This paper presents a real-time GPU (graphics processing unit) ray casting scheme for rendering isosurfaces of BCC (bodycentered cubic) volume datasets. A quartic spline field is built using the 7-direction box-spline filter accompanied with a quasiinterpolation prefilter. To obtain an interactive rendering speed on the graphics hardware, the shader code was optimized to avoid lookup table and ...

By applying finite difference formula to time discretization and the cubic B-splines for spatial variable, a numerical method for solving the inverse system of Burgers equations is presented. Also, the convergence analysis and stability for this problem are investigated and the order of convergence is obtained. By using two test problems, the accuracy of presented method is verified. Additional...

Refinable compactly supported bivariate C quartic and quintic spline function vectors on the four-directional mesh are introduced in this paper to generate matrix-valued templates for approximation and Hermite interpolatory surface subdivision schemes, respectively, for both the √ 2 and 1-to-4 split quadrilateral topological rules. These splines have their full local polynomial preservation ord...

Abstract Parametric interpolatory curves play a vital part in geometric modeling. Cubic Catmull–Rom spline is well-known tool for constructing parametric curves, but it cannot be modified once its control points are fixed. We propose novel quartic with free parameters to tackle this issue. The owns shape adjustability based on inheriting the features of cubic spline. Some modeling examples show...

In this paper we present a new kind of B-splines, called hyperbolic B-splines generated over the space spanned by hyperbolic functions and we use it to interpolate an arbitrary function on a set of points. Numerical tests for illustrating hyperbolic B-spline are presented.