create SM from array of rates v3

void CreateStretchMarkerRateEnvelope(MediaItem_Take* take, const vector<double>& pos, const vector<double>& rate) {
    double take_rate = GetMediaItemTakeInfo_Value(take, "D_PLAYRATE");
    double take_offset = GetMediaItemTakeInfo_Value(take, "D_STARTOFFS");
    auto item = (MediaItem*)GetSetMediaItemTakeInfo(take, "P_ITEM", nullptr);
    double item_len = GetMediaItemInfo_Value(item, "D_LENGTH");
    int num_sm = GetTakeNumStretchMarkers(take);

    // convert input item positions to take positions
    vector<double> tpos; tpos.reserve(pos.size());
    for (auto& p : pos) tpos.push_back(p * take_rate + take_offset);

    // prepare for stetch marker calculation
    vector<double> slope, tp;
    slope.reserve(pos.size());
    tp.reserve(pos.size());
    double dpp, disp, p, ro, dss;
    dpp = 0.0;
    disp = 0.0;
    p = 0.0;

    // calculate stretch markers
    for (size_t i = 0; i < tpos.size()-1; ++i) {
        p  += dpp;
        dss = tpos[i+1] - tpos[i];
        ro  = rate[i+1] + rate[i];
        disp += dpp - dss;
        dpp = dss / (ro/2);

        slope.push_back(1 - (2 * rate[i]) / ro);
        tp.push_back(p);
    }
    dpp = dss / rate.back();
    tp.push_back(p + dpp);
    slope.push_back(0);

    // add stretch markers
    for (int i = 0; i < pos.size(); ++i) SetTakeStretchMarker(take, -1, tp[i], &tpos[i]);

    // modify new stretch markers
    for (size_t i = 0; i < tp.size(); ++i) {
        SetTakeStretchMarker(take, i, tp[i], nullptr);
        SetTakeStretchMarkerSlope(take, i, slope[i]);
    }

    // set new item length
    SetMediaItemInfo_Value(item, "D_LENGTH", item_len + (disp + dpp) / take_rate);
}