# Mobius: R6 class representing a Möbius transformation. In PlaneGeometry: Plane Geometry

## Description

A Möbius transformation is given by a matrix of complex numbers with non-null determinant.

a

get or set a

b

get or set b

c

get or set c

d

get or set d

## Methods

#### Method new()

Create a new Mobius object.

Mobius\$new(M)
##### Arguments
M

the matrix corresponding to the Möbius transformation

##### Returns

A new Mobius object.

#### Method print()

Show instance of a Mobius object.

##### Usage
Mobius\$print(...)
...

ignored

##### Examples
Mobius\$new(rbind(c(1+1i,2),c(0,3-2i)))

#### Method getM()

Get the matrix corresponding to the Möbius transformation.

Mobius\$getM()

#### Method compose()

Compose the reference Möbius transformation with another Möbius transformation

##### Usage
Mobius\$compose(M1, left = TRUE)
##### Arguments
M1

a Mobius object

left

logical, whether to compose at left or at right (i.e. returns M1 o M0 or M0 o M1)

A Mobius object.

#### Method inverse()

Inverse of the reference Möbius transformation.

Mobius\$inverse()

A Mobius object.

#### Method power()

Power of the reference Möbius transformation.

Mobius\$power(k)
##### Arguments
k

an integer, possibly negative

##### Returns

The Möbius transformation M^k, where M is the reference Möbius transformation.

#### Method gpower()

Generalized power of the reference Möbius transformation.

Mobius\$gpower(k)
##### Arguments
k

a real number, possibly negative

##### Returns

A Mobius object, the generalized k-th power of the reference Möbius transformation.

#### Method transform()

Transformation of a point by the reference Möbius transformation.

##### Usage
Mobius\$transform(M)
M

a point or Inf

##### Returns

A point or Inf, the image of M.

##### Examples
Mob <- Mobius\$new(rbind(c(1+1i,2),c(0,3-2i)))
Mob\$transform(c(1,1))
Mob\$transform(Inf)

#### Method transformCircle()

Transformation of a circle by the reference Möbius transformation.

##### Usage
Mobius\$transformCircle(circ)
circ

a Circle object

##### Returns

A Circle object or a Line object.

#### Method transformLine()

Transformation of a line by the reference Möbius transformation.

##### Usage
Mobius\$transformLine(line)
line

a Line object

##### Returns

A Circle object or a Line object.

#### Method clone()

The objects of this class are cloneable with this method.

##### Usage
Mobius\$clone(deep = FALSE)
##### Arguments
deep

Whether to make a deep clone.

## See Also

MobiusMappingThreePoints to create a Möbius transformation, and also the compose method of the Inversion R6 class.

## Examples

 1 2 3 4 5 6 7 8 9 10 11 12 13 ## ------------------------------------------------ ## Method `Mobius\$print` ## ------------------------------------------------ Mobius\$new(rbind(c(1+1i,2),c(0,3-2i))) ## ------------------------------------------------ ## Method `Mobius\$transform` ## ------------------------------------------------ Mob <- Mobius\$new(rbind(c(1+1i,2),c(0,3-2i))) Mob\$transform(c(1,1)) Mob\$transform(Inf)

PlaneGeometry documentation built on Aug. 7, 2020, 1:06 a.m.