Changes between Version 181 and Version 182 of UvmatHelp
 Timestamp:
 Jan 26, 2015, 9:20:06 AM (6 years ago)
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UvmatHelp
v181 v182 336 336  '''Thin plate shell (tps) interpolation:''' 337 337 338 This is a multidimensional 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) 338 This is a multidimensional 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). 339 339 340 340 $$\label{sol_gene} f({\bf r})=\sum S_i \phi({\bfrr_i})+a_0+a_1x+a_2y\; $$ 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''.^ … … 631 631 * `<Tx_Ty_Tz>`: translation, (Tz=1 for the options calib_lin and calib_rescale). 632 632 633 * `<R>`: rotation matrix (in 3 lines). For the option < [https://servforge.legi.grenobleinp.fr/projects/softuvmat/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''.633 * `<R>`: rotation matrix (in 3 lines). For the option <!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''. 634 634 635 635 * <omc>: 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. … … 862 862 Perform usual PIV for each image series. 863 863 864 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]).864 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]). 865 865 866 866 Combine PIV fields: TO UPDATE**. … … 951 951 * ro2_patch: smoothing coefficient rho used for patch2. 952 952 953  '''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, andFixFlag is set to a nonzero value when it has been detected as false (using a 'fix' operation).953  '''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 nonzero value when it has been detected as false (using a 'fix' operation). 954 954 955 955 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.