Bilinear interpolation

For two-dimensional problems, if a bilinear interpolation function is employed, the influence coefficients can be computed likewise in analytical form [31]. 

Concerning the numerical accuracy, the closed form solutions of normal surface deformation have been compared to the numerical results calculated through the three methods of DS, DC-FFT, and MLMI. The influence coefficients used in the numerical analyses were obtained from three different schemes Green function, piecewise constant function, and bilinear interpolation. The relative errors, as defined in Eq (39), are given in Table 2 while Fig. 4 provides an illustration of the data. 

Fig. 4—Comparison of relative error for different schemes, (a) A comparison of relative errors for a uniform pressure on a rectangle area 2a X 2b, in which the multi-summation is calculated via DS, FFT, and MLMI, and 1C is determined through bilinear interpolation based scheme, (b) A comparison of relative errors for a uniform pressure on a rectangle area 2ax2fa, in which the multisummation is calculated via DS and 1C is determined through the Green, constant, and bilinear-based schemes, (c) A comparison of relative errors for a Hertzian pressure on a circular region in radius a, in which the multi-summation is calculated via DS, and 1C is determined through the Green, constant, and bilinear-based schemes.

Figure 12.6 Two methods of interpolation (a) The color at point P is obtained by interpolating the colors from points A and B. (b ) If we have a grid of processing elements with diagonal connections, then we can use bilinear interpolation to calculate the color at point P using the data from points A, B, C, and D.

If we also use the diagonal directions to connect our processing elements, then we can use bilinear interpolation (Akenine-Moller and Haines 2002), which is shown in... 

Figure 3 A single GCxGC peak enlarged by bilinear interpolation (left) and nearest-neighbor interpolation (right). Bilinear interpolation yields a truer (i.e, higher fidelity), more pleasing spot but nearest-neighbor interpolation more clearly shows the individual data points.

We used a bilinear interpolation method to interpolate data collected from various models onto 0.25° X 0.25° grid points. Then, we used an equidistant quantile matching method to correct monthly average data. Finally, we applied the Delta method to generate daily data for the base period and future scenarios. By these means, we obtained daily temperature and precipitation data for 518 0.25° x 0.25° grids of the upper reaches of the Yangtze River in the base period and in the future period under the three scenarios and then input these data into the VIC model. Detailed introductions to the equidistant quantile matching-based... 

Nearest neighbor (NN) interpolation and trilinear (bilinear in the present 2D example) interpolation find the reference image intensity value at position p, and update the corresponding joint histogram entry at p, while partial volume (PV) interpolation distributes the contribution of this sample over multiple histogram entries defined by its NN intensities, using the same weights as for bilinear interpolation. 

The bilinear interpolation approach, the average of the Dns for the 4 pixels surrounding the transformed output pixel is used. 

To transfer the information of the body immersed in a flow to adjacent points of the mesh, some techniques can be employed a Gaussian distribution [5] or a bilinear interpolation [6], for example. 

The bilinear interpolation provides the boundary geometric location on the computational mesh, without the need to impose boundary conditions on the nodes located on the interior of the body. 

The velocity field in the immersed boundary, v(t, Xs), is obtained by bilinear interpolation of velocity components of the fluid, Vij(t,Xs), using the adjacent nodes... 

Additionally, this work makes the distinction that the effective pressure. P, differs from the grid point pressure, P. More explicitly, the effective pressure Is the pressure which Is required to apply an Identical load to surface element mn. as would be applied by the grid point pressure field with a bilinear Interpolation. The use of the effective rather than grid point pressures was found helpful in the vicinity of the pressure spike, and was felt to provide more consistent Input to the conservative fluid flow solution procedure. ... 

The method of analysis of the uncertainty in the amount of fluid or density in the continuous phase in manometric adsorption measurements, calculated via Peng-Robinson and Bender equations of state is presented. It is applied for the evaluation of the specific surface excess amount and its uncertainty during high-pressure nitrogen adsorption by a microporous activated carbon cloth at pressures up to 17 MPa at 252.40 K. Adsorption data were analysed via the use of bilinear-interpolated data from a P-p-T matrix developed fi-om the NIST Chemistry WebBook fluid physical properties database. Deviations of calculated specific surface excess amounts from those calculated using NIST density data approach 0.2 %, considerably superior to either Peng-Robinson or Bender EoS, ranging from 6.4 to 3.0 %. 

If possible, one should interpolate the NIST data from a P-p-T matrix since this method is quick, seamless and provides density and flie specific surface excess amount within 0.2 % of the NIST-derived data over the pressure range examined. The uncertainty in these data is similar in magnitiale to those of the Bender EoS, but always overlaps the value and CSU of the NIST-derived sp ific sur ce esaoes amount. Consequently, interpolation is the superior method of choice for high-pressure and supercritical manometric adsorption analyses. Cubic or bilinear interpolation methods can be used with the former rendering exact NIST values but wifli greater CSU flian the bilinear method, which gives a maximum %-departure of - 0.2 %. Use of the latter method is recommeruled. 

Linear and bilinear interpolation were used to improving the order of approximation of the dynamic characteristics on thrombus [18]. 

The image was derived from IP Axis cameras whose main characteristics are given in Table 3. The server performs additional video compression using bilinear interpolation based on the designated bandwidth. Throughput restriction is performed by the client application. It reduces the bandwidth of the client interface to the value declared in the application window. The measurement results are related to quality indicators defined in the following recommendations (ITU-T G.lOlO Recommendation, 2001), (ITU-T P.800 Recommendation, 1996). 

It verifies the shape of the hair as a thin and long structure and replaces the verified pixels using bilinear interpolation. 

A moving point can exist anywhere within the computing rectangle, 0 x < L and 0 < y h. Bilinear interpolation is used to determine the... 

As pointed out above, all values for v x, y) and Vy x,y) are obtained by bilinear interpolation amoiig the interval midpoint values of and Vy. 

Integrated Earthquake Simulation, Fig. 4 Fictitious grid and the weights used for the bilinear interpolation... 

Once a coarse grid is made, the above bilinear interpolation can be repeatedly applied to obtain soil layer data in a grid, which is sufficiently fine for setting material properties of VFEM model for the microanalysis. As explained above, macro-micro analysis uses bounding medium theory to handle the uncertainties in the layer configurations and material properties. 

---