I currently can't sphere/cylinder map this type of chart/cuts

[ggaliens]

I am going to make it work better.

First I will try this ... combined with making the UV coordinates like the ones you showed at far right of your last images. This has been the plan that I talked about ...

Code:

Define the texture wrapping parameters. This will control what happens when a texture coordinate greater than 1.0 or less than 0.0 is encountered:

glTexParameteri( GL_TEXTURE_2D, GL_TEXTURE_WRAP_S,wrap);  
glTexParameteri( GL_TEXTURE_2D, GL_TEXTURE_WRAP_T,wrap);  

where wrap is:
GL_REPEAT : specifies that this pattern will repeat (i.e., wrap-around) if transformed texture coordinates less than 0.0 or greater than 1.0 are encountered.

GL_CLAMP : specifies that the pattern will “stick” to the value at 0.0 or 1.0.