CODEWITHSUNDEEP
javascriptarraysgeometrygraph-algorithm
HankMoody
HankMoody

Reputation: 3174

Represent a 2D circle as a 1D array (taxicab geometry, Von Neumann neighborhood)

Having a radius and an area of a circle in taxicab geometry (Von Neumann neighborhood), I would like to map all "fields" ("o" letters on the image) to 1D array indices and back.

I would like to convert from 1D array 0-based index to x, y coordinates and back (0, 0 is assumed to be the center).

   o  radius=0, area=1

   o
  ooo  radius=1, area=5
   o

   o
  ooo
 ooooo  radius=2, area=13
  ooo
   o

   o
  ooo
 ooooo
ooooooo  radius=3, area=25
 ooooo
  ooo
   o


x, y = taxicab.circlePositionFromIndex(index, radius)

index = taxicab.circleIndexFromPosition(x, y, radius)

What I have accomplished so far is this function which calculates x, y coordinates by iterating over a circle:

var _DIRECTIONS = [1, -1, -1, -1, -1, 1, 1, 1];

function indexToPosition(index, radius) {
    var i = 0;

    for (var r = 0; r <= radius; r++) {
        var x = 0, y = r;
        var direction = 0;
        var segment = 0;

        do {
            if (i === index)
                return [x, y];

            segment += 1;
            x += _DIRECTIONS[direction];
            y += _DIRECTIONS[direction+1];
            i += 1;

            if (segment === radius) {
                direction += 2;
                segment = 0;
            }
        } while (x !== 0 || y !== r);
    }

    return -1;
};

This function seems to be over-complicated for the task, there must be a simpler way. Also it works only one way.

To calculate area of a circle I'm using this function:

function area(radius) {
    return 1 + 2 * radius * (radius + 1);
}

Upvotes: 0

Views: 221

Answers (1)

MBo
MBo

Reputation: 80177

If numbering is like this: (else it could be mapped into desired coordinates)

      0
   1  2  3
4  5  6  7  8   
   9 10 11
     12

               (0,0)
        (1,0)  (1,1)   (1,2)
 (2,0)  (2,1)  (2,2)   (2,3)  (2,4)
        (3,0)  (3,1)   (3,2)
               (4,0)

then for upper triangle number of row is 

 row = Floor(Sqrt(index))

and column is

 col = index - row * row

If calculated row is larger then radius, make mirroring:

id = area - 1 - index
row_m  = Floor(Sqrt(id))
col_m = id - row_m * row_m

row = radius * 2 - row_m
col = row_m * 2 - col_m

quick check:
index = 6
row = 2
col = 6-4=2

index = 10
id = 2
row_m = 1
col_m = 1
row = 2*2-1 = 3
col = 2*1-1 = 1

Upvotes: 1

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