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