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 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189 #ifndef DOXYGEN_SKIP /* $Id: grid_tutorial.dox 14579 2008-05-30 15:41:30Z dron$ */ #endif /* DOXYGEN_SKIP */ /*! \page grid_tutorial GDAL Grid Tutorial \section grid_tutorial_intro Introduction to Gridding Gridding is a process of creating a regular grid (or call it a raster image) from the scattered data. Typically you have a set of arbitrary scattered over the region of survey measurements and you would like to convert them into the regular grid for further processing and combining with other grids. \image html gridding.png "Scattered data gridding" \image latex grid/gridding.eps "Scattered data gridding" This problem can be solved using data interpolation or approximation algorithms. But you are not limited by interpolation here. Sometimes you don't need to interpolate your data but rather compute some statistics or data metrics over the region. Statistics is valuable itself or could be used for better choosing the interpolation algorithm and parameters. That is what GDAL Grid API is about. It helps you to interpolate your data (see \ref grid_tutorial_interpolation) or compute data metrics (see \ref grid_tutorial_metrics). There are two ways of using this interface. Programmatically it is available through the \ref GDALGridCreate C function; for end users there is a \ref gdal_grid utility. The rest of this document discusses details on algorithms and their parameters implemented in GDAL Grid API. \section grid_tutorial_interpolation Interpolation of the Scattered Data \subsection grid_tutorial_interpolation_invdist Inverse Distance to a Power The Inverse Distance to a Power gridding method is a weighted average interpolator. You should supply the input arrays with the scattered data values including coordinates of every data point and output grid geometry. The function will compute interpolated value for the given position in output grid. For every grid node the resulting value \f$Z\f$ will be calculated using formula: \f[ Z=\frac{\sum_{i=1}^n{\frac{Z_i}{r_i^p}}}{\sum_{i=1}^n{\frac{1}{r_i^p}}} \f] where
• \f$Z_i\f$ is a known value at point \f$i\f$,
• \f$r\f$ is a distance from the grid node to point \f$i\f$,
• \f$p\f$ is a weighting power,
• \f$n\f$ is a number of points in \ref grid_tutorial_ellipse "search ellipse".
In this method the weighting factor \f$w\f$ is \f[ w=\frac{1}{r^p} \f] See \ref GDALGridInverseDistanceToAPowerOptions for the list of \ref GDALGridCreate parameters and \ref gdal_grid_algorithms_invdist for the list of \ref gdal_grid options. \subsection grid_tutorial_interpolation_average Moving Average The Moving Average is a simple data averaging algorithm. It uses a moving window of elliptic form to search values and averages all data points within the window. \ref grid_tutorial_ellipse "Search ellipse" can be rotated by specified angle, the center of ellipse located at the grid node. Also the minimum number of data points to average can be set, if there are not enough points in window, the grid node considered empty and will be filled with specified NODATA value. Mathematically it can be expressed with the formula: \f[ Z=\frac{\sum_{i=1}^n{Z_i}}{n} \f] where
• \f$Z\f$ is a resulting value at the grid node,
• \f$Z_i\f$ is a known value at point \f$i\f$,
• \f$n\f$ is a number of points in search \ref grid_tutorial_ellipse "search ellipse".
See \ref GDALGridMovingAverageOptions for the list of \ref GDALGridCreate parameters and \ref gdal_grid_algorithms_average for the list of \ref gdal_grid options. \subsection grid_tutorial_interpolation_nearest Nearest Neighbor The Nearest Neighbor method doesn't perform any interpolation or smoothing, it just takes the value of nearest point found in grid node search ellipse and returns it as a result. If there are no points found, the specified NODATA value will be returned. See \ref GDALGridNearestNeighborOptions for the list of \ref GDALGridCreate parameters and \ref gdal_grid_algorithms_nearest for the list of \ref gdal_grid options. \section grid_tutorial_metrics Data Metrics Computation All the metrics have the same set controlling options. See the \ref GDALGridDataMetricsOptions. \subsection grid_tutorial_metrics_min Minimum Data Value Minimum value found in grid node \ref grid_tutorial_ellipse "search ellipse". If there are no points found, the specified NODATA value will be returned. \f[ Z=\min{(Z_1,Z_2,\ldots,Z_n)} \f] where
• \f$Z\f$ is a resulting value at the grid node,
• \f$Z_i\f$ is a known value at point \f$i\f$,
• \f$n\f$ is a number of points in \ref grid_tutorial_ellipse "search ellipse".
\subsection grid_tutorial_metrics_max Maximum Data Value Maximum value found in grid node \ref grid_tutorial_ellipse "search ellipse". If there are no points found, the specified NODATA value will be returned. \f[ Z=\max{(Z_1,Z_2,\ldots,Z_n)} \f] where
• \f$Z\f$ is a resulting value at the grid node,
• \f$Z_i\f$ is a known value at point \f$i\f$,
• \f$n\f$ is a number of points in \ref grid_tutorial_ellipse "search ellipse".
\subsection grid_tutorial_metrics_range Data Range A difference between the minimum and maximum values found in grid node \ref grid_tutorial_ellipse "search ellipse". If there are no points found, the specified NODATA value will be returned. \f[ Z=\max{(Z_1,Z_2,\ldots,Z_n)}-\min{(Z_1,Z_2,\ldots,Z_n)} \f] where
• \f$Z\f$ is a resulting value at the grid node,
• \f$Z_i\f$ is a known value at point \f$i\f$,
• \f$n\f$ is a number of points in \ref grid_tutorial_ellipse "search ellipse".
\section grid_tutorial_ellipse Search Ellipse Search window in gridding algorithms specified in the form of rotated ellipse. It is described by the three parameters:
• \f$radius_1\f$ is the first radius (\f$x\f$ axis if rotation angle is 0),
• \f$radius_2\f$ is the second radius (\f$y\f$ axis if rotation angle is 0),
• \f$angle\f$ is a search ellipse rotation angle (rotated counter clockwise).
\image html ellipse.png "Search ellipse" \image latex grid/ellipse.eps "Search ellipse" Only points located inside the search ellipse (including its border line) will be used for computation. \htmlonly

$Id: grid_tutorial.dox 14579 2008-05-30 15:41:30Z dron$

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