Tension spline is a function that, for given partition x0 < x1 < . . . < xn, on each interval [xi, xi+1] satisfies differential equation (D − ρiD)u = 0, where ρi’s are prescribed nonnegative real numbers. In the literature, tension splines are used in collocation methods applied to two-points singularly perturbed boundary value problems with Dirichlet boundary conditions. In this paper, we adap...

This paper presents a simple and robust method for computing the bisector of two planar rational curves. We represent the correspondence between the foot points on two planar rational curves C1(t) and C2(r) as an implicit curve F(t; r) = 0, where F(t; r) is a bivariate polynomial B-spline function. Given two rational curves of degree m in the xy-plane, the curve F(t; r) = 0 has degree 4m 2, whi...

The Spline scalable platform for interactive environments makes it easy to build virtual worlds where multiple people interact with each other and with computer simulations in a 3D visual and audio environment. A key problem shared by Spline and many other systems is achieving accurate time synchronization of events and data streams. In Spline, synchronization is achieved through the use of tim...

Abstract In this paper, we address the problem of constructing $$C^2$$ C 2 cubic spline functions on a given arbitrary triangulation $${\mathcal {T}}$$ T . To end, endow every triangle with Wang–Shi macro-structure. The space such refined has stable dim...

This paper develops a new family of convexity-preserving splines of order n, hereby entitled the CPn-spline, that preserves convexity when derivatives at the data points satisfy some reasonable conditions. The spline comprises four components: a constant term, a first order term, and two nth order binomials. A slope-averaging-method is proposed for the general implementation of the new spline. ...

Fat conic section and fat conic spline are defined. With well established properties of fat conic splines, the problem of approximating a ruled surface by a tangent smooth cone spline can then be changed as the problem of fitting a plane fat curve by a fat conic spline. Moreover, the fitting error between the ruled surface and the cone spline can be estimated explicitly via fat conic spline fit...

In this paper, we propose a novel approach that transforms discrete volumetric data directly acquired from scanning devices into continuous spline representations with tensor-product regular structure. Our method is achieved through three major steps as follows. First, in order to capture fine features, we construct an as-smooth-as-possible frame field, satisfying a sparse set of directional co...

A T-mesh is basically a rectangular grid that allows T-junctions. Recently, Deng etal introduced splines over T-meshes, which are generalizations of T-splines invented by Sederberg etal, and proposed a dimension formula based on the B-net method. In this paper, we derive an equivalent dimension formula in a different form with the smoothing cofactor method. Mathematics subject classification: