Jingbo Liang -Tiling

Part 1: 2D Tiles A 

In the right picture, you can see the unit. Similar to the Part1:2D tiles B, Line a and Line e are replaced by Curve a and Line b and Line d are replaced by curve b.

Part 1:2D Tiles B

• In the right picture, you can see the unit. There are five lines: a, b, c, d, e. The close curve formed by a, b, d, e is known as a parallogram. Line c was used to divide it into two triangles. It repeats itself along two vectors, v1 and v2 to form the 2D tiles.

Part 2:

• In the left picture, you can see the tiles I’m trying to create (cited from: https://link.aps.org/accepted/10.1103/PhysRevB.99.100404). This 2D tile is made up of hexagons formed by two triangles colored red and blue. Codes are assigned to all intersection points. The tile repeats itself along two vectors, Vx and Vy. Two shaded triangles of one unit are shared with its repeated unit in the top. Thus, the unit I need to print is the star-like shape shown on the right.
• The geometrical changes in the z direction happen along the triangles rather than the hexagon. Because each intersection points are recorded. Curves formed by segments between any two intersection points can be formed by rs.AddCurve([point1,point2]). Then using rs.DivideCurve function to get points on each curve. Turtle is used to trace points. I used another turtle to add the changes.

• The hardest part is drawing a matrix of tiles in the plane. Turtle’s moving generated some unnecessary lines. I tried penup() and pendown(). However, it didn’t work. It’s something I need to think about more.

Part 3:

• I modified the “pot” from HW2 to make the surface. These tiles are from Part 1. Initially, my code didn’t work because the surface I generated used “polygon=rs.AddLine(points)”. You can fix it by using “polygon=rs.AddCurve(points)”. It’s hard to tell the difference visually. Their outputs are different, though. The first one adds a line, while the second adds a curve.
• Codes are here