Fragment-based Evaluation of Non-Uniform B-spline Surfaces on GPUs

Design and Manufacturing using GPUs

Graphics processing units (GPUs) have recently evolved into programmable parallel processors capable of performing general-purpose computational tasks. We present some algorithms that utilize GPUs to speed up traditional operations in design and manufacturing. One significant operation in Computer Aided Design (CAD) is the evaluation and rendering of trimmed NURBS surfaces. Another important pr...

Non Uniform Rational B Spline (NURBS) Based Non-Linear Analysis of Straight Beams with Mixed Formulations

Displacement finite element models of various beam theories have been developed traditionally using conventional finite element basis functions (i.e., cubic Hermite, equi-spaced Lagrange interpolation functions, or spectral/hp Legendre functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, tota...

Construction of Non-Uniform Basic Functions for Spline Curves and Surfaces

Non-uniform basis functions for construction of interpolating and approximating spline curves and surfaces are presented. The construction is based on the theory of B-splines and enables a continuous change from interpolation to approximation of given data. It is also possible to change the tension of the curves and surfaces.

Evaluation of NURBS Surfaces: An Overview Based on Runtime Efficiency

Pii: S0167-8396(02)00124-3

The matrix forms for curves and surfaces were largely promoted in CAD/CAM. In this paper we have presented two matrix representation formulations for arbitrary degree NURBS curves and surfaces explicitly other than recursively. The two approaches are derived from the computation of divided difference and the Marsden identity respectively. The explicit coefficient matrix of B-spline with equally...