How to find angle "a" on this shape?

[zemoddd]

I am making a procedural road generation tool for computer graphics. But I am stuck on this problem. It seems simple but I couldn't figure out even after spending hours. Please help me.

I drew the problem on the attached picture. Points P0, P1, P2 are known, length of r is also known. I need to learn how to find degree of a.

The solution is needed for automatically filling roadways between 2 points. The connection part is a portion of circle.

 

[Deleted member 4993]

I am making a procedural road generation tool for computer graphics. But I am stuck on this problem. It seems simple but I couldn't figure out even after spending hours. Please help me.

I drew the problem on the attached picture. Points P1, P2 are known, length of r is also known. I need to learn how to find degree of a.

The solution is needed for automatically filling roadways between 2 points. The connection part is a portion of circle.

If no other information is given, you cannot "calculate" the measure of "a".

 

[zemoddd]

If no other information is given, you cannot "calculate" the measure of "a".

Ah yes we know the direction of point P1 from the start. I will edit my question please wait.

 

[zemoddd]

If no other information is given, you cannot "calculate" the measure of "a".

Ok I believe given with P0 it can be solved now. Am I correct?

 

[mmm4444bot]

Are you using an xy-coordinate system, to define the locations of P0, P1, and P2?

 

[zemoddd]

Are you using an xy-coordinate system, to define the locations of P0, P1, and P2?

Yes.