function [vals] = alpha_test2(data,base)

    n = length(data);

    %transform opacity to tranclucency
    data = 1-data;

    %init alpha
    trans = data(n);

    %init results vector
    vals = zeros(1,n-1);

    %back to front
    for i=n-1:-1:1

        %alpha = alpha_{k-1}+alpha_{k}*(1-alpha_{k-1})
        trans = data(i)+trans*base^data(i);

        %store intermediate results to plot
        vals(i) = trans;
    end
end