%% Benefits of Using Grid-Based Interpolation
%% Section 1
% To illustrate the power of binary searches, consider the following example. Before the advent of electronic credit card authorizations, the only protection merchants had against fraudulent credit card purchases was to compare the account number on each customer's credit card against a list of "bad" account numbers. These lists were bound booklets with tens of thousands of card numbers arranged in ascending order. How many comparisons would be required to search through a list of 10,000 account numbers for one sale? It turns out that for any list of n ordered items, the maximum number of comparisons will be no more than the number of times you can divide the list in half, or log2(n). Therefore, the credit card search will take no more than log2(10e3) or about 13 comparisons. That's a pretty impressive if you consider how many comparisons it would take to perform a sequential search.
% By contrast, consider a problem with a scattered data set.

x = rand(20,1);
y = rand(20,1);
scatter(x,y)

% To find the points in close proximity to a query point would require many more operations. If your data can be approximated as a grid, grid-based interpolation will provide substantial savings in computation and memory usage.
% Copyright 2015 The MathWorks, Inc.