I'm writing some code for various calculations with arcs and lines and need help with some math.
I have list of arcs and need to add them together if they "overlap", here is the available variables:
Radius;
Center X Y Z;
StartAngle;
EndAngle;
I can check if the arcs have the same starting point and if their radius is the same, meaning we know that they are a part of the same circle. By adding them together I mean I should get a new arc with new starting and ending angles that cover given two arcs.
This could be solved by checking and comparing a lot of conditions but I'm looking for a more mathematical approach.
Few examples Arc{startAngle;endAngle}:
A1{350;340} B1{90;270} -> C1{350;340}
A2{225;20} B2{90;270} -> C2{90;20}
A3{225;300} B3{90;270} -> C3{90;300}
A4{340;45} B4{90;270} -> not overlapping
Edit
Here is a simple illustration to help in understanding my problem as I'm not the best in using math words.
Illustration
Best Answer
You should consider this problem as a problem with subsets of $[0,2\pi)$ (or equivalently, of $[0,360)$ using degrees). Let arc $A=[a,b)$ and $B=[c,d)$ such that $a<c<b<d$. Then $A=[a,c)\cup[c,b)$ and $B=[c,b)\cup[b,d)$ and if we 'add' (take the union) them we get $A\cup B=[a,c)\cup[c,b)\cup [c,b)\cup[b,d)=[a,d)$ which is what we wanted.