position_lineartrans: Linearly transform coordinates

In ggh4x: Hacks for 'ggplot2'

Linearly transform coordinates

Description

Transforms coordinates in two dimensions in a linear manner for layers that have an x and y parametrisation.

Usage

position_lineartrans(scale = c(1, 1), shear = c(0, 0), angle = 0, M = NULL)

Arguments

scale	A numeric of length two describing relative units with which to multiply the x and y coordinates respectively.
shear	A numeric of length two giving relative units by which to shear the output. The first number is for vertical shearing whereas the second is for horizontal shearing.
angle	A numeric noting an angle in degrees by which to rotate the input clockwise.
M	A 2 x 2 real matrix: the transformation matrix for linear mapping. Overrides other arguments if provided.

Details

Linear transformation matrices are 2 x 2 real matrices. The 'scale', 'shear' and 'rotation' arguments are convenience arguments to construct a transformation matrix. These operations occur in the order: scaling - shearing - rotating. To apply the transformations in another order, build a custom 'M' argument.

For some common transformations, you can find appropriate matrices for the 'M' argument below.

Value

A PositionLinearTrans ggproto object.

Common transformations

Identity transformations

An identity transformation, or returning the original coordinates, can be performed by using the following transformation matrix:

⁠| 1 0 |⁠
⁠| 0 1 |⁠

or

M <- matrix(c(1, 0, 0, 1), 2)

Scaling

A scaling transformation multiplies the dimension of an object by some amount. An example transformation matrix for scaling everything by a factor 2:

⁠| 2 0 |⁠
⁠| 0 2 |⁠

or

M <- matrix(c(2, 0, 0, 2), 2)

Squeezing

Similar to scaling, squeezing multiplies the dimensions by some amount that is unequal for the x and y coordinates. For example, squeezing y by half and expanding x by two:

|		2		0		|
|		0		0.5		|

or

M <- matrix(c(2, 0, 0, 0.5), 2)

Reflection

Mirroring the coordinates around one of the axes. Reflecting around the x-axis:

|		1		0		|
|		0		-1		|

or

M <- matrix(c(1, 0, 0, -1), 2)

Reflecting around the y-axis:

|		-1		0		|
|		0		1		|

or

M <- matrix(c(-1, 0, 0, 1), 2)

Projection

For projecting the coordinates on one of the axes, while collapsing everything from the other axis. Projecting onto the y-axis:

|		0		0		|
|		0		1		|

or

M <- matrix(c(0, 0, 0, 1), 2)

Projecting onto the x-axis:

|		1		0		|
|		0		0		|

or

M <- matrix(c(1, 0, 0, 0), 2)

Shearing

Tilting the coordinates horizontally or vertically. Shearing vertically by 10\

|		1		0		|
|		0.1		1		|

or

M <- matrix(c(1, 0.1, 0, 1), 2)

Shearing horizontally by 200\

|		1		2		|
|		0		1		|

or

M <- matrix(c(1, 0, 2, 1), 2)

Rotation

A rotation performs a motion around a fixed point, typically the origin the coordinate system. To rotate the coordinates by 90 degrees counter-clockwise:

|		0		-1		|
|		1		0		|

or

M <- matrix(c(0, 1, -1, 0), 2)

For a rotation around any angle \theta :

|		cos\theta		-sin\theta		|
|		sin\theta		cos\theta		|

or

M <- matrix(c(cos(theta), sin(theta), -sin(theta), cos(theta)), 2)
with 'theta' defined in radians.

Examples

df <- data.frame(x = c(0, 1, 1, 0),
                 y = c(0, 0, 1, 1))
ggplot(df, aes(x, y)) +
  geom_polygon(position = position_lineartrans(angle = 30))

# Custom transformation matrices
# Rotation
theta <- -30 * pi / 180
rot <- matrix(c(cos(theta), sin(theta), -sin(theta), cos(theta)), 2)
# Shear
shear <- matrix(c(1, 0, 1, 1), 2)

# Shear and then rotate
M <- rot %*% shear
ggplot(df, aes(x, y)) +
  geom_polygon(position = position_lineartrans(M = M))
# Alternative shear and then rotate
ggplot(df, aes(x, y)) +
  geom_polygon(position = position_lineartrans(shear = c(0, 1), angle = 30))

# Rotate and then shear
M <- shear %*% rot
ggplot(df, aes(x, y)) +
  geom_polygon(position = position_lineartrans(M = M))

ggh4x documentation built on May 29, 2024, 6:47 a.m.