/**
 * Computes a contour for a given input grid function using the <a
 * href="http://en.wikipedia.org/wiki/Marching_squares">marching
 * squares</a> algorithm. Returns the contour polygon as an array of points.
 *
 * @param grid a two-input function(x, y) that returns true for values
 * inside the contour and false for values outside the contour.
 * @param start an optional starting point [x, y] on the grid.
 * @returns polygon [[x1, y1], [x2, y2], …]
 */
d3.geom.contour = function(grid, start) {
  var s = start || d3_geom_contourStart(grid), // starting point
      c = [],    // contour polygon
      x = s[0],  // current x position
      y = s[1],  // current y position
      dx = 0,    // next x direction
      dy = 0,    // next y direction
      pdx = NaN, // previous x direction
      pdy = NaN, // previous y direction
      i = 0;

  do {
    // determine marching squares index
    i = 0;
    if (grid(x-1, y-1)) i += 1;
    if (grid(x,   y-1)) i += 2;
    if (grid(x-1, y  )) i += 4;
    if (grid(x,   y  )) i += 8;

    // determine next direction
    if (i === 6) {
      dx = pdy === -1 ? -1 : 1;
      dy = 0;
    } else if (i === 9) {
      dx = 0;
      dy = pdx === 1 ? -1 : 1;
    } else {
      dx = d3_geom_contourDx[i];
      dy = d3_geom_contourDy[i];
    }

    // update contour polygon
    if (dx != pdx && dy != pdy) {
      c.push([x, y]);
      pdx = dx;
      pdy = dy;
    }

    x += dx;
    y += dy;
  } while (s[0] != x || s[1] != y);

  return c;
};

// lookup tables for marching directions
var d3_geom_contourDx = [1, 0, 1, 1,-1, 0,-1, 1,0, 0,0,0,-1, 0,-1,NaN],
    d3_geom_contourDy = [0,-1, 0, 0, 0,-1, 0, 0,1,-1,1,1, 0,-1, 0,NaN];

function d3_geom_contourStart(grid) {
  var x = 0,
      y = 0;

  // search for a starting point; begin at origin
  // and proceed along outward-expanding diagonals
  while (true) {
    if (grid(x,y)) {
      return [x,y];
    }
    if (x === 0) {
      x = y + 1;
      y = 0;
    } else {
      x = x - 1;
      y = y + 1;
    }
  }
}