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▼ Functions

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▼ Graphics and Animations

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Introduction

• Easy Plotting: Graphs of Functions

• Advanced Plotting: Principles and First Examples

The Full Picture: Graphical Trees

Viewer, Browser, and Inspector: Interactive Manipulation

Primitives

• Attributes

• Colors

• Layout of Canvas and Scenes

• Animations

• Saving and Exporting Pictures

Importing Pictures

Cameras in 3D

Strange Effects in 3D? Accelerated OpenGL?

• Utility Functions

▼ Graphical Primitives

plot::Parallelogram2d

plot::Parallelogram3d

plot::SparseMatrixplot

• Grouping Constructs

• Transformations and Manipulating Objects

• Camera and Lights

• Graphical Attributes

• Data Manipulation and Data Types

• Customization and Data Output Control

• Programming

• Language Extensibility

• Release Notes

plot::Box – boxes in 3D

$plot::Box(`x_{min}`..`x_{max}`, `y_{min}`..`y_{max}`, `z_{min}`..`z_{max}`)$ creates the 3D box

$plot::Box([`x_{min}`, `y_{min}`, `z_{min}`], [`x_{max}`, `y_{max}`, `z_{max}`])$ produces the same box.

→ Examples

Calls:

plot::Box( $`x_{min}`$ .. $`x_{max}`$ , $`y_{min}`$ .. $`y_{max}`$ , $`z_{min}`$ .. $`z_{max}`$ , <a = amin .. amax>, Options)

plot::Box([ $`x_{min}`$ , $`y_{min}`$ , $`z_{min}`$ ], [ $`x_{max}`$ , $`y_{max}`$ , $`z_{max}`$ ], <a = amin .. amax>, Options)

Parameters:

$`x_{min}`$ , $`y_{min}`$ , $`z_{min}`$ :	the lower borders: numerical real values or arithmetical expressions of the animation parameter a. $`x_{min}`$ , $`y_{min}`$ , $`z_{min}`$ are equivalent to the attributes XMin, YMin, ZMin.
$`x_{max}`$ , $`y_{max}`$ , $`z_{max}`$ :	the upper borders: numerical real values or arithmetical expressions of the animation parameter a. $`x_{max}`$ , $`y_{max}`$ , $`z_{max}`$ are equivalent to the attributes XMax, YMax, ZMax.

Related Functions:

plot, plot::copy

Details:

plot::Box creates 3D boxes with edges parallel to the coordinate axes. Using plot::Rotate3d or plot::Transform3d one can create boxes and parallelepipeds with arbitrary orientation. Cf. examples 3 and 4.

Example 1

We draw a box consisting of its edges and a filled box:

plot(plot::Box(-3..-1, 0..2, 0..1, Filled = FALSE,
               LineColor = RGB::Black),
     plot::Box(1..3, 0..2, 0..1, Filled = TRUE,
               FillColor = RGB::Red),
     Axes = None, Scaling = Constrained)

MuPAD graphics

Example 2

The borders of a box can be animated:

plot(plot::Box([1, 1, 1], [2, 2, 2 + sin(r)], r = 0..2*PI)):

MuPAD graphics

Example 3

We want to display a cube “standing” on one of its corners. First, we define the cube:

b0 := plot::Box(0..1, 0..1, 0..1)

Now, rotating the cube to stand on a corner is equivalent to first rotating around the -axis by 45 degrees, then rotating around the -axis:

b1 := plot::Rotate3d(b0, Axis = [1, 0, 0], Angle = -PI/4):
plot(b1, Scaling = Constrained)

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b2 := plot::Rotate3d(b1, Axis = [0, 1, 0], Angle = 7*PI/36):
plot(b2, Scaling = Constrained)

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Finally, we let it rotate around the -axis:

plot(plot::Rotate3d(b2, Axis = [0, 0, 1], Angle = a,
a = 0..2*PI/3),
Scaling = Constrained)

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delete b0, b1, b2:

Example 4

A parallelepiped can be obtained from a plot::Box by a linear transformation:

plot(plot::Transform3d([0, 0, 0], [1, 1, 0,
                                   1, 1, 3,
                                   0, 3, 1],
                       plot::Box(0..1, 0..1, 0..1)),
     Scaling = Constrained,
     CameraDirection = [-27, -12, 22])

MuPAD graphics

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