David Templin's Blog

Parallel Metropolis Light Transport

In this post, I will describe an algorithm which I designed which I call "Parallel Metropolis Light Transport" (PMLT) which is a variant of Metropolis Light Transport which is amenable to parallelization on GPUs. A detailed overview of Metropolis Light Transport is available in the following post: Metropolis

Computer Science

Monads in Computer Science

This post explores the concept of a monad in computer science and its expression in various programming languages.

Mathematics

The Euclidean Metric in Spherical Coordinates

This post discusses the derivation of the expression for the Euclidean metric in spherical coordinates.

Mathematics

Universal Algebra

This post contains a collection of notes on Universal Algebra.

Artificial Intelligence

Large Language Models

This post provides a semi-technical overview of large language models (LLMs), in particular, the prototypical GPT models.

Mathematics

General Recursive Functions

This post motivates the definition of general recursive functions by demonstrating one method of deriving this definition.

Physics

The Einstein-Hilbert Action

This post describes how to derive the field equation of General Relativity from the Einstein-HIlbert action.

Differential Geometry

Covariant Derivatives of Tensor Fields

This post discusses covariant derivatives of tensor fields.

Mathematics

Curvature Tensors

This post discusses the concept of curvature in manifolds and various tensor fields which measure this curvature.

Mathematics

Covariant Derivatives

This post discusses the concept of a covariant derivative on a smooth manifold.

Mathematics

Derivatives on Normed Vector Spaces

This post explores the conception of derivatives as the best local linear approximation of a continuous function in the general setting of normed vector spaces, and generalizes classical results to spaces of functionals.

Differential Geometry

Smooth Manifolds

This post examines the basic properties of smooth manifolds and gives a few detailed examples.

Computer Science

Differentiable Programming

This post explains the basic idea of differentiable programming, providing sample code, and relating the concept to ideas from differential geometry.

Computer Graphics

Solid Angle

This post examines the concept of solid angle, the three-dimensional generalization of planar angle, and derives related mathematical formulas from scratch.

Mathematics

Parallel Metropolis-Hastings

This post examines a particular method for parallelizing the Metropolis-Hastings algorithm.

Computer Science

Counter-Based Pseudo-Random Number Generators on the GPU

This post examines the concept of a counter-based pseudo-random number generator (CBRNG), and the Squares algorithm in particular.

Computer Science

Metropolis Light Transport

This post offers a detailed explanation of Metropolis Light Transport in particular and path tracing in general, providing the relevant theoretical background.

Mathematics

Metric Tensor Fields

This post explores the concept of metric tensor fields on smooth manifolds.

Mathematics

Differential Forms

This post explores the basic idea of differential forms.

Mathematics

Exterior Algebra

This post examines the concept of the exterior algebra of a vector space.

Mathematics

Differentials

This post examines the idea of the differential of a function, relating it to concepts from differential geometry.

Mathematics

Notes on Line and Surface Integrals

This post explores line and surface integrals, relating the classical formulations to concepts from differential geometry such as the pullback of differential forms and volume forms.

Mathematics

Tensors

This post explores the mathematical concept of a tensor.

Mathematics

Cotangent Spaces

This post explores the concept of the cotangent space at a point on a smooth manifold.

Mathematics

Vector Fields

This post examines the concept of a vector field on a smooth manifold.