R/getMinCircle2.R

In JoGall/rubitrail: rubitrail, a package to analyse the output of UbiTrail, an open-source video tracking program for analysis of animal locomotion.

# These functions are sourced from the 'shotGroups()' package:
# https://github.com/dwoll/shotGroups
#
# and example files available here:
# https://github.com/dwoll/RExRepos/blob/master/R/diagBounding.R
#==========================================================================

getMinCircle2 <- function(xy) {
    stopifnot(is.matrix(xy), is.numeric(xy), nrow(xy) >= 2, ncol(xy) == 2)

    H    <- chull(xy)      # convex hull indices (vertices ordered clockwise)
    hPts <- xy[H, ]        # points that make up the convex hull

    ## min circle may touch convex hull in only two points
    ## if so, it is centered between the hull points with max distance
    maxPD  <- getMaxPairDist(hPts)
    idx    <- maxPD$idx    # index of points with max distance
    rad    <- maxPD$d / 2  # half the distance -> radius
    rangeX <- c(hPts[idx[1], 1], hPts[idx[2], 1])
    rangeY <- c(hPts[idx[1], 2], hPts[idx[2], 2])
    ctr    <- c(rangeX[1] + 0.5*diff(rangeX), rangeY[1] + 0.5*diff(rangeY))

    ## check if circle centered between hPts[pt1Idx, ] and hPts[pt2Idx, ]
    ## contains all points (all distances <= rad)
    dst2ctr <- dist(rbind(ctr, hPts[-idx, ]))      # distances to center
    if(all(as.matrix(dst2ctr)[-1, 1] <= rad)) {    # if all <= rad, we're done
        tri <- rbind(hPts[idx, ], ctr)
        return(getCircleFrom3(tri))
    }

    ## min circle touches hull in three points - Skyum algorithm
    S <- H                               # copy of hull indices that will be changed
    while(length(S) >= 2) {
        n    <- length(S)                # number of remaining hull vertices
        Sidx <- seq(along=S)             # index for vertices
        post <- (Sidx %% n) + 1          # next vertex in S
        prev <- Sidx[order(post)]        # previous vertex in S
        mIdx <- getMaxRad(xy, S)         # idx for maximum radius

        ## triangle where mIdx is vertex B in ABC
        Smax <- rbind(xy[S[prev[mIdx]], ], xy[S[mIdx], ], xy[S[post[mIdx]], ])

        ## if there's only two hull vertices, we're done
        if(n <= 2) { break }

        ## check if angle(ABC) is > 90
        ## if so, eliminate B - if not, we're done
        if(isBiggerThan90(Smax)) { S <- S[-mIdx] } else { break }
    }

    return(getCircleFrom3(Smax))
}

getMaxRad <- function(xy, S) {
    stopifnot(is.matrix(xy), is.numeric(xy), nrow(xy) >= 2, ncol(xy) == 2)
    stopifnot(is.numeric(S), length(S) >= 2, length(S) <= nrow(xy))

    n    <- length(S)                    # number of points
    Sidx <- seq(along=S)                 # index for points
    rads <- numeric(n)                   # radii for all circles
    post <- (Sidx %% n) + 1              # next point in S
    prev <- Sidx[order(post)]            # previous point in S
    for(i in Sidx) {
        pts     <- rbind(xy[S[prev[i]], ], xy[S[i], ], xy[S[post[i]], ])
        rads[i] <- getCircleFrom3(pts)$rad  # circle radius
    }

    return(which.max(rads))
}

getMaxPairDist <- function(xy) {
    stopifnot(is.matrix(xy), is.numeric(xy), ncol(xy) == 2, nrow(xy) >= 2)

    # 2D -> only convex hull is relevant
    H    <- chull(xy)      # convex hull indices (vertices ordered clockwise)
    pts  <- xy[H, ]        # points that make up the convex hull
    N    <- nrow(pts)                      # number of points on hull
    dMat <- dist(pts, method="euclidean")  # distance matrix
    idx  <- which.max(as.matrix(dMat))     # maximum distance
    i    <- (idx-1) %/% N+1                # column -> point 1
    j    <- (idx-1) %%  N+1                # row    -> point 2
    mPts <- H[c(i, j)]                     # rows with max distance
    dst  <- max(dMat)                      # max distance

    return(list(d=dst, idx=mPts))
}

getCircleFrom3 <- function(xy) {
    stopifnot(is.matrix(xy), is.numeric(xy), nrow(xy) == 3, ncol(xy) == 2)

    aa <- xy[1,  ]
    bb <- xy[2,  ]
    cc <- xy[3,  ]
    y  <- xy[ , 2]

    xDeltaA <- bb[1] - aa[1]
    yDeltaA <- bb[2] - aa[2]
    xDeltaB <- cc[1] - bb[1]
    yDeltaB <- cc[2] - bb[2]
    xDeltaC <- cc[1] - aa[1]
    yDeltaC <- cc[2] - aa[2]

    ## check if the points are collinear: qr(xy)$rank == 1, or:
    ## determinant of difference matrix = 0, no need to use det()
    dMat <- rbind(c(xDeltaA, yDeltaA), c(xDeltaB, yDeltaB))
    if(isTRUE(all.equal(dMat[1,1]*dMat[2,2] - dMat[1,2]*dMat[2,1], 0, check.attributes=FALSE))) {
        ## define the circle as the one that's centered between the points
        rangeX <- range(c(aa[1], bb[1], cc[1]))
        rangeY <- range(c(aa[2], bb[2], cc[2]))
        ctr    <- c(rangeX[1] + 0.5*diff(rangeX), rangeY[1] + 0.5*diff(rangeY))
        rad    <- sqrt((0.5*diff(rangeX))^2 + (0.5*diff(rangeY))^2)
    } else {
        rad <- prod(dist(xy)) / (2 * abs(det(cbind(xy, 1))))  # circle radius
        v1  <- rowSums(xy^2)                    # first vector in the numerator
        v2x <- c( xDeltaB, -xDeltaC,  xDeltaA)  # 2nd vector numerator for Mx
        v2y <- c(-yDeltaB,  yDeltaC, -yDeltaA)  # 2nd vector numerator for My
        ctr <- c(t(v1) %*% v2y, t(v1) %*% v2x) / (2 * (t(y) %*% v2x))  # center
    }

    return(list(ctr=ctr, rad=rad))
}

isBiggerThan90 <- function(xy) {
    stopifnot(is.matrix(xy), is.numeric(xy), nrow(xy) == 3, ncol(xy) == 2)
    d   <- dist(xy)
    dAB <- d[1]
    dAC <- d[2]
    dBC <- d[3]
    return((dAB^2 + dBC^2 - dAC^2) < 0)
}