dwp (version 1.1)

Acins: Calculate Area of Intersection inside Circle and Square with Common Center

Description

Calculate Area of Intersection inside Circle and Square with Common Center

Usage

Acins(r, s)

Value

vector of intersections of interiors of circles with squaure

Arguments

r

radius of the circle (vector or scalar)

s

half-width of the square (scalar)

Examples

 # calculate area in annulus intersecting square
s <- 10 # radius or half-width of square
r <- c(11, 12) # inner and outer radii of circle
diff(Acins(r, s)) # intersection of square and annulus
# figure to illustrate the calculated area:
theta <- seq(0, 2 * pi, length = 1500)
plot(0, xlim = max(r) * c(-1, 1), ylim = max(r) * c(-1, 1),
  xlab = "x", ylab = "y", asp = 1, bty = "n", type = "n")
xi <- r[1] * cos(theta)
yi <- r[1] * sin(theta)
xo <- r[2] * cos(theta)
yo <- r[2] * sin(theta)
i1 <- which(abs(xi) <= s & abs(yi) <= s)
i2 <- which(abs(xo) <= s & abs(yo) <= s)
i2 <- sort(i2, decreasing = TRUE)
xi <- xi[i1]
yi <- yi[i1]
xo <- xo[i2]
yo <- yo[i2]
polygon(col = 8, border = NA,
  x = c(xi[xi >= 0 & yi >= 0], xo[xo >= 0 & yo >= 0]), 
  y = c(yi[xi >= 0 & yi >= 0], yo[xo >= 0 & yo >= 0]))
polygon(col = 8, border = NA, 
  x = c(xi[xi <= 0 & yi >= 0], xo[xo <= 0 & yo >= 0]), 
  y = c(yi[xi <= 0 & yi >= 0], yo[xo <= 0 & yo >= 0]))
polygon(col = 8, border = NA,
  x = c(xi[xi <= 0 & yi <= 0], xo[xo <= 0 & yo <= 0]), 
 y = c(yi[xi <= 0 & yi <= 0], yo[xo <= 0 & yo <= 0]))
polygon(col = 8, border = NA,
 x = c(xi[xi >= 0 & yi <= 0], xo[xo >= 0 & yo <= 0]), 
 y = c(yi[xi >= 0 & yi <= 0], yo[xo >= 0 & yo <= 0]))
lines(r[1] * cos(theta), r[1]* sin(theta))
lines(r[2]* cos(theta), r[2] * sin(theta))
rect(-s, -s, s, s)
 # calculate areas in series of 1 m annuli extending to corner of square
 s <- 10.5 # radius of square (center to side)
 diff(Acins(r = 0:ceiling(sqrt(2) * s), s))