Moving an object around the the circle to the specific location in circumference

Question

Well I have run out of ideas how to approach this particular problem.See the picture below:

So the idea is that the object (dot in black) has to get to a point mark X (red X mark).However the limitation is that it has to get there without crossing the circle (i.e going in the straight line the the X mark).I was reading on some steering algorithsm but seems rather too complicated for this problem.Also I should mention that the object has the speed and velocity and position attributes which controls how its moving.

Now I was reading some ideas on how to move an object around a circumference here:

Here

However this doesn't entirely answer my question.The thing is I first need to get to the circle in order to be able to move around it.What I was thinking,was to allow the object to move towards the position in a straight line until it hits the circle and then start moving along the circumference of the circle.Also the "X" mark can be anywhere on the circle even right in-front of it (not behind on the other side of the as in this example shown in the image)

I am not a game developer and thus never came across issues like so.The idea is that there will be more than one black object trying to get to their own "X" mark on the circle from random positions.(They idea is that they will be surrounding some objects in the middle). Here is an image to show what I mean,where each black object has an X position that they need to attend to without directly going through the circle.(Sorry for my bad drawings,was using laptop track-pad to do these images)

Anyway I am kinda lost with this and would to see different on tackling this particular problem.

Answer 1

I can think of a couple ways to approach this problem.

(Figure 1) Find the closer tangent point to aim towards, then steer along the edge of the circle. This should be the path with the shortest distance.

(Figure 2) In polar coordinates, plot a path that interpolates the angle Θ and radius r from the starting point to the desired point. These points are not equidistant, so use them as intermediate waypoints for travel. Since r_point never goes below r_circle, you are guaranteed it will not cross the circle boundary.

Answer 2

It sounds like your desired motion consists of two stages: first move directly toward the target point (x) until you hit the circle; then, move around the circle to the target point, if necessary.

Since there are two stages, you could use a state machine with two states indicating which kind of motion you're currently doing.

In the first state, just set the velocity using the vector from the object to the target point, scaled to the desired speed.

You can detect if you're about to run into the circle by checking whether the next frame position (after physics updates) would be inside the circle. If that occurs, adjust it so you don't enter the circle - this could be done by simply clamping to the nearest point on the circle, or by doing a ray-circle intersection test to find the exact point of contact (but you may not need to be that accurate). In any case, once you've hit the circle, switch to the second state.

Then apply the answers to the question you linked to to move around the circle to the target point.