orthogonalProjectionToLine: Finds the orthogonal projection of a point onto a line
In nitlon/Eartheaters: Stereo Camera Calibration and Reconstruction

Description Usage Arguments Details Value Author(s) References See Also Examples

Given a 2D or 3D input point p and a 2D or 3D line, this function finds a point on the line at a minimum distance from point p. This is equivalent to the orthogonal projection of point p onto the line.

1	orthogonalProjectionToLine(p, l1 = NULL, l2 = NULL)

`p`	a vector of a single point or a matrix of multiple points
`l1`	a vector describing a point on a line or a list with line constants
`l2`	if `l1` is a point, a second point on a line

If p is a vector, the function returns a point as a vector of the same dimension. If p is a matrix, each row is treated as a point and the orthogonal projection is returned for each. These points are returned as a matrix (of the same dimension), each row being the orthogonal projection of the corresponding row in p.

The line input can be defined using one of three standard ways: two points on the line, 'm' and 'b' constants (slope and y-intercept) and direction numbers 'abc' (a vector parallel to a line through the origin). If l1 is a vector, this is taken as one point on the line and l2 must be a second point on the line. If l1 is a list, the named objects must correspond to one of these three line definitions. Two points on the line are defined as l1$l1 and l1$l2. 'm' and 'b' are defined as l1$m and l1$b. And the direction numbers 'abc' are defined as l1$a, l1$b and l1$c.

a vector if p is a vector and a matrix if p is a matrix. The returned vector or matrix will be of the same dimensions as p.

Aaron Olsen

http://paulbourke.net/geometry/pointlineplane/

distancePointToLine

## POINT INPUT: 2D VECTOR
## LINE INPUT: l1, l2
## LINE THROUGH THE ORIGIN WITH SLOPE OF ONE
orthogonalProjectionToLine(p=c(0, 5), l1=c(0, 0), l2=c(3, 3))

## POINT INPUT: 2D VECTOR
## LINE INPUT: LIST WITH l1, l2
orthogonalProjectionToLine(p=c(0, 5), l1=list(l1=c(0, 0), l2=c(3, 3)))

## POINT INPUT: 2D VECTOR
## LINE INPUT: LIST WITH m, b
## LINE WITH Y-INTERCEPT AT ONE AND SLOPE OF ONE
orthogonalProjectionToLine(p=c(0, 5), l1=list(m=1, b=0))

## POINT INPUT: 2D VECTOR
## LINE INPUT: LIST WITH VECTOR PARALLEL TO LINE THROUGH THE ORIGIN
## LINE THROUGH THE ORIGIN WITH SLOPE OF ONE
orthogonalProjectionToLine(p=c(0, 5), l1=list(a=1, b=-1, c=0))

## POINT INPUT: 2D VECTOR
## LINE INPUT: SAME AS PREVIOUS BUT WITH Z-AXIS COMPONENT
orthogonalProjectionToLine(p=c(0, 5), l1=list(a=1, b=-1, c=1))

## POINT INPUT: 3D VECTOR
## LINE INPUT: l1, l2
orthogonalProjectionToLine(p=c(0, 5, 0), l1=list(l1=c(0, 0, 0), l2=c(3, 3, 3)))

## POINT INPUT: 2D MATRIX
## LINE INPUT: l1, l2
p <- matrix(c(0,5, 0,10), nrow=2, byrow=TRUE)
orthogonalProjectionToLine(p=p, l1=list(l1=c(0, 0), l2=c(3, 3)))

## POINT INPUT: 3D MATRIX
## LINE INPUT: l1, l2
p <- matrix(c(0,5,0, 0,10,0), nrow=2, byrow=TRUE)
orthogonalProjectionToLine(p=p, l1=list(l1=c(0, 0, 0), l2=c(3, 3, 3)))