Geodesy & Geodesy +: Inverse Design Tool for Asymmetrical Self-Rising Surfaces with Color Texture
2018–2020

Geodesy + is an end-to-end tool that enables an initially flat sheet to self-transform into the input height field. The tool first flattens the height field into a 2D layout with stress information using a geometry-based optimization algorithm, then computes printing tool paths with a path planning algorithm. Although FDM printing is the fabrication method in this work, our approach can be applied to most extrusion-based printing methods in theory. The results exemplify how the tool broadens the capabilities of 4D printing with an expanded shape space, a low-cost but precise coloring technique, and an intuitive design process.

This is a collaborative effort between Morphing Matter Lab and Textiles Lab at CMU.

By Jianzhe Gu, Vidya Narayanan, Guanyun Wang, Danli Luo, Harshika Jain, Kexin Lu, Fang Qin, Sijia Wang, James McCann, Lining Yao

Publications:
ACM SCF 2020 PDF I DOI | SOURCE CODE
ACM CHI 2019 PDF | DOI


We introduce an inverse design algorithm that consists of a flattening algorithm and a tool path planner. Given an input height field, our tool computes a 2D layout of the triangle mesh with geometry-based optimization and a vertices relocation process. Inspired by the tracing procedure of automatic machine knitting, we developed a path planning method that computes continuous tool paths with varying layer thickness from the 2D layout. The algorithm finally generates the G-code for FDM printers.

We were able to 4D print a collection of 2.5D models. It shows a diverse context, ranging from different landscapes to sea creatures.

 A library of printed objects. (a) Sea star. (b) Island. (c) Face. (d) Bear. (e) Glacier. From left to right, input geometry, printing tool path with stress visualization, simulated transformed shape, 3D printed sheet with screen printing pattern before transformation and after transformation.

Our system takes as input a 2.5D height field with an optional texture map for color. The height field is first meshed into a quadrangle-dominated graph and then converted into a triangle mesh. Next, a 2D layout of the triangle mesh is computed through a geometry-based constraint optimization and a vertices relocation process in an iterative fashion. After that, we construct a tool path with appropriate shrinkage ratios by tracing the 2D mesh. Lastly, color and opacity values are computed from the texture map and local shrinkage factors.

In an earlier work, 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 design space is further extended to more complex geometries composed of a network of rising tiles (i.e., surface textures). Both design components and the computational pipeline are explained in the paper, followed by several printed geometric examples.

ACM CHI 2019 PDF | DOI
Geodesy: Self-rising 2.5D Tiles by Printing along 2D Geodesic Closed Path
By Jianzhe Gu, David E. Breen, Jenny Hu, Lifeng Zhu, Ye Tao, Tyson Van de Zande, Guanyun Wang, Yongjie Jessica Zhang, Lining Yao

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