Texture mapping is the addition of a separately defined texture or pattern to a surface (e.g. wall-paper on wall). This does not affect the "smoothness" of a surface but only changes colors. The process involves the mathematical mapping of the texture from one domain to another. All of the methods require the knowledge of the 3D World Device Coordinates (WDC), i.e., the X, Y, Z value of the surface to be texture mapped. In ray tracing, this would be the object - ray intersection point. In scan-line graphics it is more complicated since the objects are converted to Physical Device Coordinates and then scan-converted.
We can categorize texture mapping by the dimensionality involved as follows:
One-Dimensional texture domain
Two-Dimensional texture domain
Three-Dimensional texture domain
A Pixar Shutterbug image with texture mapping. Notice that the surface still appears smooth.
Reflection mapping is a method of simulating a global illumination model in scan line rendering. First the scene is rendered from the view point of the surface to be mapped. Next, this image is turned into a texture map, which is then mapped to the surface. Note that this only does a "one bounce" reflection, whereas true global illumination algorithms, such as ray tracing, will do multiple bounces.
Here is a Pixar Shutterbug image with reflection mapping.
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