Matlab Chapter6.pdf

The following statements draw arrows indicating the direction of ∇V at points in the x − y
plane:
≫ [x y] = meshgrid(−2 : .2 : 2, −2 : .2 : 2);
≫ V = x. ∧ 2 + y;
≫ dx = 2 ∗ x;
≫ dy = dx; % dy same size as dx
≫ dy(:, :) = 1; % now dy is same size as dx but all 1’s
≫ contour(x, y, V )
The ‘contour’ lines indicate families of level surfaces; the gradient at any point is perpendicular
to the level surface which passes through that point. The vectors x and y are needed in the call
to contour to specify the axes for the contour plot.
Example 2.5 (Rotation of 3-D graphs) The view function enables you to specify the angle
from which you view a 3-D graph. To see it in operation, run the following program:
2.2.2 Polar plots
≫ a = zeros(30, 30);
≫ a(:, 15) = 0.2 ∗ ones(30, 1);
≫ a(7, :) = 0.1 ∗ ones(1, 30);
≫ a(15, 15) = 1;
≫ mesh(a)
≫ for az = −37.5 : 15 : −37.5 + 360
≫ mesh(a), view(az, el)
≫ pause(0.5)
≫ end
The point (x, y) in cartesian coordinates is represented by the point (θ, r) in polar coordinates,
where
x = r cos(θ),
y = r sin(θ),
and θ varies between 0 and 2θ radians (360 ◦ ).
The command polar(θ, r) generates a polar plot of the points with angles in theta and
magnitudes in r.
As an example, the statements
References
≫ x = 0 : pi/40 : 2 ∗ pi;
≫ polar(x, sin(2 ∗ x)), grid
[1] –, “Matlab7 Graphics”, The MathWorks, 2007.
[2] –, “Matlab7 Programming”, The MathWorks, 2007.
[3] –, “Matlab7 3-D Visualization”, The MathWorks, 2007.
[4] B. Hahn and D. T. Valentine, “Essential Matlab For Engineers and Scientists”, Elsevier,
third edition, 2007.
[5] D. J. Higham and N. J. Higham, “Matlab Guide”, SIAM puplications, 2000.
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