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Manipulating Axes Aspect Ratio

Axes Aspect Ratio Properties

The axis command works by setting various axes object properties. You can set these properties directly to achieve precisely the effect you want.

Property

Description

DataAspectRatio

Sets the relative scaling of the individual axis data values. Set DataAspectRatio to [1 1 1] to display real-world objects in correct proportions. Specifying a value for DataAspectRatio overrides stretch-to-fill behavior.

DataAspectRatioMode

In auto, MATLAB® software selects axis scales that provide the highest resolution in the space available.

PlotBoxAspectRatio

Sets the proportions of the axes plot box (set box to on to see the box). Specifying a value for PlotBoxAspectRatio overrides stretch-to-fill behavior.

PlotBoxAspectRatioMode

In auto, MATLAB sets the PlotBoxAspectRatio to [1 1 1] unless you explicitly set the DataAspectRatio and/or the axis limits.

Position

Defines the location and size of the axes with a four-element vector: [left offset, bottom offset, width, height].

XLim, YLim, ZLim

Sets the minimum and maximum limits of the respective axes.

XLimMode, YLimMode, ZLimMode

In auto, MATLAB selects the axis limits.

By default, MATLAB automatically determines values for all of these properties (i.e., all the modes are auto) and then applies stretch-to-fill. You can override any property's automatic operation by specifying a value for the property or setting its mode to manual. The value you select for a particular property depends primarily on what type of data you want to display.

Much of the data visualized with MATLAB is either

  • Numerical data displayed as line or mesh plots

  • Representations of real-world objects (e.g., a dump truck or a section of the earth's topography)

In the first case, it is generally desirable to select axis limits that provide good resolution in each axis direction and to fill the available space. Real-world objects, on the other hand, need to be represented accurately in proportion, regardless of the angle of view.

Default Aspect Ratio Selection

There are two key elements to the default behavior — normalizing the axes size to the window size and stretch-to-fill.

The axes Position property specifies the location and dimensions of the axes. The third and fourth elements of the Position vector (width and height) define a rectangle in which MATLAB draws the axes (indicated by the dotted line in the following pictures). MATLAB stretches the axes to fill this rectangle.

The default value for the axes Units property is normalized to the parent figure dimensions. This means the shape of the figure window determines the shape of the position rectangle. As you change the size of the window, MATLAB reshapes the position rectangle to fit it.

The view is the 2-D projection of the plot box onto the screen.

As you can see, reshaping the axes to fit into the figure window can change the aspect ratio of the graph. MATLAB applies stretch-to-fill so the axes fill the position rectangle and in the process can distort the shape. This is generally desirable for graphs of numeric data, but not for displaying objects realistically.

MATLAB Defaults

MATLAB surface plots are well suited for visualizing mathematical functions of two variables. For example, to display a mesh plot of the function z=xe(-x2–y2)evaluated over the range -2 ≤ x ≤ 2, -4 ≤ y ≤ 4, use the statements

[X,Y] = meshgrid([-2:.15:2],[-4:.3:4]);
Z = X.*exp(-X.^2 - Y.^2);
mesh(X,Y,Z) 

The MATLAB default property values are designed to

  • Select axis limits to span the range of the data (XLimMode, YLimMode, and ZLimMode are set to auto).

  • Provide the highest resolution in the available space by setting the scale of each axis independently (DataAspectRatioMode and the PlotBoxAspectRatioMode are set to auto).

  • Draw axes that fit the position rectangle by adjusting the CameraViewAngle and then stretch-to-fill the axes if necessary.

Overriding Stretch-to-Fill

To maintain a particular shape, you can specify the size of the axes in absolute units such as inches, which are independent of the figure window size. However, this is not a good approach if you are writing a MATLAB file that you want to work with a figure window of any size. A better approach is to specify the aspect ratio of the axes and override automatic stretch-to-fill.

In cases where you want a specific aspect ratio, you can override stretching by specifying a value for these axes properties:

  • DataAspectRatio or DataAspectRatioMode

  • PlotBoxAspectRatio or PlotBoxAspectRatioMode

  • CameraViewAngle or CameraViewAngleMode

The first two sets of properties affect the aspect ratio directly. Setting either of the mode properties to manual simply disables stretch-to-fill while maintaining all current property values. In this case, MATLAB enlarges the axes until one dimension of the position rectangle constrains it.

Setting the CameraViewAngle property disables stretch-to-fill, and also prevents MATLAB from readjusting the size of the axes if you change the view.

Aspect Ratio Properties

It is important to understand how properties interact with each other, in order to obtain the results you want. The DataAspectRatio, PlotBoxAspectRatio, and the x-, y-, and z-axis limits (XLim, YLim, and ZLim properties) all place constraints on the shape of the axes.

Data Aspect Ratio

The DataAspectRatio property controls the ratio of the axis scales. For a mesh plot of the function z=xe(-x2–y2) evaluated over the range -2 ≤ x ≤ 2, -4 ≤ y ≤ 4

[X,Y] = meshgrid([-2:.15:2],[-4:.3:4]);
Z = X.*exp(-X.^2 - Y.^2);
mesh(X,Y,Z)

the values are

get(gca,'DataAspectRatio')
ans = 
     4 8 1

This means that four units in length along the x-axis cover the same data values as eight units in length along the y-axis and one unit in length along the z-axis. The axes fill the plot box, which has an aspect ratio of [1 1 1] by default.

If you want to view the mesh plot so that the relative magnitudes along each axis are equal with respect to each other, you can set the DataAspectRatio to [1 1 1].

set(gca,'DataAspectRatio',[1 1 1])

Setting the value of the DataAspectRatio property also sets the DataAspectRatioMode to manual and overrides stretch-to-fill so the specified aspect ratio is achieved.

Plot Box Aspect Ratio

Looking at the value of the PlotBoxAspectRatio for the graph in the previous section shows that it has now taken on the former value of the DataAspectRatio.

get(gca,'PlotBoxAspectRatio')
ans = 
     4 8 1

MATLAB has rescaled the plot box to accommodate the graph using the specified DataAspectRatio.

The PlotBoxAspectRatio property controls the shape of the axes plot box. MATLAB sets this property to [1 1 1] by default and adjusts the DataAspectRatio property so that graphs fill the plot box if stretching is on, or until reaching a constraint if stretch-to-fill has been overridden.

When you set the value of the DataAspectRatio and thereby prevent it from changing, MATLAB varies the PlotBoxAspectRatio instead. If you specify both the DataAspectRatio and the PlotBoxAspectRatio, MATLAB is forced to change the axis limits to obey the two constraints you have already defined.

Continuing with the mesh example, if you set both properties,

set(gca,'DataAspectRatio',[1 1 1],...
        'PlotBoxAspectRatio',[1 1 1])

MATLAB changes the axis limits to satisfy the two constraints placed on the axes.

Adjusting Axis Limits

MATLAB enables you to set the axis limits to the values you want. However, specifying a value for DataAspectRatio, PlotBoxAspectRatio, and the axis limits overconstrains the axes definition. For example, it is not possible for MATLAB to draw the axes if you set these values:

set(gca,'DataAspectRatio',[1 1 1],...
        'PlotBoxAspectRatio',[1 1 1],...
        'XLim',[-4 4],...
        'YLim',[-4 4],...
        'ZLim',[-1 1])

In this case, MATLAB ignores the setting of the PlotBoxAspectRatio and determines its value automatically. These particular values cause the PlotBoxAspectRatio to return to its calculated value.

get(gca,'PlotBoxAspectRatio')
ans =
      4 8 1

MATLAB can now draw the axes using the specified DataAspectRatio and axis limits.

Displaying Cross-Sections of Surfaces

Sometimes projecting a 3-D surface onto an x-, y-, or z-axis can aid visualization. To do this, you might change the aspect ratio, in order to make space for the projection. The following example illustrates how to do this:

  1. Create an x-y grid and z value for it:

    [x,y] = meshgrid([-2:.2:2]); 
    Z = x.*exp(-x.^2-y.^2);
    
  2. Plot the surface in 3-D; annotate with a colorbar and axis labels:

    surf(x,y,Z,gradient(Z))
    colorbar 
    xlabel('X-AXIS') 
    ylabel('Y-AXIS') 
    zlabel('Z-AXIS') 
    

  3. Use axis to change the Ymax value in to 3, stretching the plot in one direction:

    axis([-2 2 -2 3 -0.5 0.5]) % 
    
  4. Regrid the surface, setting all Y value equal to 3:

    y = 3*ones(21);
    
  5. Plaster a plot of the surface onto the Y-axis:

    hold on 
    surf(x,y,Z,gradient(Z))
    

Displaying Real Objects

If you want to display an object so that it looks realistic, you need to change MATLAB defaults. For example, this data defines a wedge-shaped patch object.

patch('Vertices',vertex_list,'Faces',vertex_connection,...
	'FaceColor','w','EdgeColor','k')
view(3)

However, this axes distorts the actual shape of the solid object defined by the data. To display it in correct proportions, set the DataAspectRatio.

set(gca,'DataAspectRatio',[1 1 1])

The units are now equal in the x-, y-, and z-directions and the axes is not being stretched to fill the position rectangle, revealing the true shape of the object.

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