New Trigonometric Basis Possessing Denominator Shape Parameters

الملخص EN

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.