After Effects Expressions

With this expression, you can animate an object along only one axis, using a Slider, and then change the direction of motion using Angle Control. Applies to the layer’s Position parameter.

p = effect("Slider Control")("Slider"); 
a = effect("Angle Control")("Angle"); 
r = degreesToRadians(a-90);
x = p*Math.cos(r);
y = p*Math.sin(r);
value + [x,y]

Analogue of the standard “Transform > Auto-Orient“, but created using the expression and the ability to adjust the degree of smoothness of the rotation animation.

try{
cornerEase = 3;
p = transform.position;
t = Math.min(Math.max(time,p.key(1).time+.001),p.key(p.numKeys).time);
pre = position.valueAtTime(t-thisComp.frameDuration*cornerEase);
post = position.valueAtTime(t+thisComp.frameDuration*cornerEase);
delta = post-pre;
orient = radiansToDegrees(Math.atan2(delta[0],-delta[1]));
value+orient+180
}catch(err){value}

Using this expression, you can shift the beginning and ending of the animation using two markers.
The first marker to shift the animation of the first two keys, that is, the beginning.
The second marker to shift the animation of the third and fourth keys, that is, the ending of the animation.

try{
if(marker.numKeys>1&&numKeys>1){
beginAnim=marker.key(1).time;
endAnim=marker.key(2).time;
markerMoveTime=endAnim-beginAnim;
keyStart=key(1).time; 
keyStartN=key(2).time;
keyEnd=key(3).time;
if(time>=beginAnim && time<=endAnim)
{if((time-beginAnim)>=(keyStartN-keyStart)){valueAtTime(keyStartN);}
else valueAtTime(keyStart+(time-beginAnim));
}
else if(time>endAnim)
{valueAtTime(keyEnd+(time-endAnim));}
else if(time<beginAnim) {valueAtTime(keyStart);}
else {value;}
}else value;
}catch(err){value;}

a = transform.anchorPoint;
p = transform.position;
x = p[0]+(a[0]-width/2);
y = p[1]+(a[1]-height/2);
[x,y]

Expression for keyless animation.

duration = 1; // Duration of animation in seconds
startVal = 0; // Start value
endVal = 100; // End value
endTime = inPoint+duration;
Math.round(linear(time,inPoint,endTime,startVal,endVal))

leader = thisComp.layer("Leader")
time < leader.inPoint || time > leader.outPoint ? 0 : 100

This expression will make the object rotate so that it always looks at the target layer.

Target = thisComp.layer("Target");
delta = thisLayer.toComp([0,0]) - Target.toComp([0,0]);
radiansToDegrees(Math.atan2(delta[1],delta[0]))+value

With this expression, you can limit the distance between two layers, so that the distance does not exceed the specified value. Applies to the Position parameter.

For 2D-layers:

centre=thisComp.layer("Centre");
radius = 512; // Maximum distance
x0=value[0]-centre.transform.position[0];
y0=value[1]-centre.transform.position[1];
distance0 = Math.sqrt(x0*x0+y0*y0);
distance = Math.min(distance0,radius);
if (distance0>radius){
distance_mult = distance/distance0;
}else{
distance_mult = 1
}
x=centre.transform.position[0]+distance_mult*x0;
y=centre.transform.position[1]+distance_mult*y0;
[x,y]

For 3D-layers:

centre=thisComp.layer("Orbit");
radius = 505;
x0=value[0]-centre.transform.position[0];
y0=value[1]-centre.transform.position[1];
z0=value[2]-centre.transform.position[2];
distance0 = Math.sqrt(x0*x0+y0*y0+z0*z0);
distance = Math.min(distance0,radius);
if (distance0>radius){
distance_mult = distance/distance0;
}else{
distance_mult = 1
}
x=centre.transform.position[0]+distance_mult*x0;
y=centre.transform.position[1]+distance_mult*y0;
z=centre.transform.position[2]+distance_mult*z0;
[x,y,z]