Matlab Chapter6.pdf

for a = 12 and b = 5.
a = 12; b = 5;
t = 0 : 0.05 : 10 ∗ pi;
x = (a + b) ∗ cos(t) − b ∗ cos(a/b + l) ∗ t);
y = (a + b) ∗ sin(t) − b ∗ sin(a/b + l) ∗ t);
plot(x, y)
axis equal
axis([−25 25 − 25 25])
grid on
title( ′ Epicycloid: a = 12, b = 5 ′ )
xlabel( ′ x(t) ′ ), ylabel( ′ y(t) ′ )
• Plot the Legendre polynomials of degrees 1 to 4 (for the properties of these polynomials,
see, help of matlab) and use the legend function to add a box that explains the line styles.
x = −1 : .01 : 1;
p1 = x;
p2 = (3/2) ∗ x. ∧ 2 − 1/2;
p3 = (5/2) ∗ x. ∧ 3 − (3/2) ∗ x;
p4 = (35/8) ∗ x. ∧ 4 − (15/4) ∗ x. ∧ 2 + 3/8;
plot(x, pl, ′ r : ′ , x, p2, ′ g − − ′ , x, p3, ′ b − . ′ , x, p4, ′ m− ′ )
box off
legend( ′ \it n = 1 ′ , ′ \it n = 2 ′ , ′ \it n = 3 ′ , ′ \it n = 4 ′ , ′ Location ′ , ′ SouthEast ′ )
xlabel( ′ x ′ , ′ FontSize ′ , 12, ′ FontAngle ′ , ′ italic ′ )
ylabel( ′ P n ′ , ′ FontSize ′ , 12, ′ FontAngle ′ , ′ italic ′ , ′ Rotation ′ , 0)
title( ′ Legendre Polynomials ′ , ′ FontSize ′ , 14)
text(−.6, .7, ′ (n + 1)P n + 1(x) = (2n + 1)xP n(x) − nP n − 1(x) ′ , . . .
′ FontSize ′ , 12, ′ FontAngle ′ , ′ italic ′ )
Remark 1.4 Generally, typing legend(’string ′ 1, ’string 2 ’,. . ., ’string n ’) will create a legend
box that puts ’string i ’ next to the color/marker/line style information for the corresponding
plot. By default, the box appears in the top right-hand (northeast) corner of the axis area. The
location of the box can be specified with the syntax legend(’,. . ., ’Location’, location), where
location is a string with possible values that include:
’North’
’NorthWest’
’NorthOutside’
’Best’
’BestOutside’
inside plot box near top
inside top left
outside plot box near top
automatically chosen to give least conflict with data
automatically chosen to leave least unused space outside plot
These values can be abbreviated as ’N’, ’NW ’, etc. In our example we chose the bottom righthand
corner. Once the plot has been drawn, the legend box can be repositioned by putting the
cursor over it and dragging it using the left mouse button. The legend function has many other
options, which can be seen by typing doc legend.
2 3-D plots
MATLAB has a variety of functions for displaying and visualizing data in 3-D, either as lines
in 3-D, or as various types of surfaces. This section provides a brief overview.
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