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____________________________________________________________________________________2D map coordinates
This is similar to the geographic information we use every day. We specify locations of cities by longitude and lattitude values using the map coordinates u and v along the two surface directions. For a cube this is clear: a cube consists of six 2D faces where u corresponds to the horizontal edge and v corresponds to the vertical edge of the individual faces. For a sphere, u corresponds to the longitude and v to the latitude.
The texture coordinates can be used to write more advanced map expressions, as will be described below. Other primitives have surface coordinates too: cylinders and cones can be measured with a height and an angle around their axes. Freeform patches have an inherent 2D coordinate system; they are defined using a distance value from their origin in two dimensions.
Comment
Polygon objects do not have an inherent surface coordinate system. A
direct mapping is therefore not possible with imported polygon objects, in which
case projection mapping must be used.
3D map coordinates systems
3D map coordinates depend on a position inside the "material cube" that is
defined by the map function. As we are not describing coordinates glued to a
surface, here we have to use real 3D coordinates x, y and z. The texture of the
surface of the object that intersects with this "material cube" depends on the
position of the object relative to the origin of the map.
