gMOIP (version 1.5.3)

inHull: Efficient test for points inside a convex hull in p dimensions.

Description

Efficient test for points inside a convex hull in p dimensions.

Usage

inHull(
  pts,
  vertices,
  hull = NULL,
  tol = mean(mean(abs(as.matrix(vertices)))) * sqrt(.Machine$double.eps)
)

Value

An integer vector of length \(n\) with values 1 (inside hull), -1 (outside hull) or 0 (on hull to precision indicated by tol).

Arguments

pts

A \(nxp\) array to test, \(n\) data points, in dimension \(p\). If you have many points to test, it is most efficient to call this function once with the entire set.

vertices

A \(mxp\) array of vertices of the convex hull. May contain redundant (non-vertex) points.

hull

Tessellation (or triangulation) generated by convhulln (only works if the dimension of the hull is \(p\)). If hull is NULL, then it will be generated.

tol

Tolerance on the tests for inclusion in the convex hull. You can think of tol as the difference a point value may be different from the values of the hull, and still be perceived as on the surface of the hull. Because of numerical slop nothing can ever be done exactly here. In higher dimensions, the numerical issues of floating point arithmetic will probably suggest a larger value of tol. tol is not used if the dimension of the hull is larger than one and not equal \(p\).

Author

Lars Relund

Examples

## In 1D
vertices <- matrix(4, ncol = 1)
pt <- matrix(c(2,4), ncol = 1, byrow = TRUE)
inHull(pt, vertices)
vertices <- matrix(c(1,4), ncol = 1)
pt <- matrix(c(1,3,4,5), ncol = 1, byrow = TRUE)
inHull(pt, vertices)

## In 2D
vertices <- matrix(c(2,4), ncol = 2)
pt <- matrix(c(2,4, 1,1), ncol = 2, byrow = TRUE)
inHull(pt, vertices)
vertices <- matrix(c(0,0, 3,3), ncol = 2, byrow = TRUE)
pt <- matrix(c(0,0, 1,1, 2,2, 3,3, 4,4), ncol = 2, byrow = TRUE)
inHull(pt, vertices)
vertices <- matrix(c(0,0, 0,3, 3,0), ncol = 2, byrow = TRUE)
pt <- matrix(c(0,0, 1,1, 4,4), ncol = 2, byrow = TRUE)
inHull(pt, vertices)

# \donttest{
## in 3D
vertices <- matrix(c(2,2,2), ncol = 3, byrow = TRUE)
pt <- matrix(c(1,1,1, 3,3,3, 2,2,2, 3,3,2), ncol = 3, byrow = TRUE)
inHull(pt, vertices)

vertices <- matrix(c(2,2,2, 4,4,4), ncol = 3, byrow = TRUE)
ini3D()
plotHull3D(vertices)
pt <- matrix(c(1,1,1, 2,2,2, 3,3,3, 4,4,4, 3,3,2), ncol = 3, byrow = TRUE)
plotPoints3D(pt, addText = TRUE)
finalize3D()
inHull(pt, vertices)

vertices <- matrix(c(1,0,0, 1,1,0, 1,0,1), ncol = 3, byrow = TRUE)
ini3D()
plotHull3D(vertices)
pt <- matrix(c(1,0.1,0.2, 3,3,2), ncol = 3, byrow = TRUE)
plotPoints3D(pt, addText = TRUE)
finalize3D()
inHull(pt, vertices)

vertices <- matrix(c(2,2,2, 2,4,4, 2,2,4, 4,4,2, 4,2,2, 2,4,2, 4,2,4, 4,4,4), ncol = 3,
            byrow = TRUE)
ini3D()
plotHull3D(vertices)
pt <- matrix(c(1,1,1, 3,3,3, 2,2,2, 3,3,2), ncol = 3, byrow = TRUE)
plotPoints3D(pt, addText = TRUE)
finalize3D()
inHull(pt, vertices)
# }

## In 5D
vertices <- matrix(c(4,0,0,0,0, 0,4,0,0,0, 0,0,4,0,0, 0,0,0,4,0, 0,0,0,0,4, 0,0,0,0,0),
            ncol = 5, byrow = TRUE)
pt <- matrix(c(0.1,0.1,0.1,0.1,0.1, 3,3,3,3,3, 2,0,0,0,0), ncol = 5, byrow = TRUE)
inHull(pt, vertices)