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/*
* GeoTools - The Open Source Java GIS Toolkit
* http://geotools.org
*
* (C) 2011, Open Source Geospatial Foundation (OSGeo)
* (C) 2005 Open Geospatial Consortium Inc.
*
* All Rights Reserved. http://www.opengis.org/legal/
*/
/**
* Quadrilateral grid coverages. The following is adapted from ISO 19123 specification.
*
* Grid coverages employ a systematic tessellation of the domain. The principal
* advantage of such tessellations is that they support a sequential enumeration of the elements of
* the domain, which makes data storage and access more efficient. The tessellation may represent
* how the data was acquired or how it was computed in a model. The domain of a grid coverage is a
* set of grid points, including their convex hull in the case of a continuous grid coverage.
*
*
Quadrilateral grid geometry
*
* A grid is a network composed of two or more sets of curves in which the
* members of each set intersect the members of the other sets in a systematic way. The curves are
* called grid lines; the points at which they intersect are {@linkplain
* org.opengis.coverage.grid.GridPoint grid points}, and the interstices between the grid lines are
* {@linkplain org.opengis.coverage.grid.GridCell grid cells}.
*
*
The most common case is the one in which the curves are straight lines, and
* there is one set of grid lines for each dimension of the grid space. In this case the {@linkplain
* org.opengis.coverage.grid.GridCell grid cells} are parallelograms or parallelepipeds. In its own
* coordinate system, such a grid is a network composed of two or more sets of equally spaced
* parallel lines in which the members of each set intersect the members of the other sets at right
* angles. It has a set of axes equal in number to the {@linkplain
* org.opengis.coverage.grid.Grid#getDimension dimension of the grid}. It has one set of grid lines
* parallel to each axis. The size of the grid is described by a sequence of integers, in which each
* integer is a count of the number of lines parallel to one of the axes. There are {@linkplain
* org.opengis.coverage.grid.GridPoint grid points} at all grid line intersections. The axes of the
* grid provide a basis for defining {@linkplain org.opengis.coverage.grid.GridCoordinates grid
* coordinates}, which are measured along the axes away from their origin, which is distinguished by
* having coordinate values of 0. Grid coordinates of grid points are integer numbers. The axes need
* to be identified to support sequencing rules for associating feature attribute value records to
* the grid points.
*
*
*
* NOTE: The dimensions (axes) of a 2-dimensional grid are often called
* row and column.
*
*
*
* A grid may be defined in terms of an external {@linkplain
* org.opengis.referencing.crs.CoordinateReferenceSystem coordinate reference system}. This requires
* additional information about the location of the grid's origin within the external coordinate
* reference system, the orientation of the grid axes, and a measure of the spacing between the grid
* lines. If the spacing is uniform, then there is an affine relationship between the grid and
* external coordinate system, and the grid is called a rectified grid. If, in addition, the
* external coordinate reference system is related to the earth by a datum, the grid is a
* georectified grid. The grid lines of a rectified grid need not meet at right angles; the spacing
* between the grid lines is constant along each axis, but need not be the same on every axis. The
* essential point is that the transformation of grid coordinates to coordinates of the external
* coordinate reference system is an affine transformation.
*
*
*
* NOTE: The word rectified implies a transformation from an image space
* to another coordinate reference system. However, grids of this form are often defined initially
* in an earth-based coordinate system and used as a basis for collecting data from sources other
* than imagery.
*
*
*
* A feature attribute value may be of any data type. However, evaluation of a
* continuous coverage is usually implemented by interpolation methods that can be applied only to
* numbers or vectors. Other data types are almost always associated with discrete coverages.
*
*
When the relationship between a {@linkplain org.opengis.coverage.grid.Grid
* grid} and an external {@linkplain org.opengis.referencing.crs.CoordinateReferenceSystem
* coordinate reference system} is not adequate to specify it in terms of an origin, an orientation,
* and spacing in that coordinate reference system, it may still be possible to transform the grid
* coordinates into coordinates in the coordinate reference system. This transformation need not be
* in analytic form; it may be a table, relating the grid points to coordinates in the external
* coordinate reference system. Such a grid is classified as a referenceable grid. If the external
* coordinate reference system is related to the earth by a datum, the grid is a georeferenceable
* grid. A referenceable grid is associated with information that allows the location of all points
* in the grid to be determined in the coordinate reference system, but the location of the points
* is not directly available from the grid coordinates, as opposed to a rectified grid where the
* location of the points in the coordinate reference system is derivable from the properties of the
* grid itself. The transformation produced by the information associated with a referenceable grid
* will produce a grid as seen in the coordinate reference system, but the grid lines of that grid
* need not be straight or orthogonal, and the grid cells may be of different shapes and sizes.
*
*
Cell structures
*
* The term "grid cell" refers to two concepts: one important from the
* perspective of data collection and portrayal, the other important from the perspective of grid
* coverage evaluation. The ambiguity of this term is a common cause of positioning error in
* evaluating or portraying grid coverages.
*
*
The feature attribute values associated with a {@linkplain
* org.opengis.coverage.grid.GridPoint grid point} represent characteristics of the real world
* measured or observed within a small space surrounding a sample point represented by the grid
* point. The grid lines connecting these points form a set of {@linkplain
* org.opengis.coverage.grid.GridCell grid cells}. A common simplifying assumption is that the
* sample space is equally divided among the sample points, so that the sample spaces are
* represented by a second set of cells congruent to the first but offset so that each has a grid
* point at its centre. Evaluation of a grid coverage is based on interpolation between grid points,
* i.e., within a grid cell bounded by the grid lines that connect the grid points that represent
* the sample points.
*
*
In the ISO 19123 International Standard, the term grid cell
* refers to the cell bounded by the grid lines that connect the grid points. The term sample
* space refers to the observed or measured space surrounding a sample point. The term
* footprint refers to a representation of a sample space in the context of some
* coordinate reference system.
*
*
In dealing with gridded data, e.g., for processing or portrayal, it is often
* assumed that the size and shape of the sample spaces are a simple function of the spatial
* distribution of the sample points, and typically that the grid cells and the sample cells are
* congruent.
*
*
In fact, the size and shape of the sample space are determined by the method
* used to measure or calculate the attribute value. In the simplest case, the sample space is the
* sample point. It is often a disc, a sphere, or a hypersphere surrounding the sample point. In the
* case of sensed data the size and shape of the sample space is also a function of the sensor model
* and its position relative to the sample point, and may be quite complex. Adjacent sample spaces
* may be coterminous or they may overlap or underlap.
*
*
In addition to affecting the size and shape of the sample space, the
* measurement technique affects the applicability of the observed or measured value to the sample
* space. It is often assumed that the recorded value represents the mean value for the sample
* space. In fact, elements of the sample space may not contribute uniformly to the result, so that
* it is better conceived as a weighted average where the weighting is a function of position within
* the sample space. Interpolation methods may be designed specifically to deal with characteristics
* of the sample space.
*
*
Transformation (e.g., rectification) between grid coordinates and an external
* coordinate reference system may distort the representation of the sample space in a way that
* causes interpolation errors.
*
* @version ISO 19123:2004
* @since GeoAPI 2.0
*/
package org.opengis.coverage.grid;