Abstract: Systems and methods are provided to perform constrained BSDF sampling in relation to various algorithms, and specifically in relation to ray tracing algorithms. In some embodiments, a method is provided to generate samples by: determining a spherical polygon on a unit hemisphere; determining, on a unit circle, a projected area corresponding to the spherical polygon on the unit hemisphere; determining a parameterization of the projected area of the spherical polygon on the unit circle; generating samples in the projected area based on the parameterization; and generating samples in the spherical polygon. The unit circle is abase of the unit hemisphere, and the projection of the projected area is along a vector perpendicular to the unit circle. The generated samples in the spherical polygon correspond to the samples in the projected area. The method may further include evaluating a rendering equation based on the generated samples in the spherical polygon.

Abstract: Systems and methods relate to the determination of accurate motion vectors, for rendering situations such as a noisy Monte Carlo integration where image object surfaces are at least partially translucent. To optimize the search for “real world” positions, this invention defines the background as first path vertices visible through multiple layers of refractive interfaces. To find matching world positions, the background is treated as a single layer morphing in a chaotic way, permitting the optimized algorithm to be executed only once. Further improving performance over the prior linear gradient descent, the present techniques can apply a cross function and numerical optimization, such as Newton's quadratic target or other convergence function, to locate pixels via a vector angle minimization. Determined motion vectors can then serve as input for services including image denoising.

Abstract: Systems and methods relate to the determination of accurate motion vectors, for rendering situations such as a noisy Monte Carlo integration where image object surfaces are at least partially translucent. To optimize the search for “real world” positions, this invention defines the background as first path vertices visible through multiple layers of refractive interfaces. To find matching world positions, the background is treated as a single layer morphing in a chaotic way, permitting the optimized algorithm to be executed only once. Further improving performance over the prior linear gradient descent, the present techniques can apply a cross function and numerical optimization, such as Newton's quadratic target or other convergence function, to locate pixels via a vector angle minimization. Determined motion vectors can then serve as input for services including image denoising.

Abstract: Systems and methods are provided to perform constrained BSDF sampling in relation to various algorithms, and specifically in relation to ray tracing algorithms. In some embodiments, a method is provided to generate samples by: determining a spherical polygon on a unit hemisphere; determining, on a unit circle, a projected area corresponding to the spherical polygon on the unit hemisphere; determining a parameterization of the projected area of the spherical polygon on the unit circle; generating samples in the projected area based on the parameterization; and generating samples in the spherical polygon. The unit circle is abase of the unit hemisphere, and the projection of the projected area is along a vector perpendicular to the unit circle. The generated samples in the spherical polygon correspond to the samples in the projected area. The method may further include evaluating a rendering equation based on the generated samples in the spherical polygon.

Abstract: Systems and methods for improving quality of rendered images. Temporal accumulation using jittered motion vectors may be performed in intermediate passes.