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Moving on to the second from the left icon on the UV mapping: Spherical mapping. As the name clearly indicates, this mapping type is ideal for plotting a 2D image across the surface of a round object. As opposed to the linear mapping, there will be no indication as to what direction is right-side up when you apply the mapping wireframe to a sphere. Let's try this:
1.) Go create a black square with a white circle in the center and a black "8" in the center of the white circle.
2.) Create a sphere in the scene and get rid of the cube.
3.) Load the 8 ball image as the texture and load the wireframe from the UV mapping panel around the sphere in sphere mapping mode (click on the sphere icon on the UV panel).
You'll see a sphere wireframe, a little larger than the sphere (this is okay, it's natural, don't panic at the size), and in orange, there is a half-circle making up the wireframe. The trick is to get the orange "slice" to be parallel to the front of your view, and to the right of the circle. And to do this, you use the Object rotate tool again. See figure 44. The right side of the sphere is where an image starts mapping. If you were to look overhead at the scene right now, the orange slice...the origin point for the mapping, would be at 3 o'clock.
Finally, what you want to do is to map the 8-ball design to the sphere twice vertically and once horizontally. Why? Because the sucker wraps around the sphere for both the front and back side. You have your choice here in mapping spheres on your own: if you want an 8-ball pattern for example, to only map once on the front face, you then create an image map where the "8" design is skinny, precisely half as wide as it should be, and map it at one revolution around the sphere, or do what I've explained above. No one is going to see the second "8" from the back unless you animate the sphere.
This should give you already some idea of the distortion in 3D space an image suffers when you map it to a curved surface. The reason why no artifacting goes on (or very little visible artifacting) is because trueSpace has anti-aliasing capability: it slightly blurs (averages) the pixels in the image so they more "comfortably" stretch and pinch along 3D curved surfaces.