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Add ocean-centric arrangement and an icosahedron net #4

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384285b
Add ocean-centric and net (for an icosahedron) options.
MattBlissett Jul 4, 2022
70df6d0
Add examples for ocean and net, and SVGs for nets.
MattBlissett Jul 4, 2022
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6 changes: 5 additions & 1 deletion README.md
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Expand Up @@ -17,6 +17,10 @@ Technically, to unfold the earth into an icosahedron, we must first consider sli

All images in `/docs` and on this page are created by running `python3 -m dymax.examples`.

SVG files suitable for printing and folding into an icosahedron are in `/svg`. They reference images in `/docs`. Open the SVG file in a text editor and change the image reference to use a different map.

![Icosahedron net](svg/a4_dymaxion.svg)

## To-Do List
1) Replace spherical coordinate conversion with Earth-Centered-Earth-Fixed for much better accuracy.
2) Get documentation working correctly.
Expand Down Expand Up @@ -49,6 +53,6 @@ xy_projection = dymax.lonlat2dymax(-118.0367, 34.8951)
*pydymax* code is [Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)](http://creativecommons.org/licenses/by-nc-sa/4.0/)

## References
* [Mike Bostock's](https://github.com/mbostock) [javascript code](http://mbostock.github.io/protovis/ex/dymax.js) and [http://mbostock.github.io/protovis/ex/dymax.html](live demo)
* [Mike Bostock's](https://github.com/mbostock) [javascript code](http://mbostock.github.io/protovis/ex/dymax.js) and [live demo](https://mbostock.github.io/protovis/ex/dymax.html)
* [general info on dymax/fuller projections](http://www.progonos.com/furuti/MapProj/Normal/ProjPoly/projPoly3.html)
* [The big wiki article on Dymaxion Maps](http://en.wikipedia.org/wiki/Dymaxion_map)
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37 changes: 33 additions & 4 deletions dymax/constants.py
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Expand Up @@ -3,10 +3,17 @@
'''Constants for Dymaxion Projection Module'''
import math
import numpy as np
from enum import Enum

### Quick Vector Functions
magnitude = lambda vector: np.sqrt(np.dot(vector, vector))

### Face arrangement
class Unfolding(Enum):
LAND = 0
OCEAN = 1
NET = 2

### Icosahedron Time
facecount, vertexcount = 20, 12

Expand Down Expand Up @@ -61,20 +68,42 @@
[1.5, 4 * math.sqrt(3) / 3.0, 300],
[1.0, 5 / (2 * math.sqrt(3)), 300],
[1.5, 2 / math.sqrt(3), 0],
[2.0, 1 / (2 * math.sqrt(3)), 0],
[1.5, 1 / math.sqrt(3), 300],
[2.5, 1 / math.sqrt(3), 60],
[3.5, 1 / math.sqrt(3), 60],
[3.5, 2 / math.sqrt(3), 120],
[4.0, 5 / (2 * math.sqrt(3)), 60],
[4.0, 7 / (2 * math.sqrt(3)), 0],
[5.0, 7 / (2 * math.sqrt(3)), 0],
[5.5, 2 / math.sqrt(3), 0],
[0.5, 1 / math.sqrt(3), 60],
[1.0, 1 / (2 * math.sqrt(3)), 0],
[4.0, 1 / (2 * math.sqrt(3)), 120],
[4.5, 2 / math.sqrt(3), 0],
[5.0, 5 / (2 * math.sqrt(3)), 60]])
dymax_translate08_special = np.array([1.5, 1 / math.sqrt(3), 300]) # if LCD < 4
dymax_translate15_special = np.array([0.5, 1 / math.sqrt(3), 60]) # if LCD < 3
dymax_translate08_special = np.array([2.0, 1 / (2 * math.sqrt(3)), 0]) # if LCD >= 4
dymax_translate15_special = np.array([5.5, 2 / math.sqrt(3), 0]) # if LCD >= 3

dymax_ocean_translate = np.array([ [5.0, 5 / (2 * math.sqrt(3)), 300],
[0.5, 4 / (2 * math.sqrt(3)), 0],
[1.0, 5 / (2 * math.sqrt(3)), 60],
[1.0, 7 / (2 * math.sqrt(3)), 120],
[4.5, 8 / (2 * math.sqrt(3)), 300],
[4.5, 4 / (2 * math.sqrt(3)), 0],
[4.0, 1 / (2 * math.sqrt(3)), 240],
[1.0, 1 / (2 * math.sqrt(3)), 120],
[1.5, 2 / (2 * math.sqrt(3)), 60],
[1.5, 4 / (2 * math.sqrt(3)), 120],
[2.0, 5 / (2 * math.sqrt(3)), 60],
[2.0, 7 / (2 * math.sqrt(3)), 120],
[3.0, 7 / (2 * math.sqrt(3)), 0],
[4.0, 7 / (2 * math.sqrt(3)), 240],
[4.0, 5 / (2 * math.sqrt(3)), 300],
[3.5, 2 / (2 * math.sqrt(3)), 300],
[2.5, 2 / (2 * math.sqrt(3)), 180],
[2.5, 4 / (2 * math.sqrt(3)), 120],
[3.0, 5 / (2 * math.sqrt(3)), 300],
[3.5, 4 / (2 * math.sqrt(3)), 0]])
dymax_ocean_translate08_special = np.array([2.0, 1 / (2 * math.sqrt(3)), 120]) # if LCD == 2 or LCD == 3

### Optimizations
garc = 2 * math.asin(math.sqrt( (5 - math.sqrt(5)) / 10))
Expand Down
32 changes: 21 additions & 11 deletions dymax/convert.py
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Expand Up @@ -27,7 +27,7 @@ def euclidean(vec_a, vec_b):

### Dymax Conversion Main Routine
@lru_cache(maxsize=2**12)
def lonlat2dymax(lon, lat, getlcd=False):
def lonlat2dymax(lon, lat, getlcd=False, unfolding=constants.Unfolding.LAND):
'''
Lon Lat 2 Dymax XY

Expand Down Expand Up @@ -71,7 +71,7 @@ def lonlat2dymax(lon, lat, getlcd=False):
tri, lcd = fuller_triangle(XYZ)

# Determine the corresponding Fuller map plane(x, y) point
x_pos, y_pos = dymax_point(tri, lcd, XYZ)
x_pos, y_pos = dymax_point(tri, lcd, XYZ, unfolding)

if getlcd: return x_pos, y_pos, lcd
else: return x_pos, y_pos
Expand Down Expand Up @@ -102,7 +102,7 @@ def vert2dymax(vert, vertset, push=.9999):
x_pos, y_pos = dymax_point(tri, hlcd, XYZ)
return x_pos, y_pos

def face2dymax(face_idx, push=.9999, atomic=False):
def face2dymax(face_idx, push=.9999, atomic=False, unfolding=constants.Unfolding.LAND):
'''
Convert Icosahedron Face to (4) XY Vertices

Expand Down Expand Up @@ -141,13 +141,13 @@ def face2dymax(face_idx, push=.9999, atomic=False):
XYZ = np.mean([up, down], axis=0)
XYZ = XYZ * push + constants.XYZcenters[face_idx] * (1-push)
tri, hlcd = fuller_triangle(XYZ)
points[jdx] = dymax_point(tri, hlcd, XYZ)
points[jdx] = dymax_point(tri, hlcd, XYZ, unfolding)
else:
points = np.zeros((3+1, 2))
for jdx in range(3):
XYZ = constants.vertices[constants.vert_indices[face_idx, jdx]] * push + constants.XYZcenters[face_idx] * (1-push)
tri, hlcd = fuller_triangle(XYZ)
points[jdx] = dymax_point(tri, hlcd, XYZ)
points[jdx] = dymax_point(tri, hlcd, XYZ, unfolding)

points[-1] = points[0] # Loop Back to Start
return points
Expand Down Expand Up @@ -246,7 +246,7 @@ def fuller_triangle(XYZ):
elif h_dist3 <= h_dist2 <= h_dist1: h_lcd = 3
return h_tri, h_lcd

def dymax_point(tri, lcd, XYZ):
def dymax_point(tri, lcd, XYZ, unfolding=constants.Unfolding.LAND):
'''
In order to rotate the given point into the template spherical
triangle, we need the spherical polar coordinates of the center
Expand All @@ -261,6 +261,8 @@ def dymax_point(tri, lcd, XYZ):
Dymaxion sub-triangle where we want to be.
XYZ : tuple of floats
Pseudo-ECEF coordinate that will be projected to dymaxion.
unfolding: enum
Either LAND, OCEAN or NET.

Returns
-------
Expand Down Expand Up @@ -320,10 +322,18 @@ def dymax_point(tri, lcd, XYZ):

### Move and Rotate as Appropriate
# You can disable the special translations for uniform triangles
if tri == 8 and lcd < 4:
xtranslate, ytranslate, rotation = constants.dymax_translate08_special
elif tri == 15 and lcd < 3:
xtranslate, ytranslate, rotation = constants.dymax_translate15_special
if unfolding == constants.Unfolding.LAND:
if tri == 8 and lcd >= 4:
xtranslate, ytranslate, rotation = constants.dymax_translate08_special
elif tri == 15 and lcd >= 3:
xtranslate, ytranslate, rotation = constants.dymax_translate15_special
else:
xtranslate, ytranslate, rotation = constants.dymax_translate[tri]
elif unfolding == constants.Unfolding.OCEAN:
if tri == 8 and (lcd == 2 or lcd == 3):
xtranslate, ytranslate, rotation = constants.dymax_ocean_translate08_special
else:
xtranslate, ytranslate, rotation = constants.dymax_ocean_translate[tri]
else:
xtranslate, ytranslate, rotation = constants.dymax_translate[tri]

Expand Down Expand Up @@ -437,4 +447,4 @@ def benchmark(verbose=True):
dymax_centers = np.zeros((constants.facecount, 2))
for fdx in range(constants.facecount):
tri, hlcd = fuller_triangle(constants.XYZcenters[fdx])
dymax_centers[fdx] = dymax_point(tri, hlcd, constants.XYZcenters[fdx])
dymax_centers[fdx] = dymax_point(tri, hlcd, constants.XYZcenters[fdx], constants.Unfolding.LAND)
8 changes: 5 additions & 3 deletions dymax/examples.py
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Expand Up @@ -247,7 +247,7 @@ def plot_coastline_vectors(verbose=True, save=False, show=True, dpi=300, resolut
plt.show()
else: plt.close()

def convert_rectimage_2_dymaximage(inFilename, outFilename, verbose=True, scale=300, speedup=1, save=False, show=True):
def convert_rectimage_2_dymaximage(inFilename, outFilename, verbose=True, scale=300, speedup=1, unfolding=constants.Unfolding.LAND, save=False, show=True):
'''
Convert rectilinear image to dymax projection image.

Expand Down Expand Up @@ -282,7 +282,7 @@ def convert_rectimage_2_dymaximage(inFilename, outFilename, verbose=True, scale=
stdout.flush() # I would add flush=True to print, but thats only in python3.3+
for j, lat in enumerate(np.linspace(90, -90, ysize/speedup, endpoint=True)):
j *= speedup
newx, newy = convert.lonlat2dymax(lon, lat)
newx, newy = convert.lonlat2dymax(lon, lat, unfolding=unfolding)
newx = int(newx*scale) - 1
newy = int(newy*scale)
try: dymaximg.putpixel((newx, newy), pix[i, j])
Expand Down Expand Up @@ -361,7 +361,7 @@ def plot_face_hq(resolution='i', save=False, show=True, verbose=True, dpi=300):
# Draw final figure bits
plt.axis('off')
plt.gca().set_aspect('equal')
if save: plt.savefig('dymax_earthmeridianstriangles.png', bbox_inches='tight', dpi=dpi, transparent=True, pad_inches=0)
if save: plt.savefig('dymax_face.png', bbox_inches='tight', dpi=dpi, transparent=True, pad_inches=0)
if show:
plt.tight_layout()
plt.show()
Expand All @@ -381,7 +381,9 @@ def run_examples(resolution='c', save=False, show=True, verbose=True):
plot_coastline_vectors(resolution=resolution, save=save, show=show)
plot_face_hq(resolution=resolution, save=save, show=show)
convert_rectimage_2_dymaximage(io.PKG_DATA+'bmng.jpg', 'dymax_bmng.png', save=save, show=show)
convert_rectimage_2_dymaximage(io.PKG_DATA+'bmng.jpg', 'dymax_net_bmng.png', unfolding=constants.Unfolding.NET, save=save, show=show)
convert_rectimage_2_dymaximage(io.PKG_DATA+'etopo1.jpg', 'dymax_etopo1.png', save=save, show=show)
convert_rectimage_2_dymaximage(io.PKG_DATA+'etopo1.jpg', 'dymax_ocean_etopo1.png', unfolding=constants.Unfolding.OCEAN, save=save, show=show)

if __name__ == '__main__':
run_examples()
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