%% PchipDemo.m
%% Overview
% Illustrates piecewise cubic Hermite interpolation by calling |pchip|
% (which evaluates the piecewise polynomial interpolating the data in the
% vectors x and y at the list of points in the vector u)
%
% As output we get plots of
%
% * the data, 
% * values obtained from |pchip|, 
% * and a smooth MATLAB graph.

%% Initialization
clear all
close all
% Define the data and evaluation points
x = [3 1 5 6 0];
y = [1 -3 2 4 2];
u = linspace(0,6,50);

%% Call |pchip|
% Evaluate piecewise cubic Hermite interpolant at all points in u
v = pchip(x,y,u);

%% Plots
% Plot the data
hold on
xlim([-1 7])
ylim([-4 5])
plot(x,y,'bo','LineWidth',2)
legend('Data','Location','NorthWest')
pause

%%
% Plot the values computed with |pchip|
plot(u,v,'g*','LineWidth',2)
legend('Data','Values from pchip','Location','NorthWest')
pause

%%
% Let MATLAB do some more interpolation to get a continuous graph
plot(u,v,'r','LineWidth',2)
legend('Data','Values from pchip','MATLAB graph','Location','NorthWest')
hold off