Largest-Triangle-Three Bucket Downsampling Graphs in C# (For an Array of Floats) http://i.imgur.com/UwhvV45.png

LTTBD.cs

public float[] Downsample(float[] array, int Length)
{
    int insert = 0;
    float[] window = new float[Length];
    float[] window_x = new float[Length];
    int bucket_size_less_start_and_end = Length - 2;
    
    float bucket_size = (float)(array.Length - 2) / bucket_size_less_start_and_end; 
    int a = 0;
    int next_a = 0;
    int max_area_point_x = 0;
    float max_area_point_y = 0f;
    window[insert] = array[a]; // Always add the first point
    window_x[insert] = 0;
    insert++;
    for (int i = 0; i < bucket_size_less_start_and_end; i++)
    {
        // Calculate point average for next bucket (containing c)
        float avg_x = 0;
        float avg_y = 0;
        int start = (int)(Math.Floor((i + 1) * bucket_size) + 1);
        int end = (int)(Math.Floor((i + 2) * bucket_size) + 1);
        if (end >= array.Length)
        {
            end = array.Length;
        }
        int span = end - start;
        for (; start < end; start++)
        {
            avg_x += start;
            avg_y += array[start];
        }
        avg_x /= span;
        avg_y /= span;

        // Get the range for this bucket
        int bucket_start = (int)(Math.Floor((i + 0) * bucket_size) + 1);
        int bucket_end = (int)(Math.Floor((i + 1) * bucket_size) + 1);

        // Point a
        float a_x = a;
        float a_y = array[a];
        float max_area = -1;
        for (; bucket_start < bucket_end; bucket_start++)
        {
            // Calculate triangle area over three buckets
            float area = Math.Abs((a_x - avg_x) * (array[bucket_start] - a_y) - (a_x - (float)bucket_start) * (avg_y - a_y)) * 0.5f;
            if (area > max_area)
            {
                max_area = area;
                max_area_point_x = bucket_start;
                max_area_point_y = array[bucket_start];
                next_a = bucket_start; // Next a is this b
            }
        }
        // Pick this point from the Bucket
        window[insert] = max_area_point_y;
        window_x[insert] = max_area_point_x;
        insert++;

        // Current a becomes the next_a (chosen b)
        a = next_a;
    }

    window[insert] = array[array.Length - 1]; // Always add last
    window_x[insert] = array.Length;

    return window;
}

Pretty good stuff!