Meshless Approximation
Meshless Approximation
Meshless approximation methods make possible the definition of a continuous function that approximates a set of values at any point =(x,y) in the domain . The approximation function is defined as , where ()=ω(-) with a weight function that depends on the radius of influence, that is, it is a radial basis function (RBF). Typical weight functions are an exponential, a cubic or quartic spline, or SPH (smoothed particle hydrodynamics). Some of them can be customized with the smoothness parameter .
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This Demonstration shows the approximation value at the desired point with a red arrow for a 2-component vector field dataset. Radius of influence can be set graphically within min and max radius interval. You can choose the weight function and adapt it with for exponential and SPH to produce different approximations.
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