Ultrasound mid-air haptic (UMH) interfaces focus acoustic energy to generate high-pressure focal points in mid-air, creating tactile sensations. When these focal points are modulated over time, they can render tactile patterns with various properties in a 3D workspace. While UMH has been used to render curves and 2D shapes, such as tactile icons, rendering 3D objects in full is nowadays an open problem, as it would require more powerful devices. To overcome this limitation, designers typically only render a representation of the intersection between the user’s hand and the virtual object. However, there is no consensus in the literature on how best to compute this intersection. This paper formalizes a pipeline for computing the intersection between a user’s hand and a 3D virtual object. Together with state-of-the-art sampling strategies, this forms an end-to-end design process for rendering 3D objects with UMH. A user study demonstrates the significant impact of intersection strategy design choices on the perception of 3D object properties, specifically infill density. We illustrate that different strategies can alter the perception of how hollow or filled an object is, which can be challenging to render in mid-air. By providing a standardized way to report and study 3D object rendering with UMH, this work aims to facilitate and motivate further exploration of perceptual effects via UMH technologies.