table,

  xColumnOrExpr and yColumnOrExpr – columns or column expressions for x and y

  maxPoints – maximum number of bins

  xyRatio (default 1, aspect ratio of the plot – if we want bins to be more square-like)

  xMin, xMax, yMin, yMax (if NaN, use min or max value of the corresponding column/column expression)

1. “decimated" table with the following columns:

        x, y, rowidx, weight, decimateKey  

where

        x, y – x and Y values of a “representative” point – a random point from the bin

        rowidx – row index of the “representative” point in the original table

        weight – total number of points in the bin

        decimateKey – a string "<xIndex>:<yIndex>”, which identifies the bin

2. decimate key information, which contains xMin, xMax, xUnit, and yUnit

            this information allows to calculate center of the bin from x and y values above

1. Calculate min and max of x and y columns OR accept them as parameters.

2. Calculate xUnit and yUnit:

    nXbins = (int)sqrt(maxPoints*xyRatio)

    nYbins = (int)sqrt(maxPoints/xyRatio)

    xUnit = (xMax - xMin)/nXs

    yUnit = (yMax - yMin)/nYs;

    // increase cell size a bit to include max values into grid

    xUnit += xUnit/1000.0/nXs;

    yUnit += yUnit/1000.0/nYs;

3. Create a map from bin key (decimateKey) to sample (“representative”) point.

    for each row

       get x and y values (xval and yval) for this row

       if either x or y and NaN or the point is not within limits, continue to the next row

       calculate decimateKey:

          xIndex = (int)((xval-xMin)/xUnit)

          yIndex = (int)((yval-yMin)/yUnit)

          decimateKey = xIndex+”:”+yIndex

      if decimateKey is already present in the map:

          increase the number of represented rows  weight for this bin by one           

          randomly decide if the current row should be chosen as a “representative”:

             if (Math.random < 1.0/weight):

                make current row representative

      else 

         add current point to the map with weight 1

4. Create an output table from the map created in step 3