Abstract

This thesis contains two distinct manuscripts both focused on real-time rendering research; an abstract for each is provided: 1. We survey methods for mapping normal vectors to a transformed surface with emphasis on the cofactor matrix form. We demonstrate that the cofactor matrix uniquely and correctly supports matrix transformations that are rank deficient or have negative determinants, while also generalizing to operations such as rotation, scaling, translation, and shearing. We derive and demonstrate the completeness of this new convention in contrast to other approaches, while also establishing its computational efficiency benefits. 2. We present SDF volumes as an efficient datastructure for calculating light transport through refractive media in real-time. Our contribution is simple to precompute, low-budget in memory, and well-suited to the chaotic paths of light inside complex refractive objects. Lending itself well to existing techniques to realize refractive and caustic effects, SDF volumes supplement the existing texture information supporting conventional polygon meshes. Techniques to amortize the cost of ray marching and relevant algorithms for realizing such effects are provided and justified.

Degree

MS

College and Department

Computational, Mathematical, and Physical Sciences; Computer Science

Rights

https://lib.byu.edu/about/copyright/

Date Submitted

2024-08-15

Document Type

Thesis

Keywords

cofactor matrix, normal transformations, inverse transpose, adjugate transpose, signed distance fields, SDF, caustics, real-time, rasterization, Ray Marching

Language

english

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