Efficient Physically Based Rendering with Analytic and Neural Approximations

Aakash KT

Abstract

Path tracing is ubiquitous for photorealistic rendering of various real-world appearances. It follows the principles of light transport adapted from physics, which describe light propagation as a set of integral equations. These equations are stochastically evaluated by tracing light rays in virtual scenes. Such stochastic evaluations with ray-tracing form the bulk of the path tracing algorithm, which is widely used in the industry.

Stochastic evaluations in path tracing converge to the correct answer in time that is inversely proportional to the square root of the number of iterations. This coupled with the fact that the underlying integrals are often complex and high dimensional results in large compute complexity. Research efforts have thus largely focused on accelerating path tracing by improving the stochastic sampling processes. However, it is interesting to look at efficient analytic approximations by making reasonable assumptions on the nature of these light transport integrals. Such analytic methods have the potential to achieve zero variance at the outset. Practically, they are often used in conjunction with stochastic methods thereby achieving lower variance than the fully stochastic counterparts.

The primary focus of this thesis is to develop new (semi-)analytic methods and improve existing ones to accelerate direct lighting computations in path tracing. We base our research on the theory of Linearly Transformed Cosines (LTC) applied for direct lighting from area lights. The LTC method produces plausible renderings by building on the principles of light transport from the ground up and has proved useful for tasks other than real-time rendering We make the following three contributions that either build on LTCs or improve it.

We first explore fully-analytic direct lighting for arbitrarily shaped area lights, built on LTCs at the core. Due to assumptions of the LTC method, it can only handle polygonal area lights. Furthermore, rendering shadows with LTCs require stochastic evaluations - our contribution here relaxes these assumptions, enabling fully-analytic direct lighting with shadows from an arbitrary shaped area light. We show that our method achieves plausible and noise-free renderings compared to semi-analytic LTCs and ground truth ray-tracing, given equal compute budget.

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