Move car to coordinate with considering z-angle

Question

I have such question:

I have a car, her coordinates (x, y, z) and z-angle (from 0 to 360 degrees).

And i have x, y, z of checkpoint.

how to calculate the angle to which need to turn the car to get to the point, taking into account its direction?

something like that:

Sorry for my English :D

Answer 1

If you draw a line between point b the target point and the x-axis you can see we always have a Triangle. When you now draw a circle which meets the new 90° corner of the triangle. The idea comes to use tan and arctan.

Is y (25) = tan(z) so z = arcTan(y)

The last Problem is that we need y when x = 1. We achieve this by dividing y and x: y / x;

So when our car is on position x = 15, y = 50 and his target is on x = 60 and y = 75

1. We calculate the different
   route.x = target.x - car.x; (= 45)
route.y = target.y - car.x; (= 25)

2. Get y when x = 1
   Y_When_X_Is_1 = route.y / route.x;

3. Calculate z
   z = arcTan(Y_When_X_Is_1);(~ 29.055)

Now you must watch of some special cases:

if route.y < 0 then z = 360 - z
if route.x < 0 then z = 180 - z
if route.x < 0 && route.y < 0 then z += 180

I hope this will help you!