Methods and systems of joint path importance sampling

A joint path importance sampling rendering method for constructing light paths through participating media like fog or smoke.

Methods and systems of joint path importance sampling are provided to construct light paths in participating media. The product of anisotropic phase functions and geometric terms across a sequence of path vertices are considered. A connection subpath is determined to join a light source subpath with a light receiver subpath with multiple intermediate vertices while considering the product of phase functions and geometry terms. A joint probability density function (“PDF”) may be factorized unidirectional or bidirectional. The joint PDF may be factorized into a product of multiple conditional PDFs, each of which corresponds to a sampling routine. Analytic importance sampling may be performed for isotropic scattering, whereas tabulated importance sampling may be performed for anisotropic scattering.

BRIEF DESCRIPTION OF THE DRAWINGS(1) The present application, in accordance with one or more various embodiments, is described in detail with reference to the following figures. The drawings are provided for purposes of illustration only and merely depict typical or example embodiments of the application. These drawings are provided to facilitate the reader's understanding of the application and shallnot be considered limiting of the breadth, scope, or applicability of the application. Itshould be noted that for clarity and ease of illustration these drawings are not necessarily made to scale.(2) FIG. 1 illustrates an exemplary configuration for joint path importance sampling.(3) FIG. 2 is a flow diagram illustrating an exemplary method 100 of joint path importance sampling.(4) FIG. 3A illustrates an exemplary process of unidirectional factorization of the joint PDF.(5) FIG. 3B illustrates that an exemplary geometric configuration for sampling a distance for unidirectional factorization of the joint PDF for sampling the distance t.sub.dc 313.(6) FIG. 3C illustrates that an exemplary geometric configuration for sampling a direction for unidirectional factorization of the joint PDF for sampling the direction ω.sub.cb 314.(7) FIG. 3D illustrates that an exemplary geometric configuration for sampling a distance for unidirectional factorization of the joint PDF for sampling the distance t.sub.cb 312.(8) FIG. 4 illustrates an exemplary process of bidirectional factorization of th