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<p><it>Abstract</it>—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-Bézier 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-Bézier polynomials are primarily used in geometric modeling, and their properties allow direct computation of points on a particle path.</p>
Approximation, Bernstein-Bézier polynomial, particle path, curvilinear grid, path line, scientific visualization, structured grid, trajectory, vector field.

R. J. Moorhead II, D. Wu and B. Hamann, "On Particle Path Generation Based on Quadrilinear Interpolation and Bernstein-Bézier Polynomials," in IEEE Transactions on Visualization & Computer Graphics, vol. 1, no. , pp. 210-217, 1995.
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