Does triangle overlap convex hull of points?

Does triangle overlap convex hull of points?

TriangleInHull(triangles, coordinates, buffer)

Arguments

triangles

Three-row matrix as produced by TriangleCentres().

coordinates

A matrix with two or three rows specifying the coordinates of points in x, y or a, b, c format.

buffer

Include triangles whose centres lie within buffer triangles widths (i.e. edge lengths) of the convex hull.

Value

TriangleInHull() returns a list with the elements:

• $inside: vector specifying whether each of a set of triangles produced by TriangleCentres() overlaps the convex hull of points specified by coordinates.

• $hull: Coordinates of convex hull of coordinates, after expansion to cover overlapping triangles.

See also

Other tiling functions: Polygon-Geometry, TriangleCentres()

Author

Martin R. Smith (martin.smith@durham.ac.uk)

Examples

set.seed(0)
nPts <- 50
a <- runif(nPts, 0.3, 0.7)
b <- 0.15 + runif(nPts, 0, 0.7 - a)
c <- 1 - a - b
coordinates <- rbind(a, b, c)

TernaryPlot(grid.lines = 5)
TernaryPoints(coordinates, pch = 3, col = 4)
triangles <- TriangleCentres(resolution = 5)
inHull <- TriangleInHull(triangles, coordinates)
polygon(inHull$hull, border = 4)
values <- rbind(triangles,
                z = ifelse(inHull$inside, "#33cc3333", "#cc333333"))
points(triangles["x", ], triangles["y", ],
       pch = ifelse(triangles["triDown", ], 6, 2),
       col = ifelse(inHull$inside, "#33cc33", "#cc3333"))
ColourTernary(values)