On particle path generation based on quadrilinear interpolation and Bernstein-Bezier polynomials

Abstract

Particle path computation in unsteady 3D vector fields given in discrete, structured form (i.e., as a hexahedral curvilinear grid) requires the local approximation of the vector field and the path. Quadrilinear interpolation and Bernstein-Bezier polynomials are used for the local vector field and path approximation. The next point in a sequence of points on a particle path is computed using this local approximation. Bernstein-Bezier polynomials are primarily used in geometric modeling, and their properties allow direct computation of points on a particle path.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>