[1.17] Help with Part Entities

[uSkizzik]

Now, this is more of a math issue than a modding issue. I'm very bad at it.
Basically, I have an Ender Dragon-like multi-part entity. I know that these are currently broken but I'm using my PR which fixes them.
So, I have all the required code to change the part positions and I've set the offsets to the wanted values. My issue is that the parts are static but they need to change their place depending on the entity's rotation.
My question is, how do I calculate the new position based on the entity's position and rotation, combined with my current offsets. I don't want to change the offsets if possible because I spent a very long time getting them pixel-perfect.

Here's a simplified version of my code (it excludes all the stage-related positioning):

public void tickPart(SkizzikPart part, double offsetX, double offsetY, double offsetZ) {
	part.setPos(this.getX() + offsetX, this.getY() + offsetY, this.getZ() + offsetZ);
}

public void aiStep() {
	this.tickPart(this.topLeftHead, -0.062F, 3.199F, 0.812F);
	this.tickPart(this.topRightHead, 0.0F, 3.073F, -1.06F);
	this.tickPart(this.bottomLeftHead, -0.062F, 1.822F, 1.125F);
	this.tickPart(this.bottomRightHead, 0.0F, 1.7F, -1.187F);
	this.tickPart(this.centerHead, 0.0F, 2.01F, -0.063F);
	this.tickPart(this.commandBlockPart, 0.63F, 0.87F, -0.03F);
	this.tickPart(this.bodyPart, -0.062F, 0.0F, -0.032F);
        
	Vec3[] vec3 = new Vec3[this.parts.length];
	for(int i = 0; i < this.parts.length; ++i) {
		vec3[i] = new Vec3(this.parts[i].getX(), this.parts[i].getY(), this.parts[i].getZ());

		this.parts[i].xo = vec3[i].x;
		this.parts[i].yo = vec3[i].y;
		this.parts[i].zo = vec3[i].z;
		this.parts[i].xOld = vec3[i].x;
		this.parts[i].yOld = vec3[i].y;
		this.parts[i].zOld = vec3[i].z;
    }
}