Confidence interval for orthogonal regression

I have not found a method to estimate confidence interval of orthogonal regression. Then I build one using bootstrap.

OrthogonalRegression <- function(x, y) {
  library("pracma")
  xnew <- seq(from=min(x), to=max(x), length.out = 100)
  replicate <- 1000
  m <- matrix(data=NA, nrow=replicate, ncol=length(xnew))
  c <- NULL
  d <- NULL
  odrx <- odregress(x, y)
  for (r in 1:replicate) {
    s <- sample(1:length(x), length(x), replace = TRUE)
    odr <- odregress(x[s], y[s])
    cc <- odr$coeff
    c <- c(c, cc[1])
    d <- c(d, cc[2])
    # Prediction
    ynew <- cbind(xnew, 1) %*% cc
    m[r, ] <- ynew
  }
  q <- apply(m, MARGIN=2, FUN=quantile, probs=c(0.025, 0.5, 0.975))
  q <- rbind(q, x=xnew)
  qb <- quantile(c, probs=c(0.025, 0.5, 0.975))
  qa <- quantile(d, probs=c(0.025, 0.5, 0.975))
 
  return(list(model=odrx,
              values=q,
              intercept=qa,
              slope=qb))
}


x <- runif(100, min=10, max=20)
y <- runif(100, min=5, max=15)+x

or <- OrthogonalRegression(x, y)

plot(x, y, bty="n", las=1)
par(xpd=FALSE)
lines(or$values["x", ], or$values["50%", ])
lines(or$values["x", ], or$values["2.5%", ], lty=2)
lines(or$values["x", ], or$values["97.5%", ], lty=2)

abline(a=or$intercept[1], b=or$slope[3], col="red")
abline(a=or$intercept[3], b=or$slope[1], col="red")