Isohedral Tiling Explorer

Instructions

This web-based application allows you to explore the space of isohedral tilings and its mechanical properties. On the left-hand side, you will see a collection of data points, each one representing a single structure. The plot can be zoomed into using the mouse wheel.

When you hover your cursor over such a data point, its mechanical properties and structure will be displayed in the center column. The picture at the bottom, which can be zoomed in using the mouse wheel, shows the structure, while the three polar plots at the top show the directional Young's modulus, Poisson's ratio, and bending stiffness of the structure. These plots show the mechanical properties of the linear material model fitted at 0.1% and 10% strain (0.1m^-1 and 5m^-1 curvature for the bending) with light and dark solid lines, respectively. Additionally, the true (simulated) properties are shown with dashed lines.
The various curves can be enabled and disabled using the checkboxes on the right, and the Young's modulus plot can additionally be switched to a logarthmic scale.

On the right-hand column, there are various options to change and adjust the plots:

• Data

  The data displayed on the x- and y-axis can be changed here. Additionally, a third data value can be visualized using the color of the data points. Normalization by relative density (ratio of structure to total area) can be activated through a checkbox, and affects the Young's modulus and bending stiffness.

• Structure families

  Isohedral tilings can be grouped into multiple families of varying complexity. Here, individual families can be activated or deactivated.

• Structure information

  While hovering your cursor over a data point, this box will show information relating to that data point, including an ID, its isohedral family, and the parameters of the structure. Parameters correspond to the ones used in the code published by Prof. Craig S. Kaplan based on his work on Escherization.

• Selection

  This box will show the indices of selected data points. It also allows you to change the selection, by changing the indices in the text field.

• Direct URL

  This allows you to store and share a permanent link to your current choice of data, families, and selection.

This application was built using D3.js and lz-string.