Do algorithms that automatically generate texture maps generally try to preserve the relative areas of the triangles in the map, or do they aim closer to giving each triangle a relatively similar area of the texture map? I would think that the more detailed areas of the mesh would have more complex textures but also smaller triangles, so I'm not quite sure how much "extra" influence we would want to give to smaller triangles.
Kent
There are multiple ways to perform UV unwrapping. According to this very informative Wikipedia page on the subject: https://en.wikipedia.org/wiki/UV_mapping, one way to map a triangle mesh to UV space is to simply unfold it at the seams. For models such as spheres that have a nicely defined surface, we could use a projection such as the equirectangular projection (https://en.wikipedia.org/wiki/Equirectangular_projection), which is often used to project the globe onto a rectangle. Although this projection is not perfect, it does create a very simple relationship between the coordinates on the sphere and their corresponding coordinates on the rectangle, so it is very practical to use!
Gyro
If the object is really really really big, is the texture gonna lose a lot of data when storing every pixel value? Seems like to compress everything into [0,1]^2 is not always stable?
Do algorithms that automatically generate texture maps generally try to preserve the relative areas of the triangles in the map, or do they aim closer to giving each triangle a relatively similar area of the texture map? I would think that the more detailed areas of the mesh would have more complex textures but also smaller triangles, so I'm not quite sure how much "extra" influence we would want to give to smaller triangles.
There are multiple ways to perform UV unwrapping. According to this very informative Wikipedia page on the subject: https://en.wikipedia.org/wiki/UV_mapping, one way to map a triangle mesh to UV space is to simply unfold it at the seams. For models such as spheres that have a nicely defined surface, we could use a projection such as the equirectangular projection (https://en.wikipedia.org/wiki/Equirectangular_projection), which is often used to project the globe onto a rectangle. Although this projection is not perfect, it does create a very simple relationship between the coordinates on the sphere and their corresponding coordinates on the rectangle, so it is very practical to use!
If the object is really really really big, is the texture gonna lose a lot of data when storing every pixel value? Seems like to compress everything into [0,1]^2 is not always stable?