Intersection of two arcs I have two circular arcs with 3 points. Is there any algorithm to check if the arcs intersect or not? I already found many algorithm for circles but I'm looking for arcs.
 A: For arcs, you have to add another step.  Clearly, 3 points define a unique circle, so given 3 points on each arc, you know what circle each arc defines.  However, each arc also subtends an angular extent from its respective circle's center.  In this respect, you may apply the usual algorithm to determine if there is an intersection between the respective circles on which each arc resides.  Let's say there is an intersection point.  Now you have to determine whether that intersection point lies on the arc.  You do this by determining, for each arc, whether the intersection point lies within the angular extent.
To illiustrate, let's say we've found an intersection point $(x^*, y^*)$.  Let's also say that we've found the arc to reside on the circle $(x_c + R \cos{t},y_c+R \sin{t})$, $t \in [0,2 \pi)$, and the arc lies in the interval $t \in [t_1,t_2]$, where $t_1$ and $t_2$ are easily found from the given endpoints of the arc.  In the same manner, we may also determine the value of $t^*$ corresponding to $(x^*,y^*)$, then all we need to do is check whether $t^* \in [t_1,t_2]$ and you are done. 
