Equal area dome subddivisions

[Christopher Jones]

These domes are recursively subdivided so that every spherical triangle has the same area.

Except at the icosahedral triangle edges, the arcs joining vertices are small circles.

They are moderately flat at the equator.

https://3dviewer.net/#model=https://chrisjones.id.au/Spherical%20Tessellations/equal_area_icosahedral_dome_top15_level2_opaque_sphere.glb

https://3dviewer.net/#model=https://chrisjones.id.au/Spherical%20Tessellations/equal_area_icosahedral_dome_top15_level3_opaque_sphere.glb

https://3dviewer.net/#model=https://chrisjones.id.au/Spherical%20Tessellations/equal_area_icosahedral_dome_top15_level4_opaque_sphere.glb

[Joël LeBlanc-Lavoie]

That's interesting. How similar are the strut lengths? Can you share the algorithm?

[Christopher Jones]

Joël

The Python script is at https://chrisjones.id.au/Spherical%20Tessellations/equal_area_recursive_icosahedral_dome_top15_opaque_sphere.py

This subdivision is into spherical triangles whose edges are arcs on the sphere, so strut lengths are not really relevant.

If the spherical triangle vertices were joined by struts, the resulting plane triangles would no longer be (exactly) equal area.

Chris

[Christopher Jones]

Sorry these links keep going to the wrong place, try

https://chrisjones.id.au/Spherical%20Tessellations/equal_area_recursive_icosahedral_dome_top15_opaque_sphere.py