plot::Arc3d

Circular and elliptical arcs in 3D

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

Syntax

```plot::Arc3d(`r`, <`[cx, cy, cz], <[nx, ny, nz]>`>, <`α .. β`>, <`a = amin .. amax`>, `options`)
plot::Arc3d(`[r1, r2]`, <`[cx, cy, cz], <[nx, ny, nz]>`>, <`α .. β`>, <`a = amin .. amax`>, `options`)
```

Description

`plot::Arc3d(r, [x, y, z], [nx, ny, nz], α .. β )` creates a circular arc with radius r and center (x, y, z) with a polar angle between α and β in the plane with the normal vector (nx, ny, nz).

```plot::Arc3d([ r1, r2], [x, y, z], [nx, ny, nz], α .. β )``` creates a corresponding elliptical arc with semi-axes `r1`, `r2`.

The angle of a point on the arc is the usual polar angle to the positive x-axis known from polar coordinates. It is measured in radians.

If no range for the polar angle is specified, a full circle/ellipse is created.

If no center point is specified, an arc with center [0, 0, 0], is created.

Attributes

AttributePurposeDefault Value
`AffectViewingBox`influence of objects on the `ViewingBox` of a scene`TRUE`
`Angle`rotation angle`0`
`AngleEnd`end of angle range`PI/2`
`AngleBegin`begin of angle range`0`
`AngleRange`angle range`0` .. `PI/2`
`Center`center of objects, rotation center[`0`, `0`, `0`]
`CenterX`center of objects, rotation center, x-component`0`
`CenterY`center of objects, rotation center, y-component`0`
`CenterZ`center of objects, rotation center, z-component`0`
`Closed`open or closed polygons`FALSE`
`Filled`filled or transparent areas and surfaces`FALSE`
`FillColor`color of areas and surfaces`RGB::LightBlue`
`FillColor2`second color of areas and surfaces for color blends`RGB::CornflowerBlue`
`FillColorType`surface filling types`Flat`
`FillColorDirection`the direction of color transitions on surfaces[`0`, `0`, `1`]
`FillColorDirectionX`x-component of the direction of color transitions on surfaces`0`
`FillColorDirectionY`y-component of the direction of color transitions on surfaces`0`
`FillColorDirectionZ`z-component of the direction of color transitions on surfaces`1`
`Frames`the number of frames in an animation`50`
`Legend`makes a legend entry
`LegendText`short explanatory text for legend
`LegendEntry`add this object to the legend?`FALSE`
`LineColor`color of lines`RGB::Blue`
`LineWidth`width of lines`0.35`
`LineColor2`color of lines`RGB::DeepPink`
`LineStyle`solid, dashed or dotted lines?`Solid`
`LinesVisible`visibility of lines`TRUE`
`LineColorType`line coloring types`Flat`
`LineColorDirection`the direction of color transitions on lines[`0`, `0`, `1`]
`LineColorDirectionX`x-component of the direction of color transitions on lines`0`
`LineColorDirectionY`y-component of the direction of color transitions on lines`0`
`LineColorDirectionZ`z-component of the direction of color transitions on lines`1`
`Name`the name of a plot object (for browser and legend)
`Normal`normal vector of circles and discs, etc. in 3D[`0`, `0`, `1`]
`NormalX`normal vector of circles and discs, etc. in 3D, x-component`0`
`NormalY`normal vector of circles and discs, etc. in 3D, y-component`0`
`NormalZ`normal vector of circles and discs, etc. in 3D, z-component`1`
`ParameterEnd`end value of the animation parameter
`ParameterName`name of the animation parameter
`ParameterBegin`initial value of the animation parameter
`ParameterRange`range of the animation parameter
`SemiAxes`semi axes of ellipses and ellipsods
`SemiAxisX`first semi axis of ellipses and ellipsods`1`
`SemiAxisY`second semi axis of ellipses and ellipsods`1`
`TimeEnd`end time of the animation`10.0`
`TimeBegin`start time of the animation`0.0`
`TimeRange`the real time span of an animation`0.0` .. `10.0`
`Title`object title
`TitleFont`font of object titles[`" sans-serif "`, `11`]
`TitlePosition`position of object titles
`TitleAlignment`horizontal alignment of titles w.r.t. their coordinates`Center`
`TitlePositionX`position of object titles, x component
`TitlePositionY`position of object titles, y component
`TitlePositionZ`position of object titles, z component
`Visible`visibility`TRUE`
`VisibleAfter`object visible after this time value
`VisibleBefore`object visible until this time value
`VisibleFromTo`object visible during this time range
`VisibleAfterEnd`object visible after its animation time ended?`TRUE`
`VisibleBeforeBegin`object visible before its animation time starts?`TRUE`

Examples

Example 1

An arc is a segment of a circle:

```circle := plot::Circle2d(3, [0, 0]): arc := plot::Arc2d(3, [0, 0], 0 .. PI/4, LineColor = RGB::Red, LineWidth = 1.5*unit::mm): plot(circle, arc)```

`delete circle, arc:`

Example 2

The center of an arc may be given as the second argument to `plot::Arc2d`:

```arc1 := plot::Arc2d(3, [1, 3], 0..PI/2, Closed = TRUE): arc2 := plot::Arc2d(3, [3, 1], -PI ..0, Closed = TRUE): plot(arc1, arc2)```

The center is accessible as the attribute `Center` of the arc object. We change the center of the second arc:

```arc2::Center := [1, 3]: plot(arc1, arc2)```

`delete arc1, arc2:`

Example 3

A filled arc is a segment of a circle, like a piece of pie:

`plot(plot::Arc2d(1, -PI/4..PI/4, Filled = TRUE))`

`plot(plot::Arc2d(1, -PI/4..PI/4, Filled = TRUE, Closed = TRUE))`

```plot(plot::Arc2d(1, -PI/4..PI/4, Filled = TRUE, FillPattern = Solid, LinesVisible = FALSE), AxesInFront = TRUE)```

Example 4

When giving a list of two radii, `plot::Arc2d` draws a segment of anellipse with the corresponding semi-axes:

```arc1 := plot::Arc2d([2, 1], 0 .. PI, Color = RGB::Blue): arc2 := plot::Arc2d([2, 1], -PI .. 0, Color = RGB::Red): plot(arc1, arc2)```

`delete arc1, arc2:`

Example 5

To plot or animate segments of a tilted ellipse, use the attribute `Angle`:

```arc:= [1, 1], [0, 0], PI/4..PI/2, Filled, Closed, FillPattern=Solid: plot(plot::Arc2d(arc, Angle=a+0, a=0..2*PI, FillColor=RGB::Red), plot::Arc2d(arc, Angle=a+1/2*PI, a=0..2*PI, FillColor=RGB::Green), plot::Arc2d(arc, Angle=a+PI, a=0..2*PI, FillColor=RGB::Yellow), plot::Arc2d(arc, Angle=a+3/2*PI, a=0..2*PI, FillColor=RGB::Blue))```

`delete arc:`

Example 6

Further examples of animated 2D arcs:

`plot(plot::Arc2d(1, a .. PI, a = 0..PI))`

`plot(plot::Arc2d([1 + a^2/2, 1 + a], -PI/2 .. PI/2, a = 0..4))`

Example 7

We plot an animated 3D arc:

`plot(plot::Arc3d(1, [0,0,0], [0,a,1-a], 0..3/2*PI, a = 0..1))`

Example 8

We plot a colored 3D arcs:

```plot(plot::Arc3d(1, [0,0,0], 0.1..2*PI-0.1, Filled, LineColor=RGB::Yellow, LineColor2=RGB::Red, LineColorType = Dichromatic, LineColorDirection=[+1,0,0], FillColor=RGB::Yellow, FillColor2=RGB::Red, FillColorType = Dichromatic, FillColorDirection=[-1,0,0] ))```

Parameters

 `r` The radius of the circle. This must be a real numerical value or an arithmetical expression of the animation parameter `a`. `r` is equivalent to the attributes `SemiAxisX`, `SemiAxisY`. `r1`, `r2` The semi-axes of an elliptical arc. They must be real numerical values or arithmetical expressions of the animation parameter `a`. `r1`, `r2` are equivalent to the attributes `SemiAxisX`, `SemiAxisY`. `cx`, `cy`, `cz` The center point. The coordinates `cx`, `cy`, `cz` must be real numerical values or arithmetical expressions of the animation parameter `a`. If no center is specified, an arc centered at the origin is created. `cx`, `cy`, `cz` are equivalent to the attribute `Center`. `nx`, `ny`, `nz` The normal vector. The coordinates `nx`, `ny`, `nz` must be real numerical values or arithmetical expressions of the animation parameter `a`. If no normal vector is specified, the arc is created in the xy-plane. `nx`, `ny`, `nz` are equivalent to the attribute `Normal`. `α .. β` The angle range in radians: `α` and `β` must be real numerical values or arithmetical expressions of the animation parameter `a`. The default range is ```0 .. 2*PI```. `α` .. `β` is equivalent to the attribute `AngleRange`. `a` Animation parameter, specified as `a```` = amin..amax```, where `amin` is the initial parameter value, and `amax` is the final parameter value.