14:440:127– Introduction to Computers for Engineers
Notes for Lecture 10
Rutgers University, Fall 2008
Instructor Blase E. Ur
Don’t forget that Exam 2 runs 11/5  11/11. 4 written(20min), 4 computer(60min)
Also, note that we’re going slightly out of order from the syllabus.
The topics in this lecture
are all in Chapter 12.
1
Interpolation
Oftentimes when you gather data, you’ll want to estimate the values of intermediate points. To do
this in Matlab, you use
interpolation
, those methods that draw lines or curves between measured
(or observed) points so that you can estimate intermediate values.
1.1
Linear Interpolation
The simplest method of interpolation is linear interpolation, which basically encompasses drawing
a line between each consecutive data point that you measure. Then, to estimate any intermediate
value, you just find that point on those lines. Note that linear interpolation
doesn’t
draw one line
that fits all of the data points.
It draws many small lines that connect every consecutive point.
Thus, each measured data point is the endpoint of a line.
To perform linear interpolation in Matlab, you use the
interp1
function. Note that the last charac
ter in the function’s name is the number ”one,”
not
the letter ”L.” The
interp1
function requires 3
input arguments: a vector containing the x points you measured, a vector containing the y points
you measured, and a third vector containing the new x values for which you want to estimate the
values of y points. The function returns a vector of estimates for those y values.
The example below shows 5 ”measured” data points, stored as x and y.
We then use
interp1
to estimate y values for x values from 1 to 5, in intervals of 0.1. Below, you can see the resulting
plot, in which the measured points are simply O’s, whereas the lines connecting those points are
actually the interpolated values. Note that the interpolated lines go through each of the measured
data points.
x=1:5;
y = [2 6 6.2 7.4 10];
newx = 1:0.1:5;
newy = interp1(x,y,newx);
plot(x,y,’O’,newx,newy)
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1.2
Cubic Spline Interpolation
Instead of drawing lines between points, you sometimes instead want to draw curves that snake
through each of those points. This method of using curves to smoothly connect points is known as
cubic spline interpolation
and is used extensively in computer graphics (i.e. keyframe animation),
image processing, and motion control for robots.
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 Fall '08
 Finch
 Regression Analysis, Spline interpolation

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