Apply transformations to a set of x, y coordinates

Usage

CoordTransform(
  xy_coords,
  angle = 0,
  center = NULL,
  xy_offset = c(0, 0),
  scalefactor = 1
)

Arguments

xy_coords: A matrix, data.frame or tibble object with numeric x, y coordinates.
angle: Numeric value specifying the degree of rotation. Use negative angles for counter-clockwise rotation. The value needs to be in the range (-360, 360)
center: Optional point (x, y) specifying the center of rotation.
xy_offset: Optional point (x, y) specifying the translation.
scalefactor: A numeric value specifying a scaling factor between (0, 3)

Value

A tbl object with transformed coordinates

Details

The coordinate system for xy_coords should match the dimensions of the image. In other words, the coordinates should map spots to the tissue section on H&E image. Translations and rotations are done by multiplying xy_coords with the following transformation matrix \(T_{final}\) as described below:

\(T(-x, -y)\): Translate coordinates to origin, i.e. (0, 0) becomes the new center
1 0 \(-center_{x}\)
0 1 \(-center_{y}\)
0 0 1
\(R\): Rotate coordinates around origin
\(cos(\alpha)\) \(-sin(\alpha)\) 0
\(sin(\alpha)\) \(cos(\alpha)\) 0
0 0 1
\(T(x, y)\): Translate coordinates back to center, or optionally to center + an xy_offset
1 0 \(center_{x} + offset_{x}\)
0 1 \(center_{y} + offset_{y}\)
0 0 1

Then, these matrices are combined to form the final transformation matrix:

\(T_{final} = T(x, y)*R*T(-x, -y)\)

Which can be used to transform our input coordinates:

\(xy_{out} = T_{final}*xy_{in}\)

The scaling is handled separated after the translations and rotations.

Author

Ludvig Larsson

Examples

# Create a data.frame with x, y coordinates
xy <- data.frame(x = 1:20, y = 1:20)

# Rotate coordinates 45 degrees clockwise around the center
xy_rotated <- CoordTransform(xy, angle = 45)
plot(xy)
points(xy_rotated, col = "red")

\(cos(\alpha)\)	\(-sin(\alpha)\)	0
\(sin(\alpha)\)	\(cos(\alpha)\)	0
0	0	1

1	0	\(center_{x} + offset_{x}\)
0	1	\(center_{y} + offset_{y}\)
0	0	1

1	0	\(-center_{x}\)
0	1	\(-center_{y}\)
0	0	1