1d:T6fd,# Calculate Area of Intersection inside Circle and Square with Common Center ```r Acins(r, s) ``` ## Arguments - `r`: radius of the circle (vector or scalar) - `s`: half-width of the square (scalar) ## Returns vector of intersections of interiors of circles with squaure ## Examples ```r # 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)) ```

Acins function