Backface Culling for Motion Blur and Depth of Field

For triangles with linear vertex motion, common practice is to backface cull a triangle if it is backfacing at both the start and end of the motion. However, this is not conservative. We derive conservative tests that guarantee that a moving triangle is backfacing over an entire time interval and over the area of a lens. In addition, we present tests for the special cases of only motion blur and only depth of field. Our techniques apply to real-time and offline rendering, and to both stochastic point sampling and analytical visibility methods. The rendering errors introduced by the previous technique can easily be detected for large defocus blur, but in the majority of cases, the errors introduced are hard to detect. We conclude that our tests are needed if one needs guaranteed artifact-free images. Finally, as a side result, we derive time-continuous Bézier edge equations.