Contents

XMesh, XSubmesh, YMesh, YSubmesh, ZMesh

Number of sample points

Value Summary

XMesh, XSubmesh, YMesh, YSubmesh, ZMeshInheritedPositive integer

Graphics Primitives

ObjectsDefault Values
plot::Function2d

XMesh: 121

XSubmesh: 0

plot::Function3d

XMesh, YMesh: 25

XSubmesh, YSubmesh: 0

plot::Implicit2d, plot::Raster, plot::VectorField2d

XMesh, YMesh: 11

plot::Implicit3d

XMesh, YMesh, ZMesh: 11

plot::VectorField3d

XMesh, YMesh, ZMesh: 7

plot::Conformal

XMesh, YMesh: 11

XSubmesh, YSubmesh: 0

plot::Inequality

XMesh, YMesh: 256

plot::Density

XMesh, YMesh: 25

plot::Matrixplot

XSubmesh, YSubmesh: 2

plot::Listplot

XSubmesh: 6

Description

The attributes XMesh etc. determine the number of sample points used for the numerical approximation of plot objects such as function graphs, implicit plots etc.

Various object types use numerical function evaluations on a discrete equidistant mesh. XMesh, YMesh, and for plot::Implicit3d also ZMesh set the number of points of this mesh. An exception of this are parameterized curves and surfaces, which use the attributes UMesh, USubmesh, VMesh, and VSubmesh.

For most of the object types listed above, the interpretation of the integers set by these attributes is as follows: In each of XRange, YRange, ZRange, the corresponding number of points is spread out equidistantly. For XMesh = 2 and XRange = 0..1, for example, evaluation takes place for x = 0 and x = 1. For XMesh = 3, a further mesh point at is used.

The exception to this rule is plot::Implicit2d: Here, the values of XMesh and YMesh determine the density of the grid usd for finding components and increasing their values helps exactly in those cases where components (i.e., lines) are missing from the plot. Decreasing XMesh and YMesh in a 2D implicit plot will not make the curves appear rougher; it may result in curves missing.

For types reacting to AdaptiveMesh and for plot::Implicit3d, this mesh is used to find initial values that can be refined further. See the documentation of the specific types and of AdaptiveMesh for details.

In general, a finer mesh (higher values) leads to a longer computation, while a coarser mesh may cause details being missed.

One may specify XMesh = nx, YMesh = ny, XSubmesh = mx, YSubmesh = mv also in the shorter Form Mesh = [nx, ny], Submesh = [mx, my].

Examples

Example 1

The notorious function oscillates wildly near the origin. The standard mesh values do not suffice to resolve the behavior of the function near the critical point:

plot(plot::Function2d(sin(1/x), x = -1 .. 1))

We get a better result with an increased value of XMesh:

plot(plot::Function2d(sin(1/x), x = -1 .. 1), XMesh = 1000)

Example 2

In the following plot, the default values of XMesh, YMesh do not suffice to produce a sufficiently smooth function graph:

plot(plot::Function3d(besselJ(0, sqrt(x^2 + y^2)), 
                      x = -20 .. 20, y = -20 .. 20)):

Increasing the default values XSubmesh = 0, YSubmesh = 0 yields a higher resolution plot. Note that this does not influence the number of mesh lines that are displayed:

plot(plot::Function3d(besselJ(0, sqrt(x^2 + y^2)), 
                      x = -20 .. 20, y = -20 .. 20,
                      XSubmesh = 2, YSubmesh = 2)):

Alternatively, we increase the values of XMesh, YMesh and use the default values XSubmesh = 0, YSubmesh = 0. This, however, increases the number of mesh lines that are displayed:

plot(plot::Function3d(besselJ(0, sqrt(x^2 + y^2)), 
                      x = -20 .. 20, y = -20 .. 20,
                      XMesh = 73, YMesh = 73)):

Yet another possibility is to use the default values of XMesh, YMesh, XSubmesh, YSubmesh and activate the adaptive mechanism to smoothen the critical regions of the plot. However, this plot consists almost completely of critical regions and the adaptive mechanism will therefore be slower than a direct calculation with a finer mesh that leads to almost the same result:

plot(plot::Function3d(besselJ(0, sqrt(x^2 + y^2)), 
                      x = -20 .. 20, y = -20 .. 20,
                      AdaptiveMesh = 2)):

Example 3

For two-dimensional implicit plots, XMesh and YMesh determine the mesh of "seed points" that are used to find components (see the documentation of plot::Implicit2d for more details). In effect, this means that if some components are missing from a plot, the values of these attributes should be increased:

plot(plot::Implicit2d(sin(2*x*y), x = -3..3, y = -3..3))

plot(plot::Implicit2d(sin(2*x*y), x = -3..3, y = -3..3,
                      XMesh = 20, YMesh = 20))

See Also

MuPAD Functions

Was this topic helpful?