initial-constrained-value.R

drawrestr <- function() {
  R <- matrix(c(-1,-1,1,-1,1,0,-1,0,0,1),ncol=2,byrow=T)
  r <- matrix(c(-3,-2.5,0.5,0.1,3.3))
  # Intersections:
  poly_x <- c(-0.1, 0.5, 0.5, 0.25, -0.1)
  poly_y <- c( 3.3, 3.3, 3.0, 2.75, 3.1)
  rint <- r / R[,2]
  z <- c(1, 1)
  x <- z[1]
  y <- z[2]
  plot(x, y, xlim=c(-2,2), ylim=c(0,4), asp=1)
  P <- list()
  M <- list()
  for (i in 1:nrow(R)) {
    int <- rint[i,1]
    slope <- -R[i,1]/R[i,2]
    if (slope == Inf || slope == -Inf) abline(v=r[i]/R[i,1], col="gray")
    else abline(rint[i,1], -R[i,1]/R[i,2], col="gray")
  }
  polygon(poly_x, poly_y, lwd=2, col="#dddddd")
  
  
  pnext <- z
  restrs <- R %*% pnext - r
  count <- 0
  
  fixsample <- function(x, ...) x[sample.int(length(x), ...)]
  while (any(restrs > 0)) {
    count <- count + 1
    next_i <- fixsample(which(restrs > 0), 1)
    d <- (R[next_i,] %*% pnext - r[next_i]) / sum(R[next_i,]^2)
    vec <- 1.5 * -d * R[next_i,]
    arrows(pnext[1], pnext[2], pnext[1]+vec[1], pnext[2]+vec[2], col="red")
    pnext <- pnext + vec
    restrs <- R %*% pnext - r
  }
}

pdf("icv.pdf", onefile=T, width=5, height=5)
set.seed(123)
drawrestr()
set.seed(234)
drawrestr()
set.seed(348)
drawrestr()
dev.off()