getMinBBox {shotGroups}

Minimum-area bounding box for a set of 2D-points

Description

Calculates the vertices of the minimum-area, possibly oriented bounding box given a set of 2D-coordinates.

Usage

getMinBBox(xy)

## S3 method for class 'data.frame'
getMinBBox(xy)

## Default S3 method:
getMinBBox(xy)

Arguments

xy

either a numerical (n x 2)-matrix with the (x,y)-coordinates of n >= 2 points (1 row of coordinates per point), or a data frame with either the variables x, y or point.x, point.y.

Details

No coordinate transforms are done (unlike in groupLocation, groupShape, groupSpread), i.e., origin is not assumed to be in top-left corner, and points are not taken relative to point of aim.
Uses the rotating calipers algorithm (Toussaint, 1983).

Value

A list with the following information about the minimum-area bounding box:

pts

a (4 x 2)-matrix containing the coordinates of the (ordered) vertices.

width

width of the box.

height

height of the box.

FoM

figure of merit, i.e., the average side length of the box: (width + height) / 2.

diag

length of box diagonal.

angle

orientation of the box' longer edge pointing up as returned by atan2, but in degree.

References

Computational Geometry Algorithms Library. 2021. CGAL Chapter 65: Bounding Volumes. https://doc.cgal.org/Manual/latest/doc_html/cgal_manual/Bounding_volumes/Chapter_main.html Toussaint, G. T. 1983. Solving geometric problems with the rotating calipers. In: Proceedings of the 1983 IEEE MELECON. Athens, Greece: IEEE Computer Society.

See Also

drawBox2, getBoundingBox, getMinCircle

Examples

# coordinates given by a suitable data frame
bb <- getMinBBox(DFsavage)               # minimum bounding box

# plot points and minimum bounding box
plot(point.y ~ point.x, data=DFsavage, asp=1,
     xlim=range(bb$pts[ , 1]), ylim=range(bb$pts[ , 2]), pch=16)
drawBox2(bb, fg='blue', colCtr='blue', pch=4, cex=2)

bb$FoM                                   # figure of merit
bb$angle                                 # box orientation

# coordinates given by a matrix
## Not run: 
xy <- matrix(round(rnorm(16, 100, 15)), ncol=2)
getMinBBox(xy)

## End(Not run)