Documentation Center

  • Trial Software
  • Product Updates

plot::Plane

Infinite plane in 3D

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

Syntax

plot::Plane([x, y, z], <[nx, ny, nz]>, <a = amin .. amax>, options)
plot::Plane(X, <N>, <a = amin .. amax>, options)
plot::Plane(XN, <a = amin .. amax>, options)
plot::Plane(p1, p2, p3, <a = amin .. amax>, options)
plot::Plane(p123, <a = amin .. amax>, options)

Description

plot::Plane(x, n) creates the (infinite) plane with normal vector n passing through the point x.

plot::Plane provides a graphical plane in 3D that does not require a specification, which part of the plane is to be seen in the picture. The visible part of the plane is determined automatically by the ViewingBox of the entire 3D scene.

The contribution of a plane of type plot::Plane to the ViewingBox of a 3D scene consists only of the single point [x, y, z] (this is p1, if the plane is specified by three points p1, p2, p3 on the plane).

Thus, two planes with the same normal but different points may be mathematically equivalent, but may produce different pictures due to different viewing boxes. Cf. Example 3.

By default, a mesh of lines is displayed on the plane. Use the attribute Mesh = [n1, n2] with positive integer values n1, n2 to control the number of mesh lines.

Attributes

AttributePurposeDefault Value
AffectViewingBoxinfluence of objects on the ViewingBox of a sceneTRUE
Colorthe main colorRGB::LightBlue
Filledfilled or transparent areas and surfacesTRUE
FillColorcolor of areas and surfacesRGB::LightBlue
Framesthe number of frames in an animation50
Legendmakes a legend entry 
LegendTextshort explanatory text for legend 
LegendEntryadd this object to the legend?FALSE
LineColorcolor of linesRGB::Black.[0.25]
LinesVisiblevisibility of linesTRUE
Meshnumber of sample points[15, 15]
Namethe name of a plot object (for browser and legend) 
Normalnormal vector of circles and discs, etc. in 3D[0, 0, 1]
NormalXnormal vector of circles and discs, etc. in 3D, x-component0
NormalYnormal vector of circles and discs, etc. in 3D, y-component0
NormalZnormal vector of circles and discs, etc. in 3D, z-component1
ParameterEndend value of the animation parameter 
ParameterNamename of the animation parameter 
ParameterBegininitial value of the animation parameter 
ParameterRangerange of the animation parameter 
Positionpositions of cameras, lights, and text objects[0, 0, 0]
PositionXx-positions of cameras, lights, and text objects0
PositionYy-positions of cameras, lights, and text objects0
PositionZz-positions of cameras, lights, and text objects0
TimeEndend time of the animation10.0
TimeBeginstart time of the animation0.0
TimeRangethe real time span of an animation0.0 .. 10.0
Titleobject title 
TitleFontfont of object titles[" sans-serif ", 11]
TitlePositionposition of object titles 
TitleAlignmenthorizontal alignment of titles w.r.t. their coordinatesCenter
TitlePositionXposition of object titles, x component 
TitlePositionYposition of object titles, y component 
TitlePositionZposition of object titles, z component 
UMeshnumber of sample points for parameter "u"15
VMeshnumber of sample points for parameter "v"15
VisiblevisibilityTRUE
VisibleAfterobject visible after this time value 
VisibleBeforeobject visible until this time value 
VisibleFromToobject visible during this time range 
VisibleAfterEndobject visible after its animation time ended?TRUE
VisibleBeforeBeginobject visible before its animation time starts?TRUE

Examples

Example 1

We generate two spheres and a plane:

plot(plot::Sphere(1, [-1, -1, -1], Color = RGB::Red),
     plot::Sphere(1, [ 1,  1,  1], Color = RGB::Green),
     plot::Plane([0, 0, 0], [0, 0, 1], Color = RGB::Blue)):

We specify an explicit ViewingBox for the scene:

plot(plot::Sphere(1, [-1, -1, -1], Color = RGB::Red),
     plot::Sphere(1, [ 1,  1,  1], Color = RGB::Green),
     plot::Plane([0, 0, 0], [0, 0, 1], Color = RGB::Blue),
     ViewingBox = [-3..8, -3..8, -3..3]):

Example 2

We demonstrate the effect of the attribute Mesh that controls the number of mesh lines displayed on planes:

plot(plot::Plane([0, 0, 0], [1, -1, 1], Color = RGB::Red,
                 Mesh = [5, 5]),
     plot::Plane([0, 1, 0], [2, 1, -1], Color = RGB::Green,
                 Mesh = [10, 10]),
     plot::Plane([1, -1, 0], [1, 1, 1], Color = RGB::Blue,
                 Mesh = [20, 20]),
     ViewingBox = [-1..3, -2..2, -2..2])

We change the number of mesh lines:

plot(plot::Plane([0, 0, 0], [1, -1, 1], Color = RGB::Red,
                 Mesh = [10, 10]),
     plot::Plane([0, 1, 0], [2, 1, -1], Color = RGB::Green,
                 Mesh = [20, 10]),
     plot::Plane([1, -1, 0], [1, 1, 1], Color = RGB::Blue,
                 Mesh = [15, 5]),
     ViewingBox = [-1..3, -2..2, -2..2])

Example 3

The contribution of a plane to the automatic ViewingBox of the whole scene consists only of the point used to specify the plane. In the following scene, this point is the origin. It lies inside the ViewingBox generated by the two spheres. Thus, the ViewingBox of the scene is determined by the two spheres only:

plot(plot::Sphere(1, [1, 1, 1], Color = RGB::Red),
     plot::Sphere(1, [-1, -1, -1], Color = RGB::Green),
     plot::Plane([0, 0, 0], [0, 0, 1], Color = RGB::Blue)):

Now, a different point [5, 0, 0] is used to specify the same plane. It does not lie inside the ViewingBox generated by the two spheres and thus enlarges the ViewingBox of the scene:

plot(plot::Sphere(1, [1, 1, 1], Color = RGB::Red),
     plot::Sphere(1, [-1, -1, -1], Color = RGB::Green),
     plot::Plane([5, 0, 0], [0, 0, 1], Color = RGB::Blue)):

Example 4

We create animated planes:

plot(plot::Plane([0, 0, 0], [cos(a), sin(a), 0], a = 0..PI,
                 Color = RGB::Red),
     plot::Plane([0, 0, 0], [0, cos(a), sin(a)], a = 0..PI,
                 Color = RGB::Green),
     plot::Plane([0, 0, a], [0, 0, 1], a = 0..1,
                 Color = RGB::Blue),
     ViewingBox = [-1..1, -1..1, -1..1])

Parameters

x, y, z

The coordinates of a point on the plane: numerical real values or arithmetical expressions in the animation parameter a.

x, y, z are equivalent to the attributes PositionX, PositionY, PositionZ.

nx, ny, nz

The components of the normal vector; nx, ny, nz must be numerical real values or arithmetical expressions in the animation parameter a. If no normal is specified, the normal (0, 0, 1) is used.

nx, ny, nz are equivalent to the attributes NormalX, NormalY, NormalZ.

X

A matrix of category Cat::Matrix with three entries that provide the coordinates x, y, z of a point on the plane.

X is equivalent to the attribute Position.

N

A matrix of category Cat::Matrix with three entries that provide the components nx, ny, nz of the normal.

N is equivalent to the attribute Normal.

XN

A matrix of category Cat::Matrix with 3 rows and 2 columns. The first column provides the coordinates x, y, z of a point on the plane, the second column provides the components nx, ny, nz of the normal.

XN is equivalent to the attributes Position, Normal.

p1, p2, p3

Three points on the plane: either lists with 3 entries each or matrices of category Cat::Matrix with 3 entries each. The point p1 correponds to the attribute Position, the normal of the plane (the attribute Normal) is computed as the cross product (p2 - p1) ×(p3 - p1).

p123

A matrix of category Cat::Matrix with 3 rows and 3 columns. Each column corresponds to a point on the plane.

a

Animation parameter, specified as a = amin..amax, where amin is the initial parameter value, and amax is the final parameter value.

See Also

MuPAD Functions

MuPAD Graphical Primitives

Was this topic helpful?