Physical Sciences and Mathematics Commons^™

A Bidirectional Formulation For Walk On Spheres, Yang Qi

Dartmouth College Master’s Theses

Poisson’s equations and Laplace’s equations are important linear partial differential equations (PDEs)
widely used in many applications. Conventional methods for solving PDEs numerically often need to
discretize the space first, making them less efficient for complex shapes. The random walk on spheres
method (WoS) is a grid-free Monte-Carlo method for solving PDEs that does not need to discrete the
space. We draw analogies between WoS and classical rendering algorithms, and find that the WoS
algorithm is conceptually identical to forward path tracing.
We show that solving the Poisson’s equation is equivalent to solving the Green’s function for every
pair of …

Correlations And Reuse For Fast And Accurate Physically Based Light Transport, Benedikt Bitterli

Dartmouth College Ph.D Dissertations

Light transport is the study of the transfer of light between emitters, surfaces, media and sensors. Fast simulations of light transport play a pivotal role in photo-realistic image synthesis, and find many applications today, including predictive manufacturing, machine learning, scientific visualization and the movie industry. In order to accurately reproduce the appearance of real scenes, light transport must closely approximate the physical laws governing the flow of light. Physically based rendering is a set of principles for codifying these laws into a mathematical model, and is the predominant rendering methodology today.

The representational power of this model is limited to …

Temporally Sliced Photon Primitives For Volumetric Time-Of-Flight Rendering, Yang Liu

Dartmouth College Master’s Theses

Traditional steady-state rendering assumes that the light transport has already reached equilibrium. In contrast, time-of-flight rendering removes this assumption and recovers the pattern of light at extremely high temporal resolutions. This novel rendering modality not only provides a way to visualize the propagation of light, but can also empower the advances in time-of-flight imaging and its corresponding applications.

Building on previous work in steady-state volumetric rendering, this thesis introduces a novel framework for deriving new Monte Carlo estimators for solving the time-of-flight rendering problem in participating media. Conceptually, our method starts with any steady-state photon primitive, like a photon plane …

Physically Based Rendering Techniques To Visualize Thin-Film Smoothed Particle Hydrodynamics Fluid Simulations, Aditya H. Prasad

Dartmouth College Undergraduate Theses

This thesis introduces a methodology and workflow I developed to visualize smoothed hydrodynamic particle based simulations for the research paper ’Thin-Film Smoothed Particle Hydrodynamics Fluid’ (2021), that I co-authored. I introduce a physically based rendering model which allows point cloud simulation data representing thin film fluids and bubbles to be rendered in a photorealistic manner. This includes simulating the optic phenomenon of thin-film interference and rendering the resulting iridescent patterns. The key to the model lies in the implementation of a physically based surface shader that accounts for the interference of infinitely many internally reflected rays in its bidirectional surface …