Question Draw a line touching to the circumference of a circle

Hi,
Say the circle is at (3, 3). How to calculate the vector position of the arrow line?

 

If the vector always hits the circle at 90 degrees then it is just Pythagoras for the diagonal minus the radius of the circle.

 

Code (CSharp):

1. line.SetPosition(0, new Vector3(0, 0, 1));
2. line.SetPosition(1, new Vector3(x, y, 1));

So if the radius is 0.5 then

Code (CSharp):

1. line.SetPosition(0, new Vector3(0, 0, 1));
2. line.SetPosition(1, new Vector3(x - 0.5f, y - 0.5f, 1));

?

Unfortunately this is not working and probably I'm missing something here. Thanks for replying.

 

You've left poor Mr Pythagoras out in the cold!

He's the one that tells us that the length of the hypotenuse of a right triangle is given by the square root of the sum of the squares of each side, to wit:

Code (csharp):

1. float len = Mathf.Sqrt( x * x + y * y);

So that's the linear distance from (0,0) to the center of the circle.

You could save some time by putting x/y into a Vector2, like-a-so:

Code (csharp):

1. Vector2 temp = new Vector2( x, y);
2.  
3. float distance = temp.magnitude; // <--- pythagoras magic done for us by the math library here
4.  
5. Vector2 tipOfArrow = temp.normalized * (distance - circleRadius);

Presto! As I said, Pythagoras minus the radius.