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As the cubic splines for and are constructed, these functions are found in piecewise polynomial form.
As an example of such a scheme, we consider the scheme generating the double-knot cubic splines.
Using splines, a parameter trajectory model is defined by means of the position of the basis functions and the order of the polynomial.
As expected, the more the splines are used, the smaller the minimum performance indices are, but at the same time, the more the computational burdens.
The parameterisation concerns the generalised coordinates that are approximated using cubic splines.
The biped joint coordinates are approximated by cubic splines functions connected at uniformly distributed knots along the motion time.
However, twice differentiable property of cubic splines was not a requirement in our approach.
They found that higher-dimensional splines offered significant improvements over standard discretization methods (although for dimensions higher than three, their algorithms are still very time-consuming).
The viscosity function was then calculated from these splines.
The control methods were evolved using genetic programming, once a suitable framework had been set up using splines to compute smooth trajectories.
The two probably best-known and most often applied radial basis functions are called multiquadrics and thin-plate splines, respectively.
An approach that was considered was to use interpolation splines to form a smoothed edge.
The knots for the splines were determined from inspection of the hazard function for males and females combined.
In each case, complex forms are first resolved into a minimum network of simple splines.
Figure 5 shows the positions of the real robot controlled by the inverse dynamic strategies with a ramp and splines references.