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Transfer functions are central to direct volume rendering because they, literally, make the data visible. Its the transfer function which maps from the scalar space of data values to optical properties like color and opacity. We'll be using this CT scan of a human tooth as a running example. After we map the data values through the transfer function in order to get these colors and opacities, we can feed them into the usual shading and compositing operations to produce a final rendering.

We call this a one-dimensional transfer function to emphasize the fact that the domain of the function is a one-dimensional space of scalar data value. Unfortunately ...