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<div id="idyll-mount"><div data-reactroot=""><div class="idyll-root"><nav class="menu"><a class="menu__item" href="/">rreusser.github.io</a><a class="menu__item" href="/sketches/">sketches</a><a class="menu__item" href="/projects/">projects</a></nav><div class="article-header"><div class="article-header__feature-container"></div><div class="article-header__content"><h1 class="hed">Projects</h1></div></div><div class=" idyll-text-container"><p>This page contains a wide variety of small projects and writeups I’ve created over the years. They mostly ride the line between mathematics and graphics. Though I wouldn’t necessarily consider it a success, the intent has been to focus not only on the math and pushing the boundaries of visualization on the web, but also on finding ways to more effectively communicate the underlying concepts. As a result, a pretty good share of these writeups are found on <a href="https://observablehq.com/">Observable</a> since it’s quite simply the best environment I’ve found for exploring and communicating interactive technical content on the web.</p><p>I hope you find something interesting!</p><p>Comments? Questions? Let me know <a href="https://twitter.com/rickyreusser">@rickyreusser</a>.</p></div><div class="projectDesc__container"><a href="https://observablehq.com/@rreusser/complex-function-plotter?collection=@rreusser/writeups" class="projectDesc"><img src="static/domain-coloring-3.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">July 29, 2020</span><h2>Complex Function Plotter</h2><p>The <span style="display:inline-block"><span> <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>n</mi><mo>+</mo><msup><mn>1</mn><mrow><mi>t</mi><mi>h</mi></mrow></msup></mrow><annotation encoding="application/x-tex">n+1^{th}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.849108em;"></span><span class="strut bottom" style="height:0.932438em;vertical-align:-0.08333em;"></span><span class="base"><span class="mord mathit">n</span><span class="mord rule" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mord rule" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mord">1</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.849108em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathit mtight">t</span><span class="mord mathit mtight">h</span></span></span></span></span></span></span></span></span></span></span></span> </span></span> iteration of my approach to domain coloring for complex functions, this time with a function parser to automatically turn a mathematical expression into GLSL code.</p></div></a><a href="https://observablehq.com/@rreusser/gpu-voronoi-diagrams-using-the-jump-flooding-algorithm?collection=@rreusser/writeups" class="projectDesc"><img src="static/jump-flooding.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">July 8, 2020</span><h2>GPU Voronoi Diagrams using the Jump Flooding Algorithm</h2><p>There are many good reasons to compute Voronoi diagrams in the geometric manner, but it’s also fun and useful to compute it as a raster image effect. This notebook computes Voronoi diagram images in <span style="display:inline-block"><span> <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>log</mi><mo>⁡</mo><mn>2</mn></msub><mo>(</mo><mi>s</mi><mi>i</mi><mi>z</mi><mi>e</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">\log_2(size)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></span><span class="base"><span class="mop"><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.20696799999999996em;"><span style="top:-2.4558600000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em;"></span></span></span></span></span><span class="mopen">(</span><span class="mord mathit">s</span><span class="mord mathit">i</span><span class="mord mathit" style="margin-right:0.04398em;">z</span><span class="mord mathit">e</span><span class="mclose">)</span></span></span></span> </span></span> passes using the Jump Flooding algorithm.</p></div></a><a href="https://rreusser.github.io/explorations/sphere-eversion/" class="projectDesc"><img src="static/eversion.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">June 29, 2020</span><h2>Sphere Eversion</h2><p>While a circle in two dimensions cannot, a sphere in three dimensions can be smoothly turned inside-out! An interactive walkthrough to help visualize the eversion of Bednorz and Bednorz.</p></div></a><a href="https://observablehq.com/@rreusser/dispersion-in-water-surface-waves" class="projectDesc"><img src="static/wake-angle.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">June 18, 2020</span><h2>Dispersion in Water Surface Waves</h2><p>I was quite surprised to learn that while Mach angles depend on an object’s speed, surface waves in water work differently and form a wake which doesn’t depend on the speed!</p></div></a><a href="https://observablehq.com/@rreusser/bakers-map?collection=@rreusser/writeups" class="projectDesc"><img src="static/bakers-map.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">June 12, 2020</span><h2>Baker’s Map</h2><p>The chaotic baker’s map results when you cut and fold dough. This notebook performs the process and allows to explore different maps.</p></div></a><a href="https://observablehq.com/@rreusser/faking-transparency-for-3d-surfaces?collection=@rreusser/writeups" class="projectDesc"><img src="static/transparency.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">June 12, 2020</span><h2>Fake Transparency for 3D Surfaces</h2><p>Transparency is not something which comes easily when rendering models on a GPU. This notebook illustrates a simple shortcut toward displaying transparent 3D surfaces with a two-pass rendering technique.</p></div></a><a href="https://observablehq.com/@rreusser/equally-distributing-points-on-a-sphere" class="projectDesc"><img src="static/sphere-points.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">May 29, 2020</span><h2>Uniformly Distributed Points on a Sphere</h2><p>A quick check to verify visually that random points are distributed evenly on the surface of a sphere.</p></div></a><a href="https://observablehq.com/@rreusser/gpgpu-boids?collection=@rreusser/writeups" class="projectDesc"><img src="static/boids.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">May 28, 2020</span><h2>GPU Boids</h2><p>Classic boids requires some sort of strategy for nearest-neighbor lookup, whether that’s a tree or brute-force pairwise interactions. This notebook follows a Particle Mesh method strategy and uses a grid to transmit locally averaged properties to neighboring boids.</p></div></a><a href="https://www.shadertoy.com/view/wdffWj" class="projectDesc"><img src="static/monte-carlo-geometry.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">May 10, 2020</span><h2>Figure Reproduction: Monte-Carlo Geometry Processing</h2><p>A reproduction of Figure 2 from Sawhney and Crane’s oustanding paper, Monte Carlo Geometry Processing. My very first foray into SDF rendering with sphere-tracing!</p></div></a><a href="https://observablehq.com/@rreusser/toiletpaperfullerenes-and-charmin-nanotubes?collection=@rreusser/writeups" class="projectDesc"><img src="static/toiletpaper.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">April 28, 2020</span><h2>Toiletpaperfullerenes and Charmin Nanotubes</h2><p>Toilet paper tubes have the curious property that you can flatten them, cut out loops, and link the loops together without fasteners. This notebook provides some instructions and implements a simple point and click editor to construct your own!</p></div></a><a href="https://observablehq.com/@rreusser/3d-reaction-diffusion?collection=@rreusser/writeups" class="projectDesc"><img src="static/reaction-diffusion.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">March 15, 2020</span><h2>3D Reaction-Diffusion</h2><p>A 3D WebGL simulation of Gray-Scott reaction-diffusion. Even though WebGL 1 only has two-dimensional textures, with enough bookkeeping, they work perfectly well for three-dimensional simulations of modest size.</p></div></a><a href="https://observablehq.com/@rreusser/3d-reaction-diffusion?collection=@rreusser/writeups" class="projectDesc"><img src="static/pca.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">March 15, 2020</span><h2>Grouping Points with Principal Component Analysis</h2><p>A response to a question about the quickest way to separate a cloud of points into two groups. Power iteration would be a bit quicker, but Principal Component Analysis (PCA) is a good start.</p></div></a><a href="https://observablehq.com/@rreusser/compound-double-pendulums?collection=@rreusser/writeups" class="projectDesc"><img src="static/pendula.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">February 23, 2020</span><h2>Double Compound Pendulums</h2><p>One million double pendulums!</p></div></a><a href="https://observablehq.com/@rreusser/integers-in-single-precision-floating-point" class="projectDesc"><img src="static/float.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">February 9, 2020</span><h2>Integers in Single-Precision Floating-Point</h2><p>You’re likely to get scolded for using a floating-point variable to represent an integer, but floating-point represents most integers perfectly well. Scroll through all of the integers representable in single-precision floating point!</p></div></a><a href="https://observablehq.com/@rreusser/half-precision-floating-point-visualized" class="projectDesc"><img src="static/half-float.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">February 9, 2020</span><h2>Half-Precision Floating-Point, Visualized</h2><p>Half-precision floating-point can be surprisingly difficult to work with. This notebook plots all possible numbers with the special cases illustrated clearly.</p></div></a><a href="https://www.shadertoy.com/view/wld3zl" class="projectDesc"><img src="static/rect-domain-coloring-shadertoy.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">December 26, 2019</span><h2>Shadertoy: Rectangular Adaptive Domain Coloring</h2><p>A Shadertoy implementation of my domain coloring technique using rectangular contours.</p></div></a><a href="https://www.shadertoy.com/view/tlcGzf" class="projectDesc"><img src="static/polar-domain-coloring-shadertoy.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">December 22, 2019</span><h2>Shadertoy: Polar Adaptive Domain Coloring</h2><p>A Shadertoy implementation of my domain coloring technique using polar contours.</p></div></a><a href="https://observablehq.com/@rreusser/binary-input" class="projectDesc"><img src="static/binary-input.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">December 12, 2019</span><h2>Binary Input</h2><p>An input field for Observable notebooks which allows you to toggle the bits.</p></div></a><a href="https://observablehq.com/@rreusser/eigen" class="projectDesc"><img src="static/eigen.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">December 10, 2019</span><h2>Linear Algebra via Eigen and WebAssembly: A proof of concept</h2><p>Numerical computing in JavaScript remains difficult due to the lack of robust, complete libraries. This notebook explores compiling a subset of the Eigen linear algebra library to WebAssembly using Emscripten and tries to remedy some of the ergonomic memory management issues which result.</p></div></a><a href="https://observablehq.com/@rreusser/2d-n-body-gravity-with-poissons-equation?collection=@rreusser/writeups" class="projectDesc"><img src="static/gravity.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">October 30, 2019</span><h2>2D (Non-physical) N-body Gravity with Poisson’s Equation</h2><p>N-body simulations get expensive very quickly, with the number of interactions growing with <span style="display:inline-block"><span> <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>O</mi><mo>(</mo><msup><mi>n</mi><mn>2</mn></msup><mo>)</mo></mrow><annotation encoding="application/x-tex">O(n^2)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.8141079999999999em;"></span><span class="strut bottom" style="height:1.064108em;vertical-align:-0.25em;"></span><span class="base"><span class="mord mathit" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord"><span class="mord mathit">n</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span> </span></span>. This notebook takes a shortcut and uses the somewhat inaccurate Particle-Mesh method to simulate 2D Newtonian gravity on a grid. It solves Poisson’s equation via an FFT and plots the results entirely on the GPU.</p></div></a><a href="https://observablehq.com/@rreusser/periodic-planar-three-body-orbits?collection=@rreusser/writeups" class="projectDesc"><img src="static/periodic-three-body-orbits.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">October 18, 2019</span><h2>Periodic Planar Three-Body Orbits</h2><p>This notebook collects over 2200 periodic, planar three-body orbits and explains one of the normal topological ways to classify them.</p></div></a><a href="https://observablehq.com/@rreusser/quick-miterless-lines-in-webgl?collection=@rreusser/writeups" class="projectDesc"><img src="static/miterless-lines.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">September 25, 2019</span><h2>Quick (miterless) Lines in WebGL</h2><p>Drawing lines is indeed hard. This notebook uses instanced rendering to turn simple vertex data into a continuous line. To simplify things, and since for many cases miters are not necessary, we simply draw a two-triangle rectangle per line segment.</p></div></a><a href="https://observablehq.com/@rreusser/finding-roots-in-the-complex-plane?collection=@rreusser/writeups" class="projectDesc"><img src="static/complex-roots.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">August 18, 2019</span><h2>Finding Roots in the Complex Plane</h2><p>Students of complex analysis will recall that a path integral quickly tells you how many roots are inside a given contour, but this notebook walks through the method of Delves and Lyness which transforms integrals around a contour into a polynomial whose roots are exactly the encircled roots!</p></div></a><a href="https://observablehq.com/@rreusser/adaptive-domain-coloring?collection=@rreusser/writeups" class="projectDesc"><img src="static/domain-coloring.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">July 26, 2019</span><h2>Domain Coloring with Adaptive Contouring</h2><p>Domain coloring for complex-valued functions is tricky since the function and rate of change may vary over many orders of magnitude. This notebook iterates on the previous technique and tries out automatic differentiation and screen-space derivatives to compute the rate of change and automatically scale contours.</p></div></a><a href="https://observablehq.com/@rreusser/instanced-webgl-circles?collection=@rreusser/writeups" class="projectDesc"><img src="static/instanced-circles.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">July 12, 2019</span><h2>Instanced WebGL Circles</h2><p>This notebook explains how to use the <code>ANGLE_instanced_arrays</code> WebGL extension to draw a <em>lot</em> of circles to the screen in a very performant manner.</p></div></a><a href="https://observablehq.com/@rreusser/simulating-the-1-d-schrodinger-equation-in-webgl?collection=@rreusser/writeups" class="projectDesc"><img src="static/schrodinger-1d.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">July 5, 2019</span><h2>GPUs, FFTs, and the 1-D Schrödinger Equation</h2><p>This notebook solves the 1D Schrödinger Equation by trivially stepping it in the frequency domain and plotting the result in the physical space. The main goal is to an exercise in computing and plotting result from start to finish entirely on the GPU.</p></div></a><a href="https://observablehq.com/@rreusser/control-panel-2-prototype-test" class="projectDesc"><img src="static/control-panel.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">March 25, 2019</span><h2>Control Panel Prototype</h2><p>Dat.gui is the gold standard in simple control GUIs. This notebook illustrates a prototype libary based on Preact and with the goal of being simple and extensible.</p></div></a><a href="http://rreusser.github.io/multiscale-turing-pattern-gallery-2/" class="projectDesc"><img src="static/turing-2.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">March 15, 2019</span><h2>Multi-Scale Turing Patterns 2</h2><p>A second set of multi-scale Turing patterns</p></div></a><a href="https://observablehq.com/@rreusser/debugging-normals-without-duplicating-geometry-data?collection=@rreusser/writeups" class="projectDesc"><img src="static/bunny-normals.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">December 17, 2018</span><h2>Drawing indexed mesh data as screen-space normals without duplicating data</h2><p>We typically just send triangles to the GPU and draw them on the screen. This notebook uses instanced rendering to draw plain, unadorned mesh data as normals with arrowheads and foreshortening.</p></div></a><a href="http://rreusser.github.io/multiscale-turing-pattern-gallery/" class="projectDesc"><img src="static/turing-1.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">October 19, 2018</span><h2>Multi-Scale Turing Patterns 1</h2><p>An implementation of multi-scale Turing patterns following the method of Jonathan McCabe.</p></div></a><a href="https://observablehq.com/@rreusser/contour-plots-with-d3-regl-and-observable?collection=@rreusser/writeups" class="projectDesc"><img src="static/contours.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">June 20, 2018</span><h2>Contour plots with D3, regl, and Observable</h2><p>My favorite WebGL extension is <code>OES_standard_derivatives</code>, used for computing screen-space derivatives. This notebook illustrates its utility in drawing constant-screen-width contour lines of any sort in a fragment shader.</p></div></a><a href="http://rreusser.github.io/aligning-3d-scans/" class="projectDesc"><img src="static/aligning-scans.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">July 28, 2018</span><h2>Aligning 3D scans</h2><p>In which I have fun rediscovering Principal Component Analysis by stating what I want from a problem, realizing Lagrange multipliers actually work, then finding out it’s just Principla Component Analysis on the normal vectors.</p></div></a><a href="https://observablehq.com/@rreusser/domain-coloring-for-complex-functions?collection=@rreusser/writeups" class="projectDesc"><img src="static/domain-coloring-old.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">June 17, 2018</span><h2>Domain Coloring for Complex Functions</h2><p>This notebook represents an early attempt at the domain coloring technique for complex analytic functions. It uses the contour line technique but depends a great deal on the particular scale of the functions plotted.</p></div></a><a href="http://rreusser.github.io/from-nothing-to-something-in-webgl-with-regl/" class="projectDesc"><img src="static/hello-regl.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">December 7, 2016</span><h2>From Nothing to Something in WebGL Using regl</h2><p>A pretty good portion of the material on this site is implemented in WebGL using Mikola Lysenko’s oustanding regl library. This post walks through my still-favorite method of getting off of the ground in and into regl.</p></div></a><a href="http://rreusser.github.io/things-i-learned-the-hard-way-using-react-native/" class="projectDesc"><img src="static/react-for-some-reason.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">May 5, 2016</span><h2>Things I Learned the Hard Way Using React Native</h2><p>This post exists because I wish someone had sat me down and told me half of these things on Day One of using React Native.</p></div></a><a href="http://rreusser.github.io/a-series-of-unfortunate-things-i-programmed-one-time/" class="projectDesc"><img src="static/hard-things.jpg" class="projectDesc__thumb"/><div class="projectDesc__meta"><span class="projectDesc__date">March 16, 2015</span><h2>A Series of Unfortunate Things I Programmed One Time</h2><p>A walkthrough of how I got started and what motivates me to seek better ways to communicate.</p></div></a></div><div class=" idyll-text-container"><div></div></div><footer class="footer"><div class="footer__content"><div class="footer_copy">© 2020 Ricky Reusser</div></div></footer></div></div></div>
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