Scaling: R6 class representing a (non-uniform) scaling

In PlaneGeometry: Plane Geometry

R6 class representing a (non-uniform) scaling

Description

A (non-uniform) scaling is given by a center, a direction vector, and a scale factor.

Active bindings

center

get or set the center

direction

get or set the direction

scale

get or set the scale factor

Methods

Public methods

• Scaling$new()

• Scaling$print()

• Scaling$transform()

• Scaling$getMatrix()

• Scaling$asAffine()

• Scaling$scaleCircle()

• Scaling$clone()

---

Method new()

Create a new Scaling object.

Usage

Scaling$new(center, direction, scale)

Arguments

center

a point, the center of the scaling

direction

a vector, the direction of the scaling

scale

a number, the scale factor

Returns

A new Scaling object.

Examples

Scaling$new(c(1,1), c(1,3), 2)

---

Method print()

Show instance of a Scaling object.

Usage

Scaling$print(...)

Arguments

...

ignored

---

Method transform()

Transform a point or several points by the reference scaling.

Usage

Scaling$transform(M)

Arguments

M

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

---

Method getMatrix()

Augmented matrix of the scaling.

Usage

Scaling$getMatrix()

Returns

A 3x3 matrix.

Examples

S <- Scaling$new(c(1,1), c(2,3), 2)
P <- c(1,5)
S$transform(P)
S$getMatrix() %*% c(P,1)

---

Method asAffine()

Convert the reference scaling to an Affine object.

Usage

Scaling$asAffine()

---

Method scaleCircle()

Scale a circle. The result is an ellipse.

Usage

Scaling$scaleCircle(circ)

Arguments

circ

a Circle object

Returns

An Ellipse object.

---

Method clone()

The objects of this class are cloneable with this method.

Usage

Scaling$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

Q <- c(1,1); w <- c(1,3); s <- 2
S <- Scaling$new(Q, w, s)
# the center is mapped to itself:
S$transform(Q)
# any vector \code{u} parallel to the direction vector is mapped to \code{s*u}:
u <- 3*w
all.equal(s*u, S$transform(u) - S$transform(c(0,0)))
# any vector perpendicular to the direction vector is mapped to itself
wt <- 3*c(-w[2], w[1])
all.equal(wt, S$transform(wt) - S$transform(c(0,0)))


## ------------------------------------------------
## Method `Scaling$new`
## ------------------------------------------------

Scaling$new(c(1,1), c(1,3), 2)

## ------------------------------------------------
## Method `Scaling$getMatrix`
## ------------------------------------------------

S <- Scaling$new(c(1,1), c(2,3), 2)
P <- c(1,5)
S$transform(P)
S$getMatrix() %*% c(P,1)

PlaneGeometry documentation built on Aug. 10, 2023, 1:09 a.m.