Some embodiments provide a system for generating a centerline connectivity representation for a set of routing shapes. During operation, the system can represent the set of routing shapes using a set of centerlines with endcap extensions. Note that an intersection between two centerlines represents an electrical connection between the two routing shapes associated with the two centerlines. Next, the system can detect two routing shapes which overlap, but whose centerlines do not intersect. The system can then create a virtual shape whose centerline intersects with the centerlines of the two routing shapes. In some embodiments, the system can modify a dimension of at least one of the two routing shapes. Next, the system can create a new routing shape which overlaps with the two routing shapes, and create virtual shapes which connect the centerline of the new shape with the centerlines of the two routing shapes.