Systems and methods for noncontact ablation of tissues or materials in/on the body using an ablation catheter that has a directional ablation unit. The ablation unit has a set of individual transducer (e.g., ultrasound) elements that are movably positioned. A position adjustment element (a deformer) is movable with respect to the ultrasonic transducer to alter the positions of the individual transducer elements and thereby alter the directions in which the transducer elements emit ultrasonic energy. In one embodiment, the ablation catheter is a lumen catheter through which a positioning/measurement catheter can be inserted. The luminal ablation catheter is inserted through the skin and into the body via conventional methods. The ablation and positioning catheters can be used to make electrical measurements with respect to the surrounding tissue, and the ablation catheter can be used to emit energy in a desired direction and/or pattern to ablate target tissue.