Pixel 2 Hex Coordinate hack

pixel2hex.java

// cellRadius is the distance from center to vertex or length of an edge
// longSpan is the long side of the triangle
// shortSpan is short side

float[][] XM = new float[][] { { 1 / (2*longSpan), -1 / cellRadius }, { 1 / longSpan, 0 } };
float[][] YM = new float[][] { { 1 / (2*longSpan), 1 / cellRadius }, { -1 / (2*longSpan), 1 / cellRadius } };

  HVector pixel2hex(PVector pv) {
    int n;
    PVector mj = floorDot(pv, matrixXM);
    int j = floor((mj.x+mj.y+2)/3);
    PVector mk = floorDot(pv, matrixYM);
    int k = floor((mk.x+mk.y+2)/3);
    return new HVector(j,k);
  }

  PVector hex2pixel(HVector hv) {
    float x, y;
    x = hv.j * (2*longSpan) + hv.k*longSpan;
    y = hv.k * cellSide;
    return new PVector(x,y,0);
  }

  PVector floorDot(PVector v, float[][] mtx) {
    float j = floor(mtx[0][0]*v.x + mtx[0][1]*v.y);
    float k = floor(mtx[1][0]*v.x + mtx[1][1]*v.y);
    return new PVector(j,k,0);
  }


/* HVector is a class derived entirely from Processing PVector but
   uses integers instead of floats */

Hi, when you say

longSpan is the long side of the triangle

to which triangle do you refer? I really like this solution but am a little bit confused on how to go about calculating longSpan, cellRadius and shortSpan. It also appears that shortSpan isn't used in the code?