Points average(const Points & points, double timerange)
{
    Points result;

    for (int i = 0; i < points.size(); ++i)
    {
        auto p = points[i];
        double start = p.first - timerange/2;
        double end = p.first + timerange/2;
        double avg = p.second;
        int num_pts_found = 1;

        int needle = i-1;
        while (needle >= 0 && points[needle].first >= start)
        {
            avg += points[needle--].second;
            ++num_pts_found;
        }

        needle = i+1;
        while (needle < points.size() && points[needle].first <= end)
        {
            avg += points[needle++].second;
            ++num_pts_found;
        }

        result.push_back({ p.first, avg/=num_pts_found });
    }

    return result;
}