Design

What's happening

28 Jan 2019

Mathematical surfaces created in a tangible form, via 3D printing.

This interdisciplinary project was inspired by the Institute of Advanced Studies’ geometry theme and developed with the Department of Mathematical Sciences.

The Maths department wanted to find a means of representing mathematical equations in physical form, so pursued a collaboration with the Design School.

The Design School has research strength in additive manufacturing, within the Design for Digital Fabrication (D4DF) Research Group, and expertise in generating 3D textures with Research Associate, James Gardner. James’ PhD study focused on the generation of biomimetic, functional textures, so he was familiar with creating data-driven models, which was central to this project. His studies bridged design, manufacturing, and biology fields to understand the functionalities of textures on plants and animals, so that James could replicate natural textures on any surface.

Transforming abstract mathematical equations into tangible realities has been completed by other researchers previously, however, research completed in this project saw the development of a novel design process that automatically converts equations into manufacturable objects. Equations with X and Y components creates a 2D output, which is often represented by curves on graph paper. When a Z component is introduced a 3D form can be represented. Created automatically with CAD software, developed by James, point clouds were imported and converted into volumetric bodies, which were suited to 3D printing. A similar process was developed to represent linear equations (2D) that sit on the mathematical surfaces (3D).

The equations that have been produced through this novel surface generation approach are:

  • Degree 2 del Pezzo surface
  • Clebsch cubic surface
  • Maximal quartic surface

Future impact for the School could mean that the software may be developed further, to enable maths students to input their own equations to produce their own 3D surfaces.

One of the world’s leading research groups in the field of Design for Additive Manufacturing and 3D Printing, the Design School was proud to be involved in this interdisciplinary project. Dr James Gardner commented,

“This symbiotic relationship between Schools has strengthened our partnership; different experts from within the University have worked in collaboration to produce tangible forms from an abstract mathematical foundation.”

The mathematical surfaces can currently be viewed at the “Inspired by Geometry” exhibition, part of the Institute of Advanced Studies led Geometry theme.

The manufacture of the mathematical surfaces was also supported by Prof. Richard Bibb, also of the D4DF Research Group, and Mr David Thompson, Additive Manufacturing Technical Supervisor from the School of Mechanical, Electrical and Manufacturing Engineering.