distanceGridUnits: Returns the distances between pairs of points on a square grid

Description

This function returns the distances in grid units between pairs of points on a square grid. This function is used in testing the accuracy of a calibration by comparing theoretical distances among grid points to measured distances.

Usage

distanceGridUnits(pairs, nx)

Arguments

pairs

a two-column matrix specifying the pairs of points between which the distance is to be found.

the number of points in the first dimension along which grid points are counted (see "Details").

Value

a vector of the distances between the specified pairs of grid points.

Details

This function returns the distances in grid units between pairs of points on a square grid. Thus, adjoining points in the same row or column would be separated by a distance of one. The returned distances can then be multiplied by the grid square size to obtain the distances between pairs of points in real-world units (e.g. mm).

The input pairs is a two-column matrix specifying the pairs of points, with the first column corresponding to one point and the second column to the other. The numbers in pairs are indices of grid points (not point coordinates themselves). The assumed numbering scheme for the grid points is as follows: the points are first numbered across the first dimension (of length nx) and then along a second dimension. For example, on a 5x4 grid points 1-5 would be across the first row, 6-10 across the second row, etc. For each row the point numbering starts in the same column. For distanceGridUnits() the number of columns does not need to be specified since this can be found from the point index in pairs. See "Examples" for an explanation of the numbering scheme.

Examples

Run this code

# NOT RUN {
## INDICES OF POINT PAIRS ON A GRID WITH 5 ROWS
pairs <- matrix(c(1,1, 5,10, 6,16, 1,20), nrow=4, ncol=2, byrow=TRUE)

## FIND THE DISTANCE BETWEEN PAIRS OF POINTS IN GRID UNITS
## NOTE LAST DISTANCE IS 5 BECAUSE IT IS A 3,4,5-TRIANGLE
distanceGridUnits(pairs, nx=5)

## FOR ILLUSTRATION, HERE IS A GRID WITH 5 ROWS AND 4 COLUMNS
xy <- cbind(rep(0:4, 4), c(rep(0, 5), rep(1, 5), rep(2, 5), rep(3, 5)))

## PLOT THESE POINTS
plot(xy)

## PLOT LINE SEGMENTS CONNECTING THE PAIRS ABOVE
segments(x0=xy[pairs[, 1], 1], y0=xy[pairs[, 1], 2],
  x1=xy[pairs[, 2], 1], y1=xy[pairs[, 2], 2],
  col=c('blue', 'red', 'purple', 'green'))
# }