getMinCircle {shotGroups}

Minimum enclosing circle for a set of 2D-points

Description

Calculates center and radius of the minimum enclosing circle given a set of 2D-coordinates.

Usage

getMinCircle(xy)

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

## Default S3 method:
getMinCircle(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 Skyum algorithm based on the convex hull.

Value

A list containing the center and radius of the circle.

ctr

a numerical 2-vector giving the (x,y)-coordinates of the circle's center.

rad

a numerical value giving the radius of the circle.

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 Fischer, K.; Gaertner, B.; Kutz, M. 2003. Fast smallest-enclosing-ball computation in high dimensions. In: Proceedings of the 11th European Symposium on Algorithms (ESA), 630-641. https://github.com/hbf/miniball Gaertner, B. 2021. Miniball: Smallest Enclosing Balls of Points. https://people.inf.ethz.ch/gaertner/subdir/software/miniball.html Skyum, S. 1991. A simple algorithm for computing the smallest enclosing circle. Information Processing Letters 37(3), 121-125. Welzl, E. 1991. Smallest enclosing disks (balls and ellipsoids). In: Maurer H. (eds), New Results and New Trends in Computer Science 555, 359-370. doi 10.1007/BFb0038202.

See Also

drawCircle, getMinBBox, getBoundingBox

Examples

# coordinates given by a suitable data frame
mc <- getMinCircle(DFsavage)

# determine axis limits so that circle will be visible
xLims <- mc$ctr[1] + c(-mc$rad, mc$rad)
yLims <- mc$ctr[2] + c(-mc$rad, mc$rad)
plot(point.y ~ point.x, data=DFsavage,
     pch=16, asp=1, xlim=xLims, ylim=yLims)
drawCircle(mc, fg='blue')

# coordinates given by a matrix
## Not run: 
xy <- matrix(round(rnorm(20, 100, 15), 2), ncol=2)
getMinCircle(xy)

## End(Not run)