This algorithm decomposes a general polygon into simple polygons and uses the “ear-clipping” algorithm to triangulate it. Polygons with holes are supported.
triangulate(x, y = NULL, z = NULL, random = TRUE, plot = FALSE, partial = NA)A three-by-n array giving the indices of the vertices of each triangle. (No vertices are added; only the original vertices are used in the triangulation.)
The array has an integer vector attribute "nextvert"
with one entry per vertex, giving the index of the next vertex to proceed counter-clockwise around outer polygon boundaries, clockwise around inner boundaries.
Coordinates of a two-dimensional polygon in a format supported by xyz.coords.
See Details for a description of proper input and
how z is handled.
Currently ignored, the triangulation is deterministic.
Whether to plot the triangulation; mainly for debugging purposes.
Currently ignored. Improper input will lead to undefined results.
R wrapper code written by Duncan Murdoch; the
earcut library has numerous authors.
Normally triangulate looks only at the x and y
coordinates. However, if one of those is constant, it is replaced
with the z coordinate if present.
The algorithm works as follows. First, it breaks the polygon into
pieces separated by NA values in x or y.
Each of these pieces should be a simple, non-self-intersecting
polygon, not intersecting the other pieces.
(Though some minor exceptions to this rule may work, none
are guaranteed). The nesting of these pieces is
determined: polygons may contain holes, and the
holes may contain other polygons.
Vertex order around the polygons does not affect the results: whether a polygon is on the outside or inside of a region is determined by nesting.
Polygons should not repeat vertices. An attempt is made to detect if the final vertex matches the first one. If so, it will be deleted with a warning.
The “outer” polygon(s) are then merged with the polygons that they immediately contain, and each of these pieces is triangulated using the ear-clipping algorithm from the references.
Finally, all the triangulated pieces are put together into one result.
This function uses the C++ version of the
earcut library from https://github.com/mapbox/earcut.hpp.
extrude3d for a solid extrusion of a polygon, polygon3d for
a flat display; both use triangulate.
theta <- seq(0, 2*pi, length.out = 25)[-25]
theta <- c(theta, NA, theta, NA, theta, NA, theta, NA, theta)
r <- c(rep(1.5, 24), NA, rep(0.5, 24), NA, rep(0.5, 24), NA, rep(0.3, 24), NA, rep(0.1, 24))
dx <- c(rep(0, 24), NA, rep(0.6, 24), NA, rep(-0.6, 24), NA, rep(-0.6, 24), NA, rep(-0.6, 24))
x <- r*cos(theta) + dx
y <- r*sin(theta)
plot(x, y, type = "n")
polygon(x, y)
triangulate(x, y, plot = TRUE)
open3d()
polygon3d(x, y, x - y, col = "red")
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