Daniel’s Large Assignment 5: Tiling

Part 1: 2D Tiles

My design process started with using the foundational code provided in class, focusing on creating unique, interconnected curves for an Escher-style tiling. I experimented with a few ideas, particularly around symmetrical forms, like frogs, bats, and fish, as I thought these shapes would tessellate naturally. However, none of these options seemed to work quite right. Next, I attempted a more abstract approach, trying to develop a human-like character, but this also didn’t produce the intended effect.

After several attempts, I found inspiration in the shape of a gingerbread man. Although the final design doesn’t look exactly like a gingerbread man, it sparked ideas that led to a pattern I found visually engaging. My brother and I looked at the pattern and saw different shapes within it—he and I thought it resembled a ghost in motion, a person riding a seahorse, or even a fox. This ambiguity added an interesting layer to the design that I hadn’t initially anticipated.

Part B

The hexagonal tiling design arranges hexagons in a staggered grid to fully cover the XY plane without overlaps or gaps. Each hexagon is created with vertices at 60-degree increments, ensuring a consistent shape. For positioning, each tile’s horizontal (x) and vertical (y) offsets are calculated to align edge-to-edge, with alternating rows shifted vertically by half a hexagon’s height. This offset pattern produces a seamless lattice. To visually confirm the tiling’s accuracy, hexagons are colored in a checkerboard pattern (pastel red and white), with alternating colors applied based on row and column indices. The design process guarantees a formal tiling that fills the plane and satisfies non-overlap requirements.

Initially, I attempted to modify the given lattice code to meet the requirements for hexagonal tiling, but encountered challenges in aligning the hexagonal tiles correctly and avoiding overlaps. Due to these difficulties, I decided to create my own code to achieve the precise positioning needed for a complete hexagonal tiling. This approach allowed me to control the angles and offsets more effectively, ultimately producing a seamless tiling that fulfills the XY plane requirements.

Part 2: 3D Printed 3D Tiles

For my 3D tile, I chose to work with the Escher-style tile I created in Part 1a. To meet the requirement of adding a geometrical change in the z-direction, I experimented with several methods. Initially, I tried using an “extrude point” technique, which would have satisfied the requirement, but I wasn’t satisfied with the overall look. Instead, I decided to add dimension by incorporating additional shapes within the tile.

To achieve this, I started by creating a smaller, nested curve inside the main Escher tile outline and raised it along the z-axis to a specified height. Then, I added a circular curve, also raised along the z-axis, and lofted these curves together to create a smooth, cohesive 3D form. This design introduces a subtle elevation change that adds visual interest and depth to the tile, while still allowing it to tile seamlessly across the XY plane. I applied a -0.2 inward offset to ensure all pieces would fit together precisely without leaving gaps.

For printing, I initially attempted to use G-code directly, but this method led to unsightly, free-standing lines during the print process. Ultimately, I opted to use Cura for slicing, which resulted in a cleaner and more professional-looking finish.

Part 3: Surface Morph

For the surface morph task, I chose to use the gourd-shaped vessel I created in Large Assignment 2: Parametric Vessels as the base surface. Using the code created in class, I applied a surface morph technique to map my tile design from Part 1 onto the gourd vessel. Initially, I encountered an issue where the surface morph was only producing a single instance of the tile along the gourd’s surface. After troubleshooting, I discovered that this was due to having two data dams in my Grasshopper script, which prevented the data from fully updating when I adjusted values. Once I corrected this by ensuring data transfer across all nodes, the tiling pattern successfully applied across the gourd surface, creating the desired effect.