UName, URange, UMin, UMax, VName, VRange, VMin, VMax, XName, XRange, XMin, XMax, YName, YRange, YMin, YMax, ZName, ZRange, ZMin, ZMax

Names and values ranges of parameters

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Value Summary

UMax, UMin, UName, VMax, VMin, VName, XMax, XMin, XName, YMax, YMin, YName, ZMax, ZMin, ZNameMandatoryMuPAD® expression
URange[UMin .. UMax]Range of arithmetical expressions
VRange[VMin .. VMax]Range of arithmetical expressions
XRange[XMin .. XMax]Range of arithmetical expressions
YRange[YMin .. YMax]Range of arithmetical expressions
ZRange[ZMin .. ZMax]Range of arithmetical expressions

Graphics Primitives

ObjectsDefault Values
plot::Curve2d, plot::Curve3d, plot::Function2d, plot::XRotate

URange, XRange: -5 .. 5

UMin, XMin: -5

UMax, XMax: 5

plot::Bars3d, plot::ClippingBox, plot::Conformal, plot::Cylindrical, plot::Density, plot::Implicit2d, plot::Implicit3d, plot::Inequality, plot::Iteration, plot::Listplot, plot::Matrixplot, plot::Polar, plot::Raster, plot::Rootlocus, plot::Sequence, plot::SparseMatrixplot, plot::Spherical, plot::Streamlines2d, plot::Sum, plot::Surface, plot::Sweep, plot::Tube, plot::VectorField2d, plot::VectorField3d 

XRange: 0 .. 5

XMin: 0

XMax: 5


XRange, YRange: -5 .. 5

XMin, YMin: -5

XMax, YMax: 5


XRange, YRange, ZRange: -1 .. 1

XMin, YMin, ZMin: -1

XMax, YMax, ZMax: 1


XRange, YRange: -1 .. 1

XMin, YMin: -1

XMax, YMax: 1


XRange: -infinity .. infinity

XMin: -infinity

XMax: infinity


UName, VName, XName, YName, ZName specify the names of parameters defining parametrized objects such as functions, curves and surfaces.

UMin, UMax, VMin, VMax, XMin, XMax, YMin, YMax, ZMin, ZMax specify the minimal and maximal values of the range of the parameters.

URange, VRange, XRange, YRange, ZRange serve as shortcuts for setting UMin, UMax etc.

In most cases, the user has no need for using these attributes explicitly, because parameter ranges are set implicitly during creation of plot objects. For example, the definition

f := plot::Function2d(sin(x), x = 0 .. 2*PI)

sets the attribute values XName = x, XMin = 0, XMax = 2*PI automatically for the function object f. In fact, you can define f by the equivalent call

f := plot::Function2d(sin(x), XName = x, XMin = 0, XMax = 2*PI).

In the interactive object browser of the MuPAD graphics tool (see section Viewer, Browser, and Inspector: Interactive Manipulation of this document), you will not see a specification such as x = 0 .. 2*PI, but you find separate entries for XName, XMin, XMax.

The use of 'X', 'Y', 'Z' as opposed to 'U', 'V' depends on the type of the object.

Functions of type plot::Function2d refer to the independent variable (“the parameter”) as XName.

Functions of type plot::Function3d refer to the two independent variables as XName, YName.

Parametrized curve of type plot::Curve2d or plot::Curve3d refer to the curve parameter as UName.

Parametrized surfaces of type plot::Surface, plot::XRotate etc. refer to the two surface parameters as UName, VName.

Various other plot objects of type plot::Implicit2d, plot::VectorField2d etc. also use the attributes XName etc. Here, the ranges from XMin to XMax etc. denote the coordinate range in which the objects are placed.

After a definition such as f := plot::Function2d(sin(x), x = 0 .. 2*PI), the parameter and its range can be accessed as the slots f::XName, f::XMin, f::XMax.

The slot f::XRange yields the range 0 .. 2*PI consisting of the values of XMin and XMax. Setting the attribute XRange is a short cut for setting XMin and XMax simultaneously. For example, setting f::XRange := -PI .. PI is equivalent to setting f::XMin := -PI and f::XMax := PI.

Of course, the analogous statements hold for YRange, ZRange, URange, VRange, too.


Example 1

We define a function object:

f1 := plot::Function2d(sin(x), x = 0.. 2*PI)

This is equivalent to:

f2 := plot::Function2d(sin(x), XName = x, XMin = 0, XMax = 2*PI)

The objects f1 and f2 have the same entries for the parameter x:

f1::XName = f1::XMin .. f1::XMax, f2::XName = f2::XRange

Changing the x range via XRange is equivalent to changing XMin and XMax separately:

f1::XRange := -PI..PI:
f2::XMin := -PI: 
f2::XMax := PI:
f1, f2

delete f1, f2: