Generalized bilinear interpolation of coordinates — bilinear

Apply a generalized bilinear interpolation to convert any coordinates from one original coordinate system to another, using the plot's 4 corner coordinates of both system.

Usage

bilinear_interpolation(
  coord,
  from_corner_coord,
  to_corner_coord,
  ordered_corner = F
)

Arguments

coord: a matrix or data.frame : coordinates to be transformed, with X and Y corresponding to the first two columns
from_corner_coord: a matrix or data.frame : corner coordinates of the plot in the original coordinate system, with X and Y corresponding to the first two columns
to_corner_coord: a matrix or data.frame : corner coordinates of the plot in the coordinate system to be projected, with the same line order as from_corner_coord and , with X and Y corresponding to the first two columns
ordered_corner: a logical, indicating if from_corner_coord and to_corner_coord rows are sorted in correct order (clockwise or counter-clockwise)

Value

a data.frame containing the converted coordinates

Details

The plot represented by the 4 coordinates in from_corner_coord must have 4 right angles, i.e. a rectangular (or square) plot.

References

C. -C. Wei and C. -H. Chen, "Generalized Bilinear Interpolation of Motion Vectors for Quad-Tree Mesh," 2008 International Conference on Intelligent Information Hiding and Multimedia Signal Processing, Harbin, China, 2008, pp. 635-638, doi: 10.1109/IIH-MSP.2008.283.

Author

Arthur Bailly

Examples

from_corner_coord <- expand.grid(X = c(0, 100), Y = c(0, 50))
rot_mat <- matrix(c(cos(-pi/6),sin(-pi/6),-sin(-pi/6),cos(-pi/6)),nrow=2)
to_corner_coord <- as.matrix(from_corner_coord) %*% rot_mat
to_corner_coord <- sweep(to_corner_coord, 2, c(50,100), FUN = "+")
coord <- expand.grid(X = seq(0,100,10), Y = seq(0,50,5))
projCoord = bilinear_interpolation(coord = coord, from_corner_coord = from_corner_coord, to_corner_coord = to_corner_coord)
# plot(coord, xlim=c(-10,150),ylim=c(-5,200), col="blue") ; points(from_corner_coord) ; points(projCoord , col="purple") ; points(to_corner_coord, col="red")