Image Warping

If you have an image of a system, you can warp the image as if each pixel were a test particle following Kepler's laws. This is an easy way to see what a disk or a system of planets would look like at a time other than when it was captured.

To make this possible, PlanetOrbits.jl can create OrbitalTransformation objects. These follow the conventions set out in CoordinateTransformations.jl and are compatible with ImageTransformations.jl.

Example:

using ImageTransformations, AstroImages, CoordinateTransformations
ot = OrbitalTransformation(
    i = 0.3,
    e = 0.0,
    M = 1.0,
    ω = 0.5,
    Ω = 0.5,
    plx = 300.0,
    
    platescale=10.0, # mas/px
    dt = 3*365.25 # days forward in time
)

img = load("input.fits")

tform_centered = ImageTransformations.recenter(ot, ImageTransformations.center(img))
img_future = warp(img_centered, ot, axes(img_centered))

# Display with AstroImages.jl
imview([img; img_future], cmap=:seaborn_icefire_gradient)

Before, and After Orbital Transformation

Note the arguments platescale and dt are required, but a and τ are not. The position of the pixel in X/Y space uniquely determines the semi-major axis and epoch of periastron passage when the rest of the orbital parameters are known. platescale in units of milliarseconds/pixel is necessary to get the overall scale of the transform correct. This is because an orbital transformation is not linear (and therefore, care must be taken when composing an OrbitalTransformation with other CoordinateTransformations). Scaling an image will change the amount of rotation that occurs at each separation. dt is the the amount of time in days to project the image forward. It can also be negative to project the image into the past.