The single-engine biplane sustained substantial damage during an aborted takeoff when the airplane veered sharply to the left during the takeoff roll, and the right wing and right horizontal stabilizer impacted the runway. The pilot reported that he used braking action to change direction when he taxied to the runway for takeoff. He stated that the tailwheel was locked while taxiing. The pilot reported that he could not see the rudder when he checked the flight controls prior to takeoff, and he did not have anyone verify the direction of the rudder when he moved the rudder pedals. Once on the runway he added power for takeoff, but immediately reduced power due to the lack of directional control. He reported that he aborted the takeoff before the airplane reached 30 knots airspeed. He reported the airplane "swerved suddenly and extremely sharply to the left causing the wingtips to scrape the runway." The inspection of the airplane revealed that the rudder control cables were rigged backwards. The airplane had undergone maintenance to have the original cable operated brakes replaced with hydraulic brakes. After the hydraulic brakes had been installed by the maintenance facility, the rudder cables were improperly rigged to the control surface. The maintenance facility's inspection of the hydraulic brake installation did not have a procedure in its inspection checklist that required an inspection of the rudder cable installation. The maintenance facility's inspection of the brakes did not detect the misrigged rudder cables.