arXiv:2611.14389v1 Announce Type: new Abstract: Two-dimensional haptic displays, such as programmable pin arrays and vibrotactile or friction-modulating touchscreens, enable tactile communication of complex shapes in a low-profile form factor. However, many shapes of interest, including CAD models, three-dimensional graphs, and map topographies, are inherently three-dimensional. This work investigates two methods for encoding 3-D information using a 2-D tactile display: (1) a single tactile height map providing coarse but quantifiable depth cues, and (2) a series of binary layers communicating sequential slices of a 3-D model, supporting more complex geometries such as overhangs and cavities. We further compare performance across two display types--a friction-modulating display and a pin array--to examine how the level of haptic abstraction affects users' ability to decode discrete 3-D information. A user study demonstrates that participants were able to effectively complete a 3-D assembly task using both strategies, achieving high accuracy across all display types. While the pin array supported faster task completion and higher-rated--though not statistically significant--user experience than the friction-modulating display for the binary-layer task, these differences did not translate to significant differences in overall usability (i.e., reassembly accuracy success). Together, these results identify design trade-offs and inform development of future surface haptic displays that support the communication and interpretation of discrete 3-D information in tactile graphics.