2007 January 18 // The Daily Render by Nikolas R. Schiller

|| 1/18/2007 || 4:27 pm || Comments Off || ||
Polar Coordinates of Austin, Texas [square]

8 tiled map

I recently read through the work of Dr. Andrew Hudson-Smith (located at the Center for Advanced Spatial Analysis in London). I was intrigued by his use of Polar Coordinates to create panoramas and synthetic planets. I had been shown how to make the panoramas before, but I hadn’t actually figured out how I could incorporate my current work with this design technique. After some experimenting I figured out some interesting new methods to display tessellated aerial photography using the Polar Coordinates filter. The results are quite amazing and show definite promise for further research…

For this experiment I used the “zoom” of Austin Quilt #2 (a square quilt projection) as my test tessellation to begin working with. I could have used any zoom from any previously made map, but since it was snowing in Austin yesterday, I thought it would be ironic to use the Polar Coordinates filter.

The process to create the panorama planets is relatively simple:
- Stitch together series of photographs
- Reduce the panorama (by default a rectangle) to a square
- Apply Polar Coordinates filter in Photoshop

What makes my experiments unique is that instead of stitching together a photograph, I am I am stitching together perfectly symmetrical square tiles (composed of tessellated aerial photography) to create a rectangle. Moreover, I am maintaining perfect ratios throughout: 1:1, 2:1, 3:1, 4:1, 5:1, 6:1, 7:1, and 8:1. For example, the source tile is 800×800 and for each polar coordinate created (below) I merely added one more tile to rectangle ([1600, 2400, 3200, 4000, 4800, 5600, 6400]x800).

For each ratio there are three images shown below:
- Rectangle with number of tiles
- Conversion of the Rectangle to Square
- Application of Polar Coordinates filter

Note: The first image of each ratio below appears to reduce in size after each tile has been been added. In order to maintain a constant width on my website, I’ve chosen to reduce each rectangle to 800 pixels in width (otherwise this entry would be 6400 pixels wide right now!). When originally manipulating the rectangles they were not reduced in size. Essentially, it was done to show the scale of the panorama at a fixed width of 800 pixels.

1 : 1

:Original:

:Converts To:

2 : 1

:Rectangle 2 Tiles Wide (reduced from: 1600×800):

:Rectangle reduced to a Square:

:Converts To:

3 : 1

:Rectangle 3 Tiles Wide (reduced from:2400×800):

:Rectangle reduced to a Square:

:Converts To:

4 : 1

:Rectangle 4 Tiles Wide (reduced from: 3200×800):

:Rectangle reduced to a Square:

:Converts To:

5 : 1

:Rectangle 5 Tiles Wide (reduced from: 4000×800):

:Rectangle reduced to a Square:

:Converts To:

6 : 1

:Rectangle 6 Tiles Wide (reduced from: 4800×800):

:Rectangle reduced to a Square:

:Converts To:

7 : 1

:Rectangle 7 Tiles Wide (reduced from: 5600×800):

:Rectangle reduced to a Square:

:Converts To:

8 : 1

:Rectangle 8 Tiles Wide (reduced from: 6400×800):

:Rectangle reduced to a Square:

:Converts To:

I am excited about what directions this technique might take my cartographic activities :) My next experiment will be to see how the application of the Polar Coordinates filter will effect each geometry of the quilt projection. This experiment was conducted using the square quilt projection, up next with be the diamond. The results should be interesting.