Largest-Triangle-Three Bucket Downsampling Graphs in C#

LargestTriangleThreeBuckets.cs

public static IEnumerable<Tuple<double, double>> LargestTriangleThreeBuckets(List<Tuple<double, double>> data, int threshold)  
{
    int dataLength = data.Count;
    if (threshold >= dataLength || threshold == 0)
        return data; // Nothing to do

    List<Tuple<double, double>> sampled = new List<Tuple<double, double>>(threshold);

    // Bucket size. Leave room for start and end data points
    double every = (double)(dataLength - 2) / (threshold - 2);

    int a = 0;
    Tuple<double, double> maxAreaPoint = new Tuple<double, double>(0,0);
    int nextA = 0;

    sampled.Add(data[a]); // Always add the first point

    for (int i = 0; i < threshold - 2; i++)
    {
        // Calculate point average for next bucket (containing c)
        double avgX = 0;
        double avgY = 0;
        int avgRangeStart = (int)(Math.Floor((i + 1) * every) + 1);
        int avgRangeEnd = (int)(Math.Floor((i + 2) * every) + 1);
        avgRangeEnd = avgRangeEnd < dataLength ? avgRangeEnd : dataLength;

        int avgRangeLength = avgRangeEnd - avgRangeStart;

        for (; avgRangeStart < avgRangeEnd; avgRangeStart++)
        {
            avgX += data[avgRangeStart].Item1; // * 1 enforces Number (value may be Date)
            avgY += data[avgRangeStart].Item2;
        }
        avgX /= avgRangeLength;

        avgY /= avgRangeLength;

        // Get the range for this bucket
        int rangeOffs = (int)(Math.Floor((i + 0) * every) + 1);
        int rangeTo = (int)(Math.Floor((i + 1) * every) + 1);

        // Point a
        double pointAx = data[a].Item1; // enforce Number (value may be Date)
        double pointAy = data[a].Item2;

        double maxArea = -1;

        for (; rangeOffs < rangeTo; rangeOffs++)
        {
            // Calculate triangle area over three buckets
            double area = Math.Abs((pointAx - avgX) * (data[rangeOffs].Item2 - pointAy) -
                                   (pointAx - data[rangeOffs].Item1) * (avgY - pointAy)
                              ) * 0.5;
            if (area > maxArea)
            {
                maxArea = area;
                maxAreaPoint = data[rangeOffs];
                nextA = rangeOffs; // Next a is this b
            }
        }

        sampled.Add(maxAreaPoint); // Pick this point from the bucket
        a = nextA; // This a is the next a (chosen b)
    }

    sampled.Add(data[dataLength - 1]); // Always add last

    return sampled;
}

Thank you very much.

a little faster if the two expressions (pointAx - avgX) and (avgY - pointAy) are moved in front of the for-loop; multiply with 0.5 can be skipped (does not change the result)