True, it’s to the left which is what I used in the code of my first reply to position the cars and where I also used Normalize to work with unit vectors and I also used width over 4 to place dots in the middle of their lanes ... and it’s also fun to look at but it seems no one checked it out :( ... In my second reply, I got sloppy because I was typing on my iPhone which I’m doing again :) ...

I'm not sure that I understand your formulation.

Did you intend A to be the projection of the car's position onto the line that is the center of the road and p1 to be it's current specific position taking into account its direction of travel?

Did you consider the following?

Left and right don't work in three dimensions. Unless you want to simulate banked turns or such, you can assume that the road is flat left-to-right and use just the x and y components to calculate the offset. If A is (ax, ay, az) and B is (bx, by, bz) then the unit vector to the right is (ay-by, bx-ax, 0).normalized . You would multiply this by the number of lanes from the center and the lane width to get the offset and then add this offset to A to get the adjusted car position and add it to B to get the adjusted destination.

If A is the car position and B is the road center for its next destination point, why would you need to calculate a move from B to A? A car going the opposite direction from the same current position would have a different destination point.

I see. Congratulations on finding a solution!

Oh, my mistake, I am very tired.
The road has two lanes, left and right.
I can create a road with two points, like this: a-------------------------------b
The line which is created by the points a and b is midle of the road.

Now, I have the point c which is the car în my program.
Initial the point is on the line a-----------------c----------------b
If direction of the car (point c) is a->b I whant to put the car in the right lane, and if the direction of the car is b->a I want to put the car in the left lane.

Like this:
a->b -----------------------------------
c

a<-b
c
a<-b -----------------------------------
I know how to put the car on the correct lane, but I don't know when to do it

I was thinking about the direction, and to put every time a point to right side of the direction of two points, so my car will be all time on the correct lane of road