Abstract: To make the extended cubic uniform B-spline curve possesses not only shape adjustability, high order continuity, exact representation of ellipse, but also variation diminishing, a piecewise combination curve based on trigonometric totally positive basis is constructed. Firstly, we use the linear combination of the T-Bézier basis, which has been proved to be an optimal normalized totally positive basis, to express the extended basis to be constructed. According to the preset properties of the curve, we deduce the properties of the extended basis, and then obtain its expression. We then represent the extended basis as the product of the T-Bézier basis and a conversion matrix. We prove the totally positive property of the matrix and then show the total positivity of the extended basis. Finally, based on the extended basis, a piecewise combination curve and surface with a shape parameter is defined, and the continuity is analyzed. The conditions and methods using the curve and surface to express the ellipse and ellipsoid are given. Experimental results show that the total positivity of the extended basis ensures the variation diminishing of the curve, and the introduction of the shape parameter provides the shape adjustment tool for the curve and surface. The curve and surface have C³ continuity and can reach C⁵ continuity when taking special parameter.