plot::Bars3d – 3D bar chart of matrix data

plot::Bars3d(A) generates a 3D bar chart with bar heights given by the entries of the matrix A.

Calls:

plot::Bars3d(A, <x = $`x_{min}`$ .. $`x_{max}`$ , y = $`y_{min}`$ .. $`y_{max}`$ >, <a = amin .. amax>, Options)

plot::Bars3d(L, <x = $`x_{min}`$ .. $`x_{max}`$ , y = $`y_{min}`$ .. $`y_{max}`$ >, <a = amin .. amax>, Options)

Parameters:

A:	an array of domain type DOM_ARRAY or a matrix of category Cat::Matrix (e.g., of type matrix or densematrix) containing real numerical values or expressions of the animation parameter . Rows/columns of the array, respectively matrix, correspond to rows/columns of the bar chart. A is equivalent to the attribute Data.
L:	a list of lists of real numerical values or expressions of the animation parameter . Each sublist of represents a row of the bar chart. L is equivalent to the attribute Data.
x:	name of the horizontal variable: an identifier or an indexed identifier. It is used as the title of the coordinate axis in direction. x is equivalent to the attribute XName.
$`x_{min}`$ .. $`x_{max}`$ :	the range of the horizontal variable: $`x_{min}`$ , $`x_{max}`$ must be numerical real value or expressions of the animation parameter . $`x_{min}`$ .. $`x_{max}`$ is equivalent to the attribute XRange.
y:	name of the vertical variable: an identifier or an indexed identifier. It is used as the title of the coordinate axis in direction. y is equivalent to the attribute YName.
$`y_{min}`$ .. $`y_{max}`$ :	the range of the vertical variable: $`y_{min}`$ , $`y_{max}`$ must be numerical real value or expressions of the animation parameter . $`y_{min}`$ .. $`y_{max}`$ is equivalent to the attribute YRange.

Related Functions:

plot, plot::copy

Details:

The rows of the matrix are plotted along the coordinate, the columns along the coordinate.

Different rows may be regarded as different classes of data. Each row has a different color determined by the the attribute Colors = [, , ...] with RGB or RGBa colors c1, c2 etc.

The simplest way to obtain a uniform coloring of all rows with the color c is to specify the attribute Color = c.
Arrays/matrices do not need to be indexed from . E.g.,

A = array( $`i_{min}`..`i_{max}`$ , $`j_{min}`..`j_{max}`$ , [..data..])

yields a bar chart with $`i_{max}` - `i_{min}` + 1$ rows and $`j_{max}` - `j_{min}` + 1$ columns, stretching from $`x_{min}`$ to $`x_{max}`$ in direction and from $`y_{min}`$ to $`y_{max}`$ in direction.

If no plot range $`x_{min}`..`x_{max}`$ , $`y_{min}`..`y_{max}`$ is specified, $`x_{min}` = `j_{min}` - 1$ , $`x_{max}` = `j_{max}`$ , $`y_{min}` = `i_{min}` - 1$ , $`y_{max}` = `i_{max}`$ is used.
When the values are specified by a list of lists and no plot range $`x_{min}`..`x_{max}`$ , $`y_{min}`..`y_{max}`$ is specified, $`x_{min}` = 0$ , $`x_{max}` = m$ , $`y_{min}` = 0$ , $`y_{max}` = n$ is used, where is the length of and is the (common) length of the sublists in . All sublists (“rows”) must have the same length.
The attribute BarStyle allows to switch the style of the bars between Boxes (bars), Lines (vertical lines), LinesPoints (vertical lines and points), and Points(points only). Cf. example 1.
The attribute Gap = or, equivalently, XGap = gx, YGap = gy allows to introduce gaps between adjacent bars. The values gx, gy may be real numerical values between and or expressions of the animation parameter a. These values set the fraction of the space reserved for a bar that is not filled by the bar.

With , , there are no gaps. With , , the gaps between adjacent bars are of the same size as the bars. With , , there bars become lines.

Values of gx, gy larger than are treated like , negative values like .

The Gap attribute has an effect only for BarStyle = Boxes.
The attribute Ground = z0 determines the value of the lower or upper face of the bars. Matrix values are displayed as bars stretching in direction from the lower face z0 to the upper face m. Matrix values are displayed as bars stretching in direction from the upper face z0 down to the lower face m.

The parameter z0 has to be a numerical real value or an expression of the animation parameter a.

If the attribute Ground = z0 is not specified, the default value is used.

Example 1

We create some random matrix data and plot them as a bar chart:

A := matrix::random(5, 10, frandom) :
plot(plot::Bars3d(A, Gap = [0.4, 0.7]))

MuPAD graphics

We create bar charts of the data with different BarStyle options:

plot(plot::Scene3d(plot::Bars3d(A, BarStyle = Boxes)),
     plot::Scene3d(plot::Bars3d(A, BarStyle = Lines)),
     plot::Scene3d(plot::Bars3d(A, BarStyle = Points)),
     plot::Scene3d(plot::Bars3d(A, BarStyle = LinesPoints)),
     PointSize = 2.0*unit::mm, LineWidth = 0.5*unit::mm
):

MuPAD graphics

delete A:

Example 2

We demonstrate the positioning of bar charts by specifying ranges for the and the coordinate. The following two bar charts are plotted in one scene. They are placed side by side via suitable ranges:

A := matrix::random(5, 5, frandom):
plot(plot::Bars3d(A, x = 0 .. 0.9, y = 0 .. 1,
                  BarStyle = LinesPoints),
     plot::Bars3d(A, x = 1.1 .. 2, y = 0 .. 1,
                  Gap = [0.3, 0.7])):

MuPAD graphics

delete A:

Example 3

We demonstrate the attributes Ground and Color:

A := matrix::random(5, 10, frandom):
plot(plot::Scene3d(plot::Bars3d(A, Ground = 0,
                                Color = RGB::Grey)),
     plot::Scene3d(plot::Bars3d(A, Ground = 0.5,
                                Color = RGB::Grey)),
     Layout = Horizontal):

MuPAD graphics

In the next call, the ground level is animated. Note that in animations one must specify ranges for the and coordinates.We include a transparent plane visualizing the ground level:

plot(plot::Bars3d(A, x = 0 .. 1, y = 0 .. 1, a = 0 .. PI,
                  Color = RGB::Grey, Gap = [0.5, 0.5],
                  Ground = sin(a)),
     plot::Surface([x, y, sin(a) + 0.001],
                   x = 0 .. 1, y = 0 .. 1, a = 0 .. PI,
                   Mesh = [2, 2], Color = RGB::Blue.[0.5])):

MuPAD graphics

delete A:

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