trilinear2Cartesian {tigers}

Trilinear Coordinates

Description

trilinear2Cartesian calculates the coordinates of a point inside a triangle given three values interpreted as proportions.

Cartesian2trilinear does the reverse operation.

Usage

trilinear2Cartesian(p, X)
Cartesian2trilinear(xy, X)

Arguments

p

a vector with three numeric values (see details).

X

a numeric matrix with 3 rows and 2 columns giving the coordinates of the triangle.

xy

a vector with two numeric values (Cartesian coordinates).

Details

The values in p do not need to sum to one since they are scaled internally.

The triangle defined by X can be of any type. The coordinates returned by trilinear2Cartesian is always inside the triangle.

Cartesian2trilinear does not check if xy is inside the triangle.

Value

trilinear2Cartesian returns a numeric matrix with a single row and two columns giving the coordinates of the point.

Cartesian2trilinear returns a numeric matrix with a single row and three columns.

Author(s)

Emmanuel Paradis

References

https://en.wikipedia.org/wiki/Trilinear_coordinates

Examples

## rectangular triangle (counterclockwise):
X <- rbind(c(0, 0), c(0, 1), c(1, 0))
plot(X, , "n", asp = 1)
polygon(X)

h <- sqrt(2) # hypothenuse length

points(trilinear2Cartesian(c(1, 1, 1), X)) # incenter
points(trilinear2Cartesian(c(1, h, h), X), pch = 2) # centroid
points(trilinear2Cartesian(c(h, 1, 1), X), pch = 3) # symmedian point
## the 3 midpoints:
points(trilinear2Cartesian(c(0, h, h), X), pch = 7)
points(trilinear2Cartesian(c(1, 0, h), X), pch = 7)
points(trilinear2Cartesian(c(1, h, 0), X), pch = 7)

legend("topright", ,
       c("incenter", "centroid", "symmedian point", "midpoints"),
       pch = c(1:3, 7))

f <- c(0.1, 0.3, 0.6)
o <- trilinear2Cartesian(f, X)
p <- Cartesian2trilinear(o, X)
p - f # < 1e-15
stopifnot(all.equal(as.vector(p), f))