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Scaling, YXRatio, ZXRatio

Scaling ratios

MuPAD® notebooks are not recommended. Use MATLAB® live scripts instead.

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.

Value Summary

ScalingInheritedAutomatic, Constrained, or Unconstrained
YXRatio, ZXRatioInheritedPositive real numberReal number

Graphics Primitives

ObjectsDefault Values
plot::CoordinateSystem2d, plot::CoordinateSystem3d

Scaling: Unconstrained


YXRatio: 1

ZXRatio: 2/3


With Scaling = Constrained, the graphics output is scaled like the model coordinates, i.e., circle appear as circles, spheres as spheres.

With Scaling = Unconstrained, the graphics output is scaled independently in each coordinate direction such that the graphics fits optimally into the viewing area. Circles may appear as ellipses, spheres as ellipsoids.

For Scaling = Unconstrained, the scaling ratios of the different coordinate directions in a 3D plot can be set via the attributes YXRatio and ZXRatio.

If the graphics consists of geometrical objects such as circles, pie charts, spheres etc., the setting Scaling = Constrained is appropriate. This prevents circles from being deformed to ellipses in the graphical output.

For the visualization of non-geometrical data (usually, in function plots etc.), a scaling constrained to model coordinates is usually not appropriate. Think of the graph of y = ex for , where the y values extend over the range , which is roughly . With Scaling = Constrained, the graphical output would consist of a narrow vertical strip with the side ratio y : x = 22025 : 10. Here, Scaling = Unconstrained is appropriate.

The default value is Scaling = Unconstrained. However, many “geometrical” objects in the MuPAD® plot library override this default setting via the “hint mechanism” (see section Primitives Requesting Special Scene Attributes: “Hints” in this document). Whenever such an object is plotted in a scene, the whole scene uses Scaling = Constrained. A complete list of these “geometrical objects” such as circles, spheres, cones etc. is given further up on this help page.

With Scaling = Automatic, the graphics uses Scaling = Constrained for plots in which the coordinate ranges to be displayed have a ratio close to 1 : 1 in 2D or 1 : 1 : 1 in 3D. Otherwise, Scaling = Unconstrained is used.

The attributes YXRatio = r1 and ZXRatio = r2 only have an effect in 3D with Scaling = Unconstrained. The graphical scene is scaled to a box with side ratios z : y : x = r2: r1: 1. On the screen, the bounding box of the scene looks like a box with these side ratios.


Example 1

We plot a scene containing a function graph and some circles highlighting the extrema. Because the circle sends the “hint”Scaling = Constrained, this scaling is used for the whole scene. Consequently, the circles appear as circles:

plot(plot::Function2d(sin(x), x = 0 .. 2*PI),
     plot::Circle2d(0.2, [PI/2, 1], Color = RGB::Black),
     plot::Circle2d(0.2, [3*PI/2, -1], Color = RGB::Black),
     BorderWidth = 1.0*unit::mm,
     Header = "Scaling = Constrained")

With Scaling = UnConstrained, we get a better fit of the plot in the canvas. However, the circles are deformed to ellipses:

plot(plot::Function2d(sin(x), x = 0 .. 2*PI),
     plot::Circle2d(0.2, [PI/2, 1], Color = RGB::Black),
     plot::Circle2d(0.2, [3*PI/2, -1], Color = RGB::Black),
     Scaling = Unconstrained, BorderWidth = 1.0*unit::mm,
     Header = "Scaling = Unconstrained")

Example 2

A sphere of type plot::Sphere sends the “hint” Scaling = Constrained. With this scaling, YXRatio, ZXRatio have no effect:

s := plot::Sphere(1, [0, 0, 0]):
plot(s, BorderWidth = 0.5*unit::mm, 
     Header = "Scaling = Constrained",
     YXRatio = 3, ZXRatio = 10)

We use Scaling = Unconstrained. With the default values YXRatio = 1, ZXRatio = 2/3, the objects in a 3D scene are displayed like a box with side ratios X : Y : Z = 3 : 3 : 2:

plot(s, BorderWidth = 0.5*unit::mm, 
     Scaling = Unconstrained, Header = "X:Y:Z = 3:3:2")

We request different scaling ratios:

plot(s, BorderWidth = 0.5*unit::mm, Header = "X:Y:Z = 5:5:1",
     Scaling = Unconstrained, YXRatio = 1, ZXRatio = 1/5, 
     BorderWidth = 0.5*unit::mm)

plot(s, BorderWidth = 0.5*unit::mm, Header = "X:Y:Z = 7:3:1",
     Scaling = Unconstrained, YXRatio = 3/7, ZXRatio = 1/7, 
     BorderWidth = 0.5*unit::mm)

delete s:
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