Mid-air haptics technologies are able to convey haptic sensations without any direct contact between the user and the haptic interface. One representative example of this technology is ultrasound haptics, which uses ultrasonic phased arrays to deliver haptic sensations. Research on ultrasound haptics is only in its beginnings, and the literature still lacks principled perception studies in this domain. This paper presents a series of human subject experiments investigating important perceptual aspects related to the rendering of 2D shapes by an ultrasound haptic interface (the Ultrahaptics STRATOS platform). We carried out four user studies aiming at evaluating (i) the absolute detection threshold for a static focal point rendered via amplitude modulation, (ii) the absolute detection and identification thresholds for line patterns rendered via spatiotemporal modulation, (iii) the ability to discriminate different line orientations, and (iv) the ability to perceive virtual bumps and holes. These results shed light on the rendering capabilities and limitations of this novel technology for 2D shapes.