%Q1

close all
clear all



t = [2.0  2.2  2.4  3.3  3.5  3.7  3.9  4.5  4.8  5.0];
x = [120  130  130  140  140  130  140  150  160  170];
y = [100  180  200  180  150  180  200  220  240  250];



% cubic spline

PX = spline(t,x);
PY = spline(t,y);


% evalute the splines and then plot

T = linspace(2.0, 5.0, 100);

figure
plot(x,y,'o'); hold on
plot(ppval(PX,T),ppval(PY,T),'r-');

%Q2
% Data for HW 6, Problem 2

% Part a:
%t = [2.0  2.33  2.67  3.0  3.33  3.67  4.0  4.33  4.67  5.0];

% Part b:
%t = [2.0  2.8   3.1   3.4  3.48  3.52  3.6  3.9   4.2   5.0];

% Part c:
%t = [2.0  2.2   2.42  2.66 2.92  3.21  3.53 3.88  4.21  5.0];





x = [120  130  130  140  140  130  140  150  160  170];
y = [100  180  200  180  150  180  200  220  240  250];

PX = spline(t,x);
PY = spline(t,y);

T = linspace(2, 5, 100);

figure
plot(x,y,'o'); hold on
plot(ppval(PX,T),ppval(PY,T),'r-');45