Cone tracing

Cone tracing and beam tracing are a derivative of the ray tracing algorithm that replaces rays, which have no thickness, with thick rays.

This is done for two reasons:

The energy reaching the pixel comes from the whole solid angle by which the eyes see the pixel in the scene, not from its central sample. This yields the key notion of pixel footprint on surfaces or in the texture space, which is the back projection of the pixel on the scene.

The description above corresponds to the pinhole camera simplified optics classically used in computer graphics. Note that this approach can also represent a lens-based camera and thus depth of field effects, using a cone whose cross-section decreases from the lens size to zero at the focal plane, and then increases.

Moreover, a real optical system does not focus on exact points because of diffraction and imperfections. This can be modeled as a point spread function (PSF) weighted within a solid angle larger than the pixel.

Ray-tracing images suffer strong aliasing because the "projected geometric signal" has very high frequencies exceeding the Nyquist-Shannon maximal frequency that can be represented using the pixel sampling rate, so that the input signal has to be low-pass filtered - i.e., integrated over a solid angle around the pixel center.

Note that contrary to intuition, the filter should not be the pixel footprint since a box filter has poor spectral properties. Conversely, the ideal sinc function is not practical, having infinite support and possibly negative values. A Gaussian or a Lanczos filter are considered good compromises.

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