Geodesy: Self-rising 2.5D Tiles by Printing along 2D Geodesic Closed Path

Thermoplastic and Fused Deposition Modeling (FDM) based 4D printing is rapidly expanding to allow for space- and material-saving 2D printed sheets morphing into 3D shapes when heated. However, to our knowledge, all the known examples are either origami-based models with obvious folding hinges, or beam-based models with holes on the morphing surfaces. Morphing a flat thermoplastic sheet into continuous double-curvature surfaces remains a challenge, both in terms of a tailored toolpath-planning strategy and a computational model that simulates it.
In Geodesy, we focus on the morphing of continuous double-curvature surfaces or surface textures. We suggest a unique tool path - printing thermoplastics along 2D closed geodesic paths to form a surface with one raised continuous double-curvature tiles when exposed to heat. The shape space is further extended to more complex geometries composed of a network of rising tiles (i.e., surface textures). Both design components and a mass-spring-model-based computational pipeline are explained in the paper, followed by several printed geometric examples.