planeR

ChrisToJ
2014-09-19

A “shiny” application to determine the best-fitting plane
for a set of five 3D points

The problem

In biology (e. g. 3D microscopy reconstruction) and
in geology (e. g. landmark measurements) and
in many other research areas it is sometimes necessary to determine a plain that best fits to a set of data points.
And often these data points are hard to obtain.

planeR can determine a plane from as few as five 3D point measurements.

Visualisation example

The normal vector (blue line) of the best-fitting plane is determined by orthogonal distance regression.

3D model

The five 3D measurement points are shown in red, the centroid of the points is shown in green.

Calculation example

M <- matrix(c(2, 1, 0, 2, 0, 1, 1,.5,
              .5, 1,0,.7, 1,.2,.5), 3)
# centroid of the points in matrix M
centroid <- apply(M, 1, mean)
centred <- sweep(M, 1, centroid, "-")
# normal vector of best-fitting plane
s <- svd(centred)
normal <- s$u[,match(min(s$d), s$d)]
centroid

[1] 1.40 0.34 0.54

normal

[1] -0.1326  0.6688  0.7316

Summary

planeR offers the following features:

  • flexible user input
  • centroid calculation
  • normal vector calculation
  • interactive 3D visualisation
  • good documentation

Please share the link with everybody who might be interested!