#  venn
#'
#' Plot to-scale Venn diagram
#'
#' Plot a Venn diagram (with two groups), to scale, either with circles
#'   or with squares.
#'
#' @param setA Total area of set A.
#'
#' @param setB Total area of set B.
#'
#' @param both Area of intersection of sets A and B.
#'
#' @param method Indicates whether to plot circles or squares.
#'
#' @param labels Labels for the two sets.  (`NULL` for no labels.)
#'
#' @param col Colors of the two sets.
#'
#' @details
#' Plots a to-scale Venn diagram with two sets, so that the relative
#'   areas of the two sets and their intersection are exact.
#'
#' @importFrom stats uniroot
#' @export
#' @return
#' None.
#'
#' @examples
#' venn(setA=86, setB=1622, both=10)
#' venn(setA=86, setB=1622, both=10, method="square")
#'
#' @keywords
#' hplot
venn <-
    function(setA=50, setB=50, both=25,
             method=c("circle", "square"), labels=c("A","B"),
             col=c("blue","red"))
{
    if(setA < 0 || setB < 0 || both < 0)
        stop("The arguments must by non-negative.\n")
    if(both > setA || both > setB)
        stop("both must be < each of setA, setB.\n")
    setAonly <- setA-both
    setBonly <- setB-both

    method <- match.arg(method)

    if(method=="square") {
        # 1/2 lengths of the sides
        rA <- sqrt(setAonly + both)/2
        rB <- sqrt(setBonly + both)/2

        # y-axis location of centers of circles
        yA <- yB <- 0

        # x-axis location of centers of circles
        xA <- 0
        if(both==0) { # no overlap
            xB <- rA+rB+min(c(rA,rB))/4
        }
        else {
            if(setAonly == 0 || setBonly == 0) {
                xB <- 0
            }
            else {
                xB <- rA + rB - both/min(c(rA,rB))/2
            }
        }

        # center at (0,0)
        ctr <- (min(c(xA-rA,xB-rB)) + max(c(xA+rA,xB+rB)))/2
        xA <- xA - ctr
        xB <- xB - ctr

        ctr <- (min(c(yA-rA,yB-rB)) + max(c(yA+rA,yB+rB)))/2
        yA <- yA - ctr
        yB <- yB - ctr

        # x- and y-axis limits
        xli <- c(xA-rA,xB+rB)
        yli <- c(-1,1)*max(c(rA,rB))
        xli <- yli <- c(min(c(xli[1],yli[1])),
                        max(c(xli[2],yli[2])))

        # create empty plot figure
        par(pty="s",bty="n",mar=c(0.1,0.1,0.1,0.1))
        plot(0, 0, type="n", xlab="", ylab="", xaxt="n", yaxt="n",
             xlim=xli, ylim=yli)

        # plot the rectangles
        rect(xA-rA,yA-rA,xA+rA,yA+rA,lwd=2,border=col[1],angle=0)
        rect(xB-rB,yB-rB,xB+rB,yB+rB,lwd=2,border=col[2],angle=0)

        if(!is.null(labels)) {
            gap <- ((xB+rB)-xA)*0.02
            text(xA-rA+gap,yA,labels[1],adj=c(0,0), col=col[1])
            text(xB+rB-gap,yB,labels[2],adj=c(1,0),col=col[2])
        }
    }
    else {


        # radiuses of the circles
        rA <- sqrt((setAonly + both)/pi)
        rB <- sqrt((setBonly + both)/pi)

        # y-axis location of centers of circles
        yA <- yB <- 0

        ##############################
        # the key subroutine
        ##############################
        # find distance between circle centers to give a particular area
        #     we assume here that rB >= rA
        find.distance <-
            function(rA,rB,area)
            {
                # find area of overlap for two circles given radiuses
                #     and given distance betwen their centers
                find.overlap <-
                    function(rA,rB,d.betw.ctrs)
                    {
                        if(d.betw.ctrs == rB-rA) return(pi*rA^2)
                        if(d.betw.ctrs == rB+rA) return(0)

                        x <- (d.betw.ctrs^2 +rA^2 - rB^2)/(2*d.betw.ctrs)
                        y <- sqrt(rA^2 - x^2)

                        if(x >= 0)
                            return(asin(y/rA)*rA^2 - y*x +
                                   asin(y/rB)*rB^2 - y*(d.betw.ctrs-x))
                        else
                            return(rA^2*pi - asin(y/rA)*rA^2 - y*x +
                                   asin(y/rB)*rB^2 - y*(d.betw.ctrs-x))
                    }

                g <- function(d,rA,rB,area) find.overlap(rA,rB,d)-area
                uniroot(g,lower=rB-rA,upper=rB+rA, rA=rA, rB=rB,area=area)$root
            }
        ##############################
        # back to the venn() function
        ##############################

        # x-axis location of centers of circles
        xA <- 0
        if(both==0) { # no overlap
            xB <- rA+rB+min(c(rA,rB))/4
        }
        else {
            if(setAonly == 0 || setBonly == 0) {
                xB <- abs(rB-rA)/2
            }
            else {
                xB <- find.distance(min(c(rA,rB)),max(c(rA,rB)),both)
            }
        }

        # x- and y-axis limits
        xli <- yli <- c(min(c(xA-rA,yA-rA,xB-rB,yB-rB)),
                        max(c(xA+rA,yA+rA,xB+rB,yB+rB)))

        # adjust the centers to make picture symmetric
        yB <- yA <- mean(yli)

        left <- min(c(xA-rA,xB-rB)) - xli[1]
        right <- xli[2] - max(c(xA+rA,xB+rB))
        shift <- (left+right)/2 - left
        xA <- xA + shift
        xB <- xB + shift

        # create empty plot figure
        par(pty="s",bty="n",mar=c(0.1,0.1,0.1,0.1))
        plot(0, 0, type="n", xlab="", ylab="", xaxt="n", yaxt="n",
             xlim=xli, ylim=yli)

        # plot the circles
        z <- seq(0,2*pi,length=201)
        lines(rA*cos(z)+xA,rA*sin(z)+yA,lwd=2,col=col[1])
        lines(rB*cos(z)+xB,rB*sin(z)+yB,lwd=2,col=col[2])

        if(!is.null(labels)) {
            gap <- ((xB+rB)-xA)*0.02
            text(xA-rA+gap,yA,labels[1],adj=c(0,0),col=col[1])
            text(xB+rB-gap,yB,labels[2],adj=c(1,0),col=col[2])
        }
    }
    return(invisible())
}


######################################################################
# venn3
#
# Function to draw a venn diagram with 3 groups, "to scale",
# using rectangles
######################################################################

# I think this isn't working right

#venn3 <-
#function(A=17, B=37, C=55,
#         AB=9, AC=12, BC=28,
#         ABC=9, labels=c("A","B","C"),
#         col=c("black","blue","red"))
#{
#  # make A < B < C
#  if(A > B) {
#    x <- B;  B <- A;  A <- x
#    x <- BC;  BC <- AC;  AC <- x
#  }
#  if(B > C) {
#    x <- C; C <- B; B <- x
#    x <- AC; AC <- AB; AB <- x
#  }
#
#
#  x3 <- BC/sqrt(B)
#  y3 <- ABC/x3
#  y2 <- BC/x3-y3
#  y4 <- (AB-ABC)/x3
#  x2 <- AC/(y3+y4) - x3
#  x1 <- sqrt(C)-x2-x3
#  x4 <- sqrt(A)-x2-x3
#  x5 <- sqrt(B)-x3-x4
#  y1 <- sqrt(C)-y2-y3-y4
#  y5 <- sqrt(A)-y3-y4
#  x <- cumsum(c(0,x1,x2,x3,x4,x5))
#  y <- cumsum(c(0,y1,y2,y3,y4,y5))
#
#
#  lim <- c(0, max(c(x,y)))
#
#  if(max(x) < max(y))
#    x <- x + (max(y)-max(x))/2
#  else
#    y <- y + (max(x)-max(y))/2
#
#  oldmar <- par("mar")
#  oldpty <- par("pty")
#  oldbty <- par("bty")
#  on.exit(par(mar=oldmar,bty=oldbty,pty=oldpty))
#  par(mar=rep(1.1,4),bty="n",pty="s")
#  plot(0,0,type="n",xlab="",ylab="",xaxt="n",yaxt="n",xlim=lim,ylim=lim)
#
#  rect(x[1],y[1],x[4],y[5],lwd=3, border=col[1])
#
#  rect(x[3],y[2],x[6],y[4],lwd=3,border=col[2])
#
#  rect(x[2],y[3],x[5],y[6],lwd=3,border=col[3])
#
#  gap <- (x[5]-x[1])*0.02
#  text(x[1]+gap,y[1]+gap,labels[3],adj=c(0,0),col=col[1])
#  text(x[6]-gap,y[2]+gap,labels[2],adj=c(1,0),col=col[2])
#  text(x[2]+gap,y[6]-gap,labels[1],adj=c(0,1),col=col[3])
#  invisible()
#}
