Ultrasound mid-air haptic interfaces can display highly reconfigurable vibrotactile shapes in mid-air for human-computer interaction (HCI) applications. The choice of stimulus shape, spatial, temporal and modulation parameters yields a complex design space, yet relatively little is known about the impact of these design choices on perceived stimulus properties. We define the combination of a spatial discretization of an abstract shape and a set of rules for the temporal display order and intensity modulation of the resulting points as a sampling strategy. We developed DOLPHIN, an open-source framework to aid in designing mid-air stimuli. DOLPHIN allows the study of the impact of rendering parameters on perceived stimulus properties. This platform-agnostic framework standardizes stimulus descriptions as a step toward more replicability and easier communication in the field. It enables reproduction of stimuli between perceptual experiments and ensures stimuli used in applications correspond to those evaluated in prior perceptual studies. We validated DOLPHIN's usability by conducting a user study assessing the impact of sampling strategy design on curvature discrimination for dynamic mid-air haptic stimuli. The Weber fractions for just-noticeable differences (JNDs) in curvature were found to range between 1 and 1.4, yet no significant effect of the number of spatial sampling points on curvature discrimination was found. This result shows a practical use-case for DOLPHIN and provides insight into rendering mid-air haptic curvature.