Help to find an algorithm for creating cells by spiral on the hexagonal field.
Look at the image:
Let's imagine an dimensionless 2d array. The X axis is the blue line, Y is horizontal, spiral is red.
I need to add cells from the central point x0y0 to point N by spiral
Tell me the way to solve the problem, please. Thank you!
I'd suggest changing the cells numbering sligtly, so that X remains the same when you go down and right (or up and left). Then simple algorithm like the following should work:
int x=0, y=0;
add(x, y); // add the first cell
int N=1
for( int N=1; <some condition>; ++N ) {
for(int i=0; i<N; ++i) add(++x, y); // move right
for(int i=0; i<N-1; ++i) add(x, ++y); // move down right. Note N-1
for(int i=0; i<N; ++i) add(--x, ++y); // move down left
for(int i=0; i<N; ++i) add(--x, y); // move left
for(int i=0; i<N; ++i) add(x, --y); // move up left
for(int i=0; i<N; ++i) add(++x, --y); // move up right
}
This generates the points as follows:
After a transformation we get:
(the circles have a diameter of 1)
Here's a function to get position i
:
void getHexPosition( int i, ref double x, ref double y )
{
if ( i == 0 ) { x = y = 0; return; }
int layer = (int) Math.Round( Math.Sqrt( i/3.0 ) );
int firstIdxInLayer = 3*layer*(layer-1) + 1;
int side = (i - firstIdxInLayer) / layer; // note: this is integer division
int idx = (i - firstIdxInLayer) % layer;
x = layer * Math.Cos( (side - 1) * Math.PI/3 ) + (idx + 1) * Math.Cos( (side + 1) * Math.PI/3 );
y = -layer * Math.Sin( (side - 1) * Math.PI/3 ) - (idx + 1) * Math.Sin( (side + 1) * Math.PI/3 );
}
Scaling the result by Math.Sqrt(.75)
gives
If you're interested in the skewed coordinates like in shura's answer:
int[] h = { 1, 1, 0, -1, -1, 0, 1, 1, 0 };
void getHexSkewedPosition( int i, ref int hx, ref int hy )
{
if ( i == 0 ) { hx = hy = 0; return; }
int layer = (int) Math.Round( Math.Sqrt( i/3.0 ) );
int firstIdxInLayer = 3*layer*(layer-1) + 1;
int side = (i - firstIdxInLayer) / layer;
int idx = (i - firstIdxInLayer) % layer;
hx = layer*h[side+0] + (idx+1) * h[side+2];
hy = layer*h[side+1] + (idx+1) * h[side+3];
}
void getHexPosition( int i, ref double hx, ref double hy )
{
int x = 0, y = 0;
getHexSkewedPosition( i, ref x, ref y );
hx = x - y * .5;
hy = y * Math.Sqrt( .75 );
}
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