Revisiting variable radius circles in constructive geometric constraint solving Original Research Article

Variable-radius circles are common constructs in planar constraint solving and are usually not handled completely by algebraic constraint solvers. This work offers a set of basic constructive methods for the complete treatment of variable radius circles determined by the simultaneous placement of two other rigid geometric objects. The variable radius circle is defined by geometric constraints that determine both the circumference and the center point. There are two constraints between the variable radius circle and each of the rigid geometric objects. The problem has been classified into two groups according to whether the relative movement between the two rigid objects is a translation or a rotation. The number of solutions in each case is also given.