Area of a Polygon
Calculates the area and length of a polygon given by the vertices in the
vectors x and y.
polyarea(x, y) poly_length(x, y) poly_center(x, y) poly_crossings(L1, L2)
x |
x-coordinates of the vertices defining the polygon |
y |
y-coordinates of the vertices |
L1, L2 |
matrices of type |
polyarea calculates the area of a polygon defined by the vertices
with coordinates x and y. Areas to the left of the vertices
are positive, those to the right are counted negative.
The computation is based on the Gauss polygon area formula. The polygon automatically be closed, that is the last point need not be / should not be the same as the first.
If some points of self-intersection of the polygon line are not in the vertex set, the calculation will be inexact. The sum of all areas will be returned, parts that are circulated in the mathematically negative sense will be counted as negative in this sum.
If x, y are matrices of the same size, the areas of all
polygons defined by corresponding columns are computed.
poly_center calculates the center (of mass) of the figure defined by
the polygon. Self-intersections should be avoided in this case.
The mathematical orientation of the polygon does not have influence on the
center coordinates.
poly_length calculates the length of the polygon
poly_crossings calculates the crossing points of two polygons given
as matrices with x- and y-coordinates in the first and second row. Can be
used for finding the crossing points of parametrizised curves.
Area or length of the polygon resp. sum of the enclosed areas; or the coordinates of the center of gravity.
poly_crossings returns a matrix with column names x and
y representing the crossing points.
# Zu Chongzhi's calculation of pi (China, about 480 A.D.),
# approximating the circle from inside by a regular 12288-polygon(!):
phi <- seq(0, 2*pi, len=3*2^12+1)
x <- cos(phi)
y <- sin(phi)
pi_approx <- polyarea(x, y)
print(pi_approx, digits=8) #=> 3.1415925 or 355/113
poly_length(x, y) #=> 6.2831852 where 2*pi is 6.2831853
x1 <- x + 0.5; y1 <- y + 0.5
x2 <- rev(x1); y2 <- rev(y1)
poly_center(x1, y1) #=> 0.5 0.5
poly_center(x2, y2) #=> 0.5 0.5
# A simple example
L1 <- matrix(c(0, 0.5, 1, 1, 2,
0, 1, 1, 0.5, 0), nrow = 2, byrow = TRUE)
L2 <- matrix(c(0.5, 0.75, 1.25, 1.25,
0, 0.75, 0.75, 0 ), nrow = 2, byrow = TRUE)
P <- poly_crossings(L1, L2)
P
## x y
## [1,] 1.00 0.750
## [2,] 1.25 0.375
## Not run:
# Crossings of Logarithmic and Archimedian spirals
# Logarithmic spiral
a <- 1; b <- 0.1
t <- seq(0, 5*pi, length.out = 200)
xl <- a*exp(b*t)*cos(t) - 1
yl <- a*exp(b*t)*sin(t)
plot(xl, yl, type = "l", lwd = 2, col = "blue",
xlim = c(-6, 3), ylim = c(-3, 4), xlab = "", ylab = "",
main = "Intersecting Logarithmic and Archimedian spirals")
grid()
# Archimedian spiral
a <- 0; b <- 0.25
r <- a + b*t
xa <- r * cos(t)
ya <- r*sin(t)
lines(xa, ya, type = "l", lwd = 2, col = "red")
legend(-6.2, -1.0, c("Logarithmic", "Archimedian"),
lwd = 2, col = c("blue", "red"), bg = "whitesmoke")
L1 <- rbind(xl, yl)
L2 <- rbind(xa, ya)
P <- poly_crossings(L1, L2)
points(P)
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.