https://github.com/hcschuetz/sphere-texturing

texture layouts for spheres
https://github.com/hcschuetz/sphere-texturing

geometry icosphere octasphere sphere texture-generation texture-mapping

Last synced: 3 months ago
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texture layouts for spheres

• Host: GitHub
• URL: https://github.com/hcschuetz/sphere-texturing
• Owner: hcschuetz
• License: mit
• Created: 2024-05-15T15:41:02.000Z (about 1 year ago)
• Default Branch: main
• Last Pushed: 2024-08-10T00:33:31.000Z (10 months ago)
• Last Synced: 2024-08-10T23:24:45.319Z (10 months ago)
• Topics: geometry, icosphere, octasphere, sphere, texture-generation, texture-mapping
• Language: TypeScript
• Homepage: https://hcschuetz.github.io/sphere-texturing/map-transformations/dist/
• Size: 16.2 MB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE.txt

Awesome Lists containing this project

README

        
Sub-Projects

------------

Sub-projects in this repository:

- Experiments with texture mappings

  ([source](./earth/), [web app](https://hcschuetz.github.io/sphere-texturing/earth/dist/))

- A presentation on map/texture transformations

  ([source](./map-transformations/),

  [web app](https://hcschuetz.github.io/sphere-texturing/map-transformations/dist/))

Texture Layouts For Spheres

===========================

The most common way to render a sphere is based on the latitude/longitude grid

as it is used for the earth:

Select two opposite points on the sphere as the "poles",

a bunch of equidistant "meridians", and a bunch of equidistant "parallels".

Introduce a vertex at each intersection of a meridian and a parallel

and connect neighboring vertices.

This divides the sphere into a set of quadrangles.

Dividing each quadrangle along one of its diagonals

gives a triangulation of the sphere.

The natural texture for such a "lat/long sphere" is a map with a

[equirectangular projection](https://en.wikipedia.org/wiki/Equirectangular_projection).

This is easy to implement and good enough for many applications.

But while the distance between meridians gets smaller and smaller near the poles

on the sphere,

the meridians have a constant distance on the map.

This leads to some drawbacks:

- Equirectangular maps are heavily distorted.

- Texture memory is wasted.

- Half of the triangles around the poles are degenerated on the sphere

  and thus the corresponding parts of the texture/map are not rendered.

To avoid these drawbacks

this project investigates texture mappings based on octaspheres and icospheres.

See the README files of the subprojects for more details.

Relation to Paper Maps

----------------------

Projections from a sphere to a plane

are not only needed for textures in computer graphics,

but also for traditional paper maps of the Earth.

There are several desirable properties of such a projection such as

the accurate representation of distances, areas, angles and compass directions.

It is not possible to achieve all these goals in a single projection.

Thus over the centuries many different projections have been developed,

each based on some choice or compromise between the goals according to some use case.

(And actually the simplicity of a mapping is another aspect that might

be considered in the trade-off.)

From the vast amount of resources discussing sphere-to-plane projections

here are just a few:

- A nice [overview video](https://www.youtube.com/watch?v=bpp0xCknQAQ)

  on map projections with some math background.

- [Gene Keyes' discussion of map projections](https://www.genekeyes.com/FULLER/BF-1-intro.html)

  is interesting here for two reasons:

  - It discusses projections based on an octahedron and an icosahedron.

    (See appendix 2 of [part 2](https://www.genekeyes.com/FULLER/BF-2-1943.html)

    for an icosahedral map similar to ours.)

  - It deals with paper maps that are actually folded to 3D objects.

- [This video](https://www.youtube.com/watch?v=vfOcYUWfVqE) (mentioned by Keyes)

  shows a map unfolding somewhat similar to ours.

Notice the following differences between mappings to paper and mappings to a texture:

- In contrast to paper maps,

  textures should be easily applicable to a triangulated sphere.

- For projections between a sphere and a texture

  it is a bit less important to minimize various kinds of distortions

  if the distortions introduced by the projection

  will be reversed when the texture is applied to a sphere.

  But while the user will not see a distorted surface,

  mapping distortions will cause the available level of detail to vary across the sphere.

  And typically we want to limit this variation.

- Maps try to be contiguous (at least on the continents) so that nearby points

  on the earth will also be nearby on the map.

  For textures this is not important,

  provided we have a good "sewing" mechanism.

  This allows us to use more cuts in the mapping to improve other aspects

  such as reducing distortion and arranging the map in a memory-efficient way.

Thus the trade-offs differ between paper maps and textures and may lead

to different solutions.

For example in our octahedral and icosahedral projections we save memory

by moving triangles from the south-pole region to the gaps between

triangles in the north-pole region.

Such a representation would be confusing on a map directly viewed by a user.