces can be <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy=false>(</mml:mo><mml:mn mathvariant=normal>2</mml:mn><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant=normal>1</mml:mn><mml:mo stretchy=false>)</mml:mo></mml:mrow></mml:msup><mml:mo> </mml:mo><mml:mo> </mml:mo><mml:mo stretchy=false>(</mml:mo><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=normal>1,2</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant=normal>3</mml:mn><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo stretchy=false>)</mml:mo></mml:math> 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 <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:mrow><mml:msup><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant=normal>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math> continuous jointing two DT BB-like patches over the triangular domain is deduced." @default.
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• W2898096247 date "2018-10-24" @default.
• W2898096247 modified "2023-10-17" @default.
• W2898096247 title "New Trigonometric Basis Possessing Denominator Shape Parameters" @default.
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• W2898096247 doi "https://doi.org/10.1155/2018/9569834" @default.
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