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Volume Rendering Integral
Given functions for color and opacity (where 0 = transparent and = opaque), the color for a ray is given by




Discretization



: opacity (0 = transparent, = opaque)
: normalized transparency (0 = opaque, 1 = transparent)
: normalized opacity (0 = transparent, 1 = opaque)



We only want opaque pixels to emit color:


Volume Rendering Integral
Given functions for color and opacity (where 0 = transparent and = opaque), the color for a ray is given by




Discretization



: opacity (0 = transparent, = opaque)
: normalized transparency (0 = opaque, 1 = transparent)
: normalized opacity (0 = transparent, 1 = opaque)



We only want opaque pixels to emit color:


Back-to-Front Evaluation
Start:

Update:


Front-to-Back Evaluation
Start:


Update:



Early abort if