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PlaneGeometry (version 1.6.0)

Shear: R6 class representing a shear transformation

Description

A shear is given by a vertex, two perpendicular vectors, and an angle.

Arguments

Active bindings

vertex

get or set the vertex

vector

get or set the first vector

ratio

get or set the ratio between the length of vector and the length of the second vector, perpendicular to the first one

angle

get or set the angle

degrees

get or set the degrees field

Methods

Method new()

Create a new Shear object.

Usage

Shear$new(vertex, vector, ratio, angle, degrees = TRUE)

Arguments

vertex

a point

vector

a vector

ratio

a positive number, the ratio between the length of vector and the length of the second vector, perpendicular to the first one

angle

an angle strictly between -90 degrees and 90 degrees

degrees

logical, whether angle is given in degrees

Returns

A new Shear object.

Examples

Shear$new(c(1,1), c(1,3), 0.5, 30)

Method print()

Show instance of a Shear object.

Usage

Shear$print(...)

Arguments

...

ignored

Method transform()

Transform a point or several points by the reference shear.

Usage

Shear$transform(M)

Arguments

M

a point or a two-column matrix of points, one point per row

Method getMatrix()

Augmented matrix of the shear.

Usage

Shear$getMatrix()

Returns

A 3x3 matrix.

Examples

S <- Shear$new(c(1,1), c(1,3), 0.5, 30)
S$getMatrix()

Method asAffine()

Convert the reference shear to an Affine object.

Usage

Shear$asAffine()

Examples

Shear$new(c(0,0), c(1,0), 1, atan(30), FALSE)$asAffine()

Method clone()

The objects of this class are cloneable with this method.

Usage

Shear$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

References

R. Goldman, An Integrated Introduction to Computer Graphics and Geometric Modeling. CRC Press, 2009.

Examples

Run this code
P <- c(0,0); w <- c(1,0); ratio <- 1; angle <- 45
shear <- Shear$new(P, w, ratio, angle)
wt <- ratio * c(-w[2], w[1])
Q <- P + w; R <- Q + wt; S <- P + wt
A <- shear$transform(P)
B <- shear$transform(Q)
C <- shear$transform(R)
D <- shear$transform(S)
plot(0, 0, type = "n", asp = 1, xlim = c(0,1), ylim = c(0,2))
lines(rbind(P,Q,R,S,P), lwd = 2) # unit square
lines(rbind(A,B,C,D,A), lwd = 2, col = "blue") # image by the shear


## ------------------------------------------------
## Method `Shear$new`
## ------------------------------------------------

Shear$new(c(1,1), c(1,3), 0.5, 30)

## ------------------------------------------------
## Method `Shear$getMatrix`
## ------------------------------------------------

S <- Shear$new(c(1,1), c(1,3), 0.5, 30)
S$getMatrix()

## ------------------------------------------------
## Method `Shear$asAffine`
## ------------------------------------------------

Shear$new(c(0,0), c(1,0), 1, atan(30), FALSE)$asAffine()

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