Position compression using relative coordinates in Javascript

Question

Goodafternoon. I have a set of coordinates

[ [ 52.52132, 4.52342 ], [ 52.52144, 4.52352 ], [ 52.52154, 4.52354 ], [ 52.52166, 4.52376 ] ]

How can I transform this that the first position (the first two coordinates) become the base. And all the following positions are relative distances to that base?

So, completely pseudo example:

This

[ [ 52.52132, 4.52342 ], [ 52.52144, 4.52352 ], [ 52.52154, 4.52354 ], [ 52.52166, 4.52376 ] ]

Would then become something like this:

[ [ 52.52132, 4.52342 ], [ 0.4123, 0.1232 ], [ 0.1232, 0.5523 ], [ 0.1233, 0.1232 ] ]

Where the first part [ 52.52132, 4.52342 ] is the starting point. And all other coordinates are relative to the previous one.

Answer 1

Is this what your after..

I'm not sure how your getting 0.4123, 0.1232, As 52.52144 - 52.52132 = 0.00012

Also if what your after is a simple LatLng compression / decompression system. I've done a little one here, it's a very simple compressor,.. It does what your after works out the different. But does multiple loops of multiplying the diffs by 1 10 100 1000, etc. And keeps track of what would return the smallest stringified result. In then store the multiplier as the first element.

eg. Your example would compress to -> 5,52.52132,4.52342,12,10,10,2,12,22

The 5 would equal a difference mutliplier of 100000, it will use that to work out what to divide the difference by. Adding say zlib to this would most likely then compress even more.

var g = [ [ 52.52132, 4.52342 ], [ 52.52144, 4.52352 ], [ 52.52154, 4.52354 ], [ 52.52166, 4.52376 ] ],
    n = g.slice(0,1);

function compressLatLng(g) {
  var smallest = null, r, mul;
  if (!g.length) return '';
  for (var l = 1; l < 6; l ++) {
    mul = Math.pow(10, l);
    r = [l,g[0][0],g[0][1]];
    for (var k = 1; k < g.length; k ++) {
      r.push(
        ((g[k][0] - g[k-1][0])*mul).toFixed(5)*1,
        ((g[k][1] - g[k-1][1])*mul).toFixed(5)*1
      );
    }
    var j = r.join(',');
    if (!smallest) smallest = j;
    else if (j.length < smallest.length) smallest = j;
  }  
  return smallest;
}

function uncompressLatLng(s) {
  var r = s.split(',');
  if (!r.length) return [];
  var mul = Math.pow(10,r[0]);
  var j = [[r[1]*1, r[2]*1]];
  var last = j[0];
  for (var l = 3; l < r.length; l += 2) {
    var t = [
      (last[0] + r[l] / mul).toFixed(5)*1,
      (last[1] + r[l+1] / mul).toFixed(5)*1
    ];
    j.push(t);
    last = t;
  }
  return j;
}


for (var l = 1; l < g.length; l ++) {
  n.push([
    (g[l][0] - g[l-1][0]).toFixed(5)*1,
    (g[l][1] - g[l-1][1]).toFixed(5)*1
  ]);
}

console.log('O:Original S:Simple C:Compressed U:Uncompressed');
console.log('O: ' + JSON.stringify(g));
console.log('S: ' + JSON.stringify(n));
var compressed = compressLatLng(g);
console.log('C: ' + compressed);
console.log('U: ' + JSON.stringify(uncompressLatLng(compressed)));