`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

`2xn`

with x- and y-coordinates.-
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.
`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.

`trapz`

, `arclength`

# 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)

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