Drexel University  ENGR 231 Linear Engineering Systems, Fall 2011
Copyright 2011, Drexel University
Page 1
Lab 5  Homogeneous Coordinate Transformations
Goals:
1. Perform homogeneous coordinate transformations, as in section 2.7.
2. Display animations using transformations.
Prelab  Drawing shapes with MATLAB
As the title of the lab suggests, we will be applying the concepts of homogeneous
coordinates from
Lay, Section 2.7
, to perform some basic image transformations via MATLAB.
However, before we may begin transforming basic images, we introduce the concept of drawing
shapes and polygons with MATLAB.
Shapes can be plotted in MATLAB by using the
fill
function. Similar to the
plot
function, this takes a set of coordinates and a color, and plots a 2D image. The coordinate pairs
passed to the fill function however determine the
vertices
of a polygon. When the function is
called, MATLAB will start at the first coordinate pair, draw a line segment to the next one, and
so on until the last coordinate pair is reached. MATLAB will then draw a final segment to close
the object and fill it with the specified color.
Note the when using the fill command, the order
of the points matter!
Let’s examine the following example. Suppose we wanted to plot a red object with the
following vertices:
Vertex
1
2
3
X – Coordinates
0.0
0.5
1.0
Y – Coordinates
0.0
1.5
0.0
First, we form a matrix of all of the above points with the
x
coordinates in the first row and
y

coordinates in the second row. Each column thus represents a vertex coordinate pair in 2D (
again
note that the order matters
). The actual code to do this and to then plot the object is shown below
in Example 1.
Ex 1:
%% Plot the Three Above Vertices as a Red Polygon
% Form the coordinate matrix
triangle = [0 0.5 1.0
0 1.5 0.0];
% Call the fill function. First input is the xvalues of the vertices
% and second input is the yvalues
fill(triangle(1,:),triangle(2,:),
'r'
)
axis
equal
Executing the code in Example 1 produces the following image:
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Copyright 2011, Drexel University
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0.5
0
0.5
1
1.5
0
0.5
1
1.5
Prelab Part 2 – Image Transformations in Homogeneous Coordinates
Now suppose we wanted to transform the above image based on some of the concepts we
learned about in Section 2.7. For instance, to performing a rotation about the origin we know that
the transformation looks like:
Rot(
T
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 Fall '10
 OlehTretiak
 Geometry, Coordinate system, Linear Engineering Systems

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