# https://stackoverflow.com/questions/35194048/using-r-how-to-calculate
#-the-distance-from-one-point-to-a-line
# http://mathworld.wolfram.com/Point-LineDistance2-Dimensional.html
# Kimberling, C. "Triangle Centers and Central Triangles." Congr.
# Numer. 129, 1-295, 1998.
.dist2d <- function(a, b, c) {
    v1 <- b - c
    v2 <- a - b
    m <- cbind(v1, v2)
    d <- abs(det(m)) / sqrt(sum(v1 * v1))
    return(d)
}


.secondDerivativeEstimate <- function(v) {
    nv <- length(v)
    res <- rep(NA, nv)
    for (i in seq(2, nv - 1)) {
        res[i] <- v[i + 1] + v[i - 1] - (2 * v[i])
    }
    return(res)
}


.curveElbow <- function(var, perplexity, pvalCutoff = 0.05) {
    len <- length(perplexity)
    a <- c(var[1], perplexity[1])
    b <- c(var[len], perplexity[len])
    res <- rep(NA, len)
    for (i in seq_along(var)) {
        res[i] <- .dist2d(c(var[i], perplexity[i]), a, b)
    }
    elbow <- which.max(res)
    ix <- var > var[elbow]
    perplexitySde <- .secondDerivativeEstimate(perplexity)
    perplexitySdeSd <- stats::sd(perplexitySde[ix], na.rm = TRUE)
    perplexitySdeMean <- mean(perplexitySde[ix], na.rm = TRUE)
    perplexitySdePval <-
        stats::pnorm(perplexitySde,
            mean = perplexitySdeMean,
            sd = perplexitySdeSd,
            lower.tail = FALSE)
    # other <- which(ix & perplexitySdePval < pvalCutoff)
    return(list(elbow = var[elbow]))
}