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UV mapping is a 3D modeling process of making a 2D image representing a 3D model. The map transforms the 3D object onto an image known as a texture. In contrast to "X", "Y" and "Z", which are the coordinates for the original 3D object in the modeling space, "U" and "V" are the coordinates of the transformed object. This creates the effect of painting the image onto the surface of the 3D object. To put it simply, UV texturing permits polygons that make up a 3D object to be painted with color from an image. The image is called a UV texture map, but it's just an ordinary image. The UV mapping process involves assigning pixels in the image to surface mappings on the polygon, usually done by "programmatically" copying a triangle shaped piece of the image map and pasting it onto a triangle on the object. UV is the alternative to XY, it only maps into a texture space than into the geometric space of the object. But the rendering computation uses the UV texture coordinates to determine how to paint the three dimensional surface. The examples given here are all of procedural geometry, no actual polygonal examples are given, which is a shame because it is more understandable with polygonal UV mapping . In the example to the right, a sphere is given a checkered texture, first without and then with UV mapping. Without UV mapping, the checkers tile XYZ space and the sphere is carved out of them. With UV mapping, the checkers tile UV space and points on the sphere map to this space according to their latitude and longitude.
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