# Changes between Version 181 and Version 182 of UvmatHelp

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Timestamp:
Jan 26, 2015, 9:20:06 AM (9 years ago)
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 v181 - '''Thin plate shell (tps) interpolation:''' This is a multi-dimensional generalisation of the spline interpolation/smoothing, an optimum way to interpolate data with minimal  curvature of the interpolating function. The result at an interpolation position vector ${\bf r}$ is expressed in the form, (see ThinPlateShell) This is a multi-dimensional generalisation of the spline interpolation/smoothing, an optimum way to interpolate data with minimal  curvature of the interpolating function. The result at an interpolation position vector ${\bf r}$ is expressed in the form, (see ThinPlateShell). $$\label{sol_gene} f({\bf r})=\sum S_i \phi({\bf|r-r_i}|)+a_0+a_1x+a_2y\;$$ where ${\bf r_i}$ are the positions of the measurement points (the ''centres''). Each ''centre'' can be viewed as the source of an axisymmetric field  $\phi$ of the form $\phi(r)=r^2\log (r)$. The weights $S_i$ and the linar coefficients $a_0,a_1,a_2$ are the thin plate shell (tps) coefficients which determine the interpolated value at any point. The spatial derivatives are similarly obtained at any point by analytical differentiation of the source functions $\phi(r)$. These tps weights, with the corresponding centre coordinates, therefore contain all the information needed for interpolation at any point. We call that a ''tps field representation''.^ * : translation, (Tz=1 for the options calib_lin and calib_rescale). * : rotation matrix (in 3 lines). For the option <[https://servforge.legi.grenoble-inp.fr/projects/soft-uvmat/search?q=wiki%3ACalibrationType !CalibrationType]>= 'rescale', [[BR]] R (i=1)= [pxcmx 0 0] R (i=2)= [0 pxcmy 0] R (i=3)= [0 0 1], [[BR]]where pxcmx and pxcmy are the scaling factors along ''x'' and ''y''. * : rotation matrix (in 3 lines). For the option = 'rescale', [[BR]] R (i=1)= [pxcmx 0 0] R (i=2)= [0 pxcmy 0] R (i=3)= [0 0 1], [[BR]]where pxcmx and pxcmy are the scaling factors along ''x'' and ''y''. * : 3 components of the rotation vector (this is for diagnostic use, it is redondant with the matrix R used for actual coordinate transforms). The physical coordinate axis are transformed to the image coordinate axis by a composition of the translation T and the rotation. Perform usual PIV for each image series. For PIV near a staigth wall, it is advised to create a grid for each image series, corresponding to a common array of physical positions. This can be done by the upper menu bar option '''[!Tools/Make Grid]''' in the GUI '''uvmat'''( see section [#a9.2Grids Grids]). For PIV near a staigth wall, it is advised to create a grid for each image series, corresponding to a common array of physical positions. This can be done by the upper menu bar option '''[!Tools/Make Grid]''' in the GUI '''uvmat''' (see section [#a9.2Grids Grids]). Combine PIV fields: TO UPDATE**. * ro2_patch: smoothing coefficient rho used for patch2. - '''List of field variables (old CIVx conventions):''' a set of velocity vectors is defined by a 1D array of position coordinates x, y, and z for 3D civ, and a corresponding array for each of the velocity components u, v, and w for 3C civ. The field is therefore defined on an arbitrary set of point, without restriction to a regular mesh. Additional arrays are used to keep track of the quality of the PIV process leading to each vector. The image correlation maximum is represented by vec_C (a real number between 0 and 1). A flag vec_F represents a warning on the vector quality (see the list of values below). Another flag FixFlag marks false vectors: !FixFlag=0 for good vectors, and FixFlag is set to a non-zero value when it has been detected as false (using a 'fix' operation). - '''List of field variables (old CIVx conventions):''' a set of velocity vectors is defined by a 1D array of position coordinates x, y, and z for 3D civ, and a corresponding array for each of the velocity components u, v, and w for 3C civ. The field is therefore defined on an arbitrary set of point, without restriction to a regular mesh. Additional arrays are used to keep track of the quality of the PIV process leading to each vector. The image correlation maximum is represented by vec_C (a real number between 0 and 1). A flag vec_F represents a warning on the vector quality (see the list of values below). Another flag !FixFlag marks false vectors: !FixFlag=0 for good vectors, and !FixFlag is set to a non-zero value when it has been detected as false (using a 'fix' operation). The names of the fields (variables) resulting from each operation are given in the following table. Each column corresponds to an operation. 'filter1' and 'interp1' both result from the patch1 interpolation on the same points, with and without smoothing respectively. The first line is the name of the constant representing the number of vectors (the dimension of the arrays). The next successive lines indicate the variable names for the position and velocity components, the image correlation 'c', the 'flag' about civ quality and 'fix' flag (only available for civ1 and civ2), and the spatial derivatives obtained from the patch operations.