Interpolation of shearing Transform2D getting unintended results

[bombzj]

Godot version

3.5.stable, 4.0.dev

System information

Windows 10 x64

Issue description

with a Shearing Transform2D as follows

After interpolation, it changes to ((1, 0), (-0, 1.414214), (0, 0))

code as follows
var t = Transform2D()
t.y = Vector2.ONE
var result = t.interpolate_with(t, 0.5)
print(result)

Steps to reproduce

GDScript
extends Node2D

func _ready():
var t = Transform2D()
t.y = Vector2.ONE
var result = t.interpolate_with(t, 0.5)
print(result)

Minimal reproduction project

interp.zip

[lawnjelly]

I'm not sure the existing interpolate_with code is meant to deal with shearing. It seems to decompose into origin, rotation (float), scale (Vector2) and interpolate these.

Dealing with interpolating complex bases is not trivial afaik, so I'm not surprised it doesn't attempt it.

(I resort to lerping in the physics interpolation, when such bases are detected. This is not "correct" but can work through small deltas to bases .. albeit with some warping. I don't know if there is a general solution for this problem that will work for large differences, would need a mathemagician.)

[bombzj]

Transform2D contains 3 Vector2 (origin, x, y) which is basically a 3x2 matrix, decompose it into origin, rotation, scale will lose a float in information. Maybe decomposing it into origin, rotation, shear/skew(y), scale will do better. May I have a try(PR) on this?

[lawnjelly]

Transform2D contains 3 Vector2 (origin, x, y) which is basically a 3x2 matrix, decompose it into origin, rotation, scale will lose a float in information. Maybe decomposing it into origin, rotation, shear/skew(y), scale will do better. May I have a try(PR) on this?

Sure, feel free to have a go, you need no permission to try a PR! 😁