This paper presents formulas for constructing quadratic minimal splines, which explicitly depend on the components of a generating vector function. Formulas various approximation functionals splines used as coefficients in local methods are obtained. Examples special cases schemes, known quasi-interpolation, provided. Results numerical experiments approximating circular arc by considered.

In 1988, Worsey and Piper constructed a trivariate macro-element based on C1 quadratic splines defined over a split of a tetrahedron into 24 subtetrahedra. However, this local element can only be used to construct a corresponding macro-element spline space over tetrahedral partitions that satisfy some very restrictive geometric constraints. We show that by further refining their split, it is po...

In 1988, Worsey and Piper constructed a trivariate macro-element based on C quadratic splines defined over a split of a tetrahedron into 24 subtetrahedra. However, this local element can only be used to construct a corresponding macro-element spline space over tetrahedral partitions that satisfy some very restrictive geometric constraints. We show that by further refining their split, it is pos...

We characterize of the Bernstein-Bezier (BB) form of an implicitly deened bivariate polynomial over a triangle, such that the zero contour of the polynomial deenes a smooth and single sheeted real algebraic curve segment. We call a piecewise G k-continuous chain of such real algebraic curve segments in BB-form as an A-spline (short for algebraic spline). We prove that the degree n A-splines can...

Starting with a shape-preserving C 1 quadratic spline, we show how knots can be removed to produce a new spline which is within a speciied tolerance of the original one, and which has the same shape properties. We give speciic algorithms and some numerical examples, and also show how the method can be used to compute approximate best free-knot splines. Finally, we discuss how to handle noisy da...