**Most Recent Posts:**

2022-10-30 Rapidly Solving Sudoku, N-Queens, Pentomino Placement, and More, With Knuth’s Algorithm X and Dancing Links.

2022-08-09 Calculating Discrete Sums With Umbral Calculus

2022-08-02 Calculating the Similarity of Histograms or PDFs & Interpolating Them Using the p-Wasserstein Distance

2022-07-21 Rounding Modes For Integer Division

237 posts grouped by the following categories:

- Other Publications
- Graphics
- Original Research / Inventions
- Programming
- Game Dev
- Math
- Machine Learning
- Cryptography
- DSP
- Audio Synth / Audio Programming
- Quantum Programming
- Network Programming
- Soft Skills / Not Directly About Tech
- Electronics

(Posts TODO – to help me remember things I’d like to write up at some point https://blog.demofox.org/2018/11/22/posts-todo/)

# Other Publications

2021-08-04 Ray Tracing Gems II Chapter 24 “Using Blue Noise for Ray Traced Soft Shadows”

**Simple But Effective Verlet Game Physics – GDC India 2021**

Slides: https://drive.google.com/drive/folders/1D_ZNhz_LRYHLUuDYY3-ge6cP0CSfTfc_

Youtube Video: https://www.youtube.com/watch?v=zfkaMWIo3XM

**Spatiotemporal Blue Noise Masks – EGSR 2022**

EGSR 2022 Presentation (Youtube): https://www.youtube.com/watch?v=4nM2FbLnOqQ

EGSR 2022 Paper: https://diglib.eg.org/handle/10.2312/sr20221161

Code and pregenerated textures: https://github.com/NVIDIAGameWorks/SpatiotemporalBlueNoiseSDK

NVIDIA Blog post part 1: https://developer.nvidia.com/blog/rendering-in-real-time-with-spatiotemporal-blue-noise-textures-part-1/

NVIDIA Blog post part 2: https://developer.nvidia.com/blog/rendering-in-real-time-with-spatiotemporal-blue-noise-textures-part-2/

Arxiv Paper on scalar valued STBN: https://arxiv.org/abs/2112.09629

# Graphics

2022-02-26 Image Sharpening Convolution Kernels

2022-02-01 Two Low Discrepancy Grids: Plus Shaped Sampling LDG, and R2 LDG

2022-01-01 Interleaved Gradient Noise: A Different Kind of Low Discrepancy Sequence

2021-12-29 Why Can’t You Design Noise in Frequency Space?

2021-12-27 Not All Blue Noise is Created Equal Part 2

2021-04-11 Perlin Noise Experiments

2020-11-04 Frequency Domain Image Compression and Filtering

2020-07-11 Interpolating Data Over Arbitrary Shapes With Laplace’s Equation and Walk on Spheres

2020-06-14 Casual Shadertoy Path Tracing 3: Fresnel, Rough Refraction & Absorption, Orbit Camera

2020-06-06 Casual Shadertoy Path Tracing 2: Image Improvement and Glossy Reflections

2020-05-25 Casual Shadertoy Path Tracing 1: Basic Camera, Diffuse, Emissive

2020-05-16 Using Blue Noise For Raytraced Soft Shadows

2020-05-10 Ray Marching Fog With Blue Noise

2019-12-07 Bezier Triangles

2019-06-25 Generating Blue Noise Textures With Void And Cluster

2018-11-16 How To: Data Lookups Via Raytracing

2018-08-12 Not All Blue Noise is Created Equal

2018-08-07 Tiled Blue Noise

2018-07-13 Blending an HDR color into a U8 Buffer

2018-07-04 Pathtraced Depth of Field & Bokeh

2018-04-16 Prefix Sums and Summed Area Tables

2018-03-24 An Idea: Raytracing Lookup Tables

2018-03-19 A Very Quick DirectX Raytracing API Primer

2018-03-10 Don’t Convert sRGB U8 to Linear U8!

2018-01-30 What the Heck is Blue Noise?

2017-11-26 Dissecting “Tiny Clouds”

2017-11-03 Animating Noise For Integration Over Time 2: Uniform Over Time

2017-10-31 Animating Noise For Integration Over Time

2017-10-25 Transmuting White Noise To Blue, Red, Green, Purple

2017-10-20 Generating Blue Noise Sample Points With Mitchell’s Best Candidate Algorithm

2017-10-01 Calculating the Distance Between Points in “Wrap Around” (Toroidal) Space

2017-07-10 WebGL PBR Implementation

2017-07-01 Why Are Some Shadows Soft And Other Shadows Hard?

2017-01-09 Raytracing Reflection, Refraction, Fresnel, Total Internal Reflection, and Beer’s Law

2016-09-21 Path Tracing – Getting Started With Diffuse and Emissive

2016-07-28 Fourier Transform (And Inverse) Of Images

2016-03-14 Using Wang Tiles to Simulate Turing Machines

2016-03-05 Matrix Form of Bezier Curves

2016-03-02 Actually Making Signed Distance Field Textures With JFA

2016-02-29 Fast Voronoi Diagrams and Distance Field Textures on the GPU With the Jump Flooding Algorithm

2016-02-21 G-Buffer Upsizing

2016-02-03 Failed Shadertoy “Dust” Game – Browsers Need To Compile Shaders Off the Main Thread!

2016-01-16 Making a Ray Traced Snake Game in Shadertoy

2015-08-19 Gaussian Blur

2015-08-18 Box Blur

2015-08-15 Resizing Images With Bicubic Interpolation

2015-08-09 Cubic Hermite Rectangles

2015-06-19 What is Pre-multiplied Alpha and Why Does it Matter?

2015-04-30 Bilinear Filtering & Bilinear Interpolation

2015-04-23 FlipQuad & FlipTri Antialiasing

2015-04-23 4-Rook Antialiasing (RGSS)

2015-04-22 Quincunx Antialiasing

2015-01-17 Bresenham’s Drawing Algorithms

2014-08-13 Wang Tiling

2014-08-11 Temporal supersampling, flipquads and real time raytracing

2014-06-30 Distance Field Textures

2014-06-22 Analytic Fog Density

2014-02-07 Lots of Skyboxes!

2014-02-03 Converting RGB to Grayscale

2014-01-27 A trip through the Graphics Pipeline

2014-01-22 Shadertoy – WebGLSL pixel shaders

2012-09-25 How to Render the Mandelbrot Set

2012-05-03 MoriRT: Pixel and Geometry Caching to Aid Real Time Raytracing

# Original Research / Inventions

2019-03-22 Linear Fit Search

2018-04-23 Taking a Stroll Between The Pixels

2017-05-07 Improved Storage Space Efficiency of GPU Texture Sampler Bezier Curve Evaluation

2016-12-16 Evaluating Points on Analytical Surfaces and in Analytical Volumes Using the GPU Texture Sampler

2016-12-10 Failed Experiment: The GPU Texture Sampler is Turing Complete But That Fact is Pretty Useless

2016-12-08 Evaluating Polynomials with the GPU Texture Sampler

2016-02-22 GPU Texture Sampler Bezier Curve Evaluation

2015-01-24 DAPSE Preview

# Programming

2022-10-30 Rapidly Solving Sudoku, N-Queens, Pentomino Placement, and More, With Knuth’s Algorithm X and Dancing Links.

2022-07-21 Rounding Modes For Integer Division

2020-10-25 When Life Gives You Lemons, Make Random Numbers

2020-06-23 Weighted Round Robin (Weighted Random Integers) Using The Golden Ratio Low Discrepancy Sequence

2019-08-10 Measuring Debug STL Container Perf Cost in MSVC

2017-11-21 Demystifying Floating Point Precision

2017-06-20 SIMD / GPU Friendly Branchless Binary Search

2016-12-06 The Secret to Writing Fast Code / How Fast Code Gets Slow

2016-11-13 Minimizing Code Complexity by Programming Declaratively

2016-10-14 A Data Point for MSVC vs Clang Code Generation

2016-10-03 Is Code Faster Than Data? Examining Hash Tables

2016-09-26 Is Code Faster Than Data? Switch Statements vs. Arrays

2016-09-23 Exploring Compile Time Hashing

2016-05-18 Who Cares About Dynamic Array Growth Strategies?

2016-04-09 Turning a Truth Table Into A digital Circuit (ANF)

2016-02-09 How and Why Cleaning Up Code or Processes Gives Multiplicative Benefits

2015-12-20 Simplifying Boolean Expressions With Karnaugh Maps

2015-12-18 What Happens When you Mix Hash Tables and Binary Searching?

2015-12-14 O(1) Data Lookups With Minimal Perfect Hashing

2015-03-09 HyperLogLog: Estimate Unique Value Counts Like The Pros

2015-02-25 Avoiding The Performance Hazzards of std::function

2015-02-22 Count Min Sketch: A Probabilistic Histogram

2015-02-13 Writing a Basic Search Engine AKA Calculating Similarity of Histograms with Dot Product

2015-02-08 Estimating Set Membership With a Bloom Filter

2015-02-05 Getting Strongly Typed Typedefs Using Phantom Types

2015-02-03 Estimating Counts of Distinct Values with KMV

2013-09-13 External C++ Header Guards

2013-09-09 Alloca and Realloc – Useful Tools, Not Ancient Relics

2013-07-08 Is pre-increment really faster than post increment? Part 2

2013-07-07 A Super Tiny Random Number Generator

2013-07-06 Fast & Lightweight Random “Shuffle” Functionality – FIXED!

2013-07-06 The Incredible Time Traveling Random Number Generator

2013-06-18 Why do you hate me rand()?!

2013-06-08 Fast & Lightweight Random “Shuffle” Functionality

2013-06-08 Efficiently Generate Random Numbers Without Repeats

2013-06-05 Is pre-increment really faster than post increment? Part 1

2013-05-21 The Black Art of sizeof() aka Compile Time Type Deduction

2013-05-11 Lists of Macro Lists

2013-05-07 Macro Lists For The Win – Side B

2013-05-03 Macro Lists For The Win

2013-05-01 Permutation Programming Without Maintenance Nightmares

2012-11-28 Mechanical Computer Quest Part I

# Game Dev

2020-03-01 Using Low Discrepancy Sequences & Blue Noise in Loot Drop Tables for Games

2017-09-30 Half Tile Offset Streaming World Grids

2016-04-01 Game Development Needs Data Pipeline Middleware

2014-01-11 Getting Ideal Disk Reads on the Cheap

2012-09-24 Bias And Gain Are Your Friend

2012-09-21 Anatomy of a Skeletal Animation System Part 3

2012-09-21 Anatomy of a Skeletal Animation System Part 2

2012-09-21 Anatomy of a Skeletal Animation System Part 1

2012-09-09 Recording lagless demo videos of a laggy game

# Math

2022-08-09 Calculating Discrete Sums With Umbral Calculus

2022-08-02 Calculating the Similarity of Histograms or PDFs & Interpolating Them Using the p-Wasserstein Distance

2022-07-12 Calculating SVD and PCA in C++

2022-07-10 Programming PCA From Scratch In C++

2022-06-29 Piecewise Least Squares Curve Fitting

2022-06-06 Fitting Data Points With Weighted Least Squares

2022-03-02 Sampling Importance Resampling

2022-03-01 Picking Fairly From A List of Unknown Size With Reservoir Sampling

2022-02-26 The Discrete Cosine Transform, and Derivatives

2022-02-20 Adjusting Point Sets in Frequency Space Using a Differentiable Fourier Transform

2022-01-29 Distance Between Points on a “Toroidal Disk”

2021-04-01 Mean Squared Error is Variance

2020-11-25 Multiple Importance Sampling in 1D

2020-07-26 Irrational Numbers

2020-07-17 Using Low Discrepancy Sequences With Rejection Sampling

2020-06-04 A Link Between Russian Roulette and Rejection Sampling / Importance Sampling

2020-05-03 Guess a Number Between 1 and 10

2020-03-17 Basic Methods For Finding Zeroes and Mins / Maxes of Functions

2020-03-12 Using White Noise to Choose Between Red Noise and Blue Noise

2020-03-10 How Do I Calculate Variance in 1 Pass?

2020-02-09 A Fun 2d Rotation Matrix Derivation

2019-12-01 Calculating Information Entropy

2019-10-25 Bayes’ Theorem Intuition

2019-07-30 Dice, Distributions & Noise Colors

2019-06-1 Taking the Max of Uniform Random Numbers

2019-05-25 Generating Random Numbers From a Specific Distribution With The Metropolis Algorithm (MCMC)

2018-06-12 Monte Carlo Integration Explanation in 1D

2017-08-08 Generating Random Numbers From a Specific Distribution With Rejection Sampling

2017-08-05 Generating Random Numbers From a Specific Distribution By Inverting the CDF

2017-07-25 Counting Bits & The Normal Distribution

2017-05-29 When Random Numbers Are Too Random: Low Discrepancy Sequences

2017-04-10 Solving N equations and N unknowns: The Fine Print (Gauss Jordan Elimination)

2017-03-31 Orthogonal Projection Matrix Plainly Explained

2017-03-13 Neural Network Gradients: Backpropagation, Dual Numbers, Finite Differences

2017-02-20 Multivariable Dual Numbers & Automatic Differentiation

2017-02-07 A Geometric Interpretation of Neural Networks

2017-01-02 Incremental Least Squares Surface and Hyper-Volume Fitting

2016-12-22 Incremental Least Squares Curve Fitting

2016-08-23 Incremental Averaging

2016-08-11 Understanding The Discrete Fourier Transform

2016-03-11 A Sixth Way To Calculate Sine Without Trig

2016-02-19 Normalized Vector Interpolation TL;DR

2015-11-13 Hiding a Lookup Table in a Modulus Operation

2015-09-15 Solving Nested Modulus Equations

2015-09-12 Solving Simultaneous Congruences (Chinese Remainder Theorem)

2015-09-10 Modular Multiplicative Inverse

2015-08-08 Cubic Hermite Interpolation

2015-08-05 Lagrange Rectangles

2015-08-02 Finite Differences

2015-07-28 Rectangular Bezier Patches

2015-07-08 Lagrange Interpolation

2015-07-05 The De Casteljau Algorithm for Evaluating Bezier Curves

2015-06-14 A Fifth Way to Calculate Sine Without Trig

2015-05-25 Easy Binomial Expansion & Bezier Curve Formulas

2015-01-24 Programmatically Calculating GCD and LCM

2014-12-30 Dual Numbers & Automatic Differentiation

2014-12-27 Using Imaginary Numbers To Rotate 2D Vectors

2014-11-04 Four Ways to Calculate Sine Without Trig

2014-08-28 One Dimensional Bezier Curves

2014-08-14 Counting in Binary is a Fractal

2014-08-10 What if My Equation DOESN’T Equal Zero??

2014-03-22 Bezier Curves Part 2 (and Bezier Surfaces)

2014-03-09 Implicit vs Parametric vs Explicit Surfaces

2014-03-04 Bezier Curves

2014-02-20 Soft Maximum vs Hard Maximum

2013-11-13 Transformation Matrix Basics

2013-10-12 Converting To and From Polar / Spherical Coordinates Made Easy

2013-09-17 How to Test Randomness of Numbers

# Machine Learning

2019-05-11 Markov Chain Text Generation

2017-12-23 C++ Differentiable Programming: Searching For An Optimal Dither Pattern

2017-03-15 Neural Network Recipe: Recognize Handwritten Digits With 95% Accuracy

2017-03-09 How to Train Neural Networks With Backpropagation

2012-10-23 B.A.M. Neural Networks

# Cryptography

2016-10-19 Low Tech Homomorphic Encryption

2016-04-30 Shamir’s Quest: Collect Any 3 Keys To Unlock The Secret!

2015-09-05 Improving the Security of the Super Simple Symmetric Leveled Homomorphic Encryption Implementation

2015-09-05 Super Simple Symmetric Leveled Homomorphic Encryption Implementation

2014-05-18 Feistel Networks – Do They Have to use XOR?

2012-09-17 Encryption 101: Realistic Security

2012-09-16 Cryptography 101: Encryption – Asymmetric Keys

2012-09-15 Cryptography 101: Encryption – Symmetric Keys

2012-09-15 Cryptography 101: Encryption – One Time Pad

2012-09-12 Cryptography 101: Hashing

# DSP

2020-01-24 IIR Audio & Data Filters – Featuring Biquads

2020-01-15 FIR Audio & Data Filters

# Audio Synth / Audio Programming

2018-03-05 Granular Audio Synthesis

2016-07-01 Intro To Audio Synthesis For Music Presentation

2016-06-23 The Beating Effect

2016-06-16 Synthesizing a Plucked String Sound With the Karplus-Strong Algorithm

2015-04-19 Frequency Domain Audio Synthesis – With IFFT and Oscillators

2015-04-14 Decibels (dB) and Amplitude

2015-03-23 DIY Synth: Convolution Reverb & 1D Discrete Convolution of Audio Samples

2015-03-17 DIY Synth: Multitap Reverb

2015-03-17 DIY Synth: Delay Effect (Echo)

2015-03-16 DIY Synth: Flange Effect

2015-03-14 DIY Synth: Basic Drum

2012-06-18 DIY Synth 3: Sampling, Mixing, and Band Limited Wave Forms

2012-05-19 DIY Synth 2: Common Wave Forms

2012-05-14 DIY Synth 1: Sound Output

# Quantum Programming

2015-11-06 Quantum Computing For Programmers Part 2: Multiple Qubits

2015-10-17 Quantum Computing For Programmers Part Ib: Bloch Sphere

2015-10-17 Quantum Computing For Programmers Part I: One Qubit

2015-10-12 Quantum Computing References

# Network Programming

2018-6-04 A Neat Trick For Compressing Networked State Data

# Soft Skills / Not Directly About Tech

2017-11-16 My Old Master: On Optimism

2017-07-03 A Tool To Debug Teams (Knoster)

2017-03-17 Plastic Bag Ban – Semi Reusable Bag Kiosks a Better Solution?

2017-01-24 My Old Master: How to Correct as a Mentor or a Teacher

2015-06-18 Adventures in Learning How to Publish a Research Paper Part 1

2015-05-24 No Bad Code, Creeping Normality and Social Structure Code Organization

2014-07-21 Situational Leadership

## Electronics

2021-07-11 Inverting a Button Press (Featuring Current Dividers)

2021-06-27 Resistance and Voltage Dividers

2021-06-15 Voltage, Amps, Resistance and LEDs (Ohm’s Law)