Class of Pixel Grids
Description
The class "pgrid"
(for pixel grid) represents regular quantizations of measures on
(bounded subsets of) R^d. Currently only square quantizations of measures on a rectangles
are supported, which in 2d can be thought of as grey scale images.
Details
Objects of class "pgrid"
can be created by the function
pgrid
, and are most commonly used as input to the function
transport
. There are methods plot
, print
and
summary
for this class.
An object of class "pgrid"
contains the following elements:
structure 
the structure of the grid. Currently only "square" and "rectangular" are supported.

dimension  the dimension d of the space in which the grid is embedded. Must be >=2. 
n 
the number of pixels along the various coordinates, a vector of length dimension .

N  the total number of pixels. 
boundary  the outer boundary of the "picture" (i.e. of the support of the measure). A vector of 
length 2*dimension , where the odd entries contain the left and the even entries 

contain the right endpoints of the various coordinates.  
gridtriple  the rule for generating the pixel centres along the various coordinates. 
A dim by 3 matrix where each row is of the form c(start, end, step) .


generators 
the pixel centres along the various coordinates. A list of length dim where the 
i th element is a vector of length n[i] .


mass  the array of masses in each pixel / at each pixel centre. In 2d orientation corresponds 
to the standard orientation of images, see e.g. image . This means that 

pixels are arranged on coordinate axes in the order of their indices.  
Author(s)
Dominic Schuhmacher dschuhm1@unigoettingen.de
See Also
Constructor function pgrid
.
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