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(What does "Endorsed by" mean?)Point Matrix. To represent a straight-line image in computer memory, we must store a list of all the endpoints of the line segments that comprise the image. If the point
Suppose there are
We then store the point matrix
Consider the list of points
The corresponding point matrix is
Line Matrix. The next thing we need to know is which pairs of points
to connect with lines. To store this information for
The order of
All the numbers in the line matrix
To specify line segments connecting the four points of Example 1 into a quadrilateral, we use the line matrix
Alternatively, we can specify line segments to form a triangle from the first
three points plus a line from
Figure 1 shows the points
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Demo 1 (MATLAB). Use your editor to enter the following MATLAB function file. Save it as vgraphl.m.
function vgraphl (points, lines);
% vgraphl (points, lines) plots the points as *'s and
% connects the points with specified lines. The points
% matrix should be 2xN, and the lines matrix should be 2xM.
% The field of view is preset to (-50,50) on both axes.
%
% Written by Richard T. Behrens, October 1989
%
m=length(lines); % find the number of
% lines.
axis([-50 50 -50 50]) % set the axis scales
axis('square')
plot(points(1,:),points(2,:),'*') % plot the points as *
hold on % keep the points...
for i=i:m % while plotting the
% lines
plot([points(1,lines(1,i)) points(1,lines(2,i))],..
[points(2,lines(2,lines(1,i)) points(2,lines(2,i))],'-')
end
hold off
After you have saved the function file, run MATLAB and type the following to enter the point and line matrices. (We begin with the transposes of the matrices to make them easier to enter.)
>> G = [
0.6052 -0.4728;
-0.4366 3.5555;
-2.6644 7.9629;
-7.2541 10.7547;
-12.5091 11.5633;
-12.5895 15.1372;
-6.5602 13.7536;
-31.2815 -7.7994;
-38.8314 -9.9874;
-44.0593 -1.1537;
-38.8314 2.5453;
-39.4017 9.4594;
-39.3192 15.0932;
-45.9561 23.4158]
>> G = G'
>> H = [
1 2;
2 3;
3 4;
4 5;
4 7;
5 6;
8 9;
9 10;
10 11;
11 12;
12 13;
12 14]
>> H = H'At this point you should use MATLAB's “save” command to save these matrices to a disk file. Type
>> save dippersAfter you have saved the matrices, use the function VGRAPH1 to draw
the image by typing
≫ vgraph1(G,H)The advantage of storing points and lines separately is that an object
can be moved and scaled by operating only on the point matrix
Surfaces and Objects. To describe a surface in three dimensions is a fairly complex task, especially if the surface is curved. For this reason, we will be satisfied with points and lines, sometimes visualizing flat surfaces based on the lines. On the other hand, it is a fairly simple matter to group the points and lines into distinct objects. We can define an object matrix K with one column for each object giving the ranges of points and lines associated with that object. Each column is defined as
As with the line matrix
Consider again Demo 1. We could group the points in
The first column of
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This work is licensed by Louis Scharf under a Creative Commons Attribution License (CC-BY 3.0), and is an Open Educational Resource.
Last edited by Daniel Williamson on Sep 17, 2009 1:29 pm -0500.
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