# project2segment

##### Move Point To Nearest Line

Given a point pattern and a line segment pattern, this function moves each point to the closest location on a line segment.

##### Usage

`project2segment(X, Y)`

##### Arguments

- X
A point pattern (object of class

`"ppp"`

).- Y
A line segment pattern (object of class

`"psp"`

).

##### Details

For each point `x`

in the point pattern `X`

, this function
finds the closest line segment `y`

in the line segment pattern
`Y`

. It then `projects' the point `x`

onto the line segment
`y`

by finding the position `z`

along `y`

which is closest to `x`

. This position `z`

is returned,
along with supplementary information.

##### Value

A list with the following components. Each component has length equal to
the number of points in `X`

, and its entries correspond to the
points of `X`

.

Point pattern (object of class `"ppp"`

containing the projected points.

Integer vector identifying the nearest segment to each point.

Numeric vector of distances from each point of `X`

to
the corresponding projected point.

Numeric vector giving the scaled parametric coordinate \(0 \le t_p \le 1\) of the position of the projected point along the segment.

For example suppose mapXY[2] = 5 and tp[2] = 0.33. Then Y[5] is the line segment lying closest to X[2]. The projection of the point X[2] onto the segment Y[5] is the point Xproj[2], which lies one-third of the way between the first and second endpoints of the line segment Y[5].

##### See Also

`nearestsegment`

for a faster way to determine
which segment is closest to each point.

##### Examples

```
# NOT RUN {
X <- rstrat(square(1), 5)
Y <- as.psp(matrix(runif(20), 5, 4), window=owin())
plot(Y, lwd=3, col="green")
plot(X, add=TRUE, col="red", pch=16)
v <- project2segment(X,Y)
Xproj <- v$Xproj
plot(Xproj, add=TRUE, pch=16)
arrows(X$x, X$y, Xproj$x, Xproj$y, angle=10, length=0.15, col="red")
# }
```

*Documentation reproduced from package spatstat, version 1.55-1, License: GPL (>= 2)*