List of my saved Desmos graphs

Bomb 💣

2024/03/08 • 3,676 bytes • 21 expressions • 1 note • slider animation

$\displaystyle{c\left(u\right)+\frac{0.06}{\left|c_{n}\left(u\right)\right|}\left(c_{n}\left(u\right)\cos\left(v\right)+c_{n}\left(u\right)\times\frac{c'\left(u\right)}{\left|c'\left(u\right)\right|}\sin\left(v\right)\right)}$

Desmos JSON

Ammonite 3D

2024/03/08 • 22,211 bytes • 108 expressions • 30 notes • 10 folders • slider animation

3D version of my original "Ammonite" graph - https://www.desmos.com/calculator/z7zooq9zsh

Desmos JSON

Jellyfish

2024/03/04 • 5,970 bytes • 29 expressions • 1 note • 3 folders • slider animation

$\displaystyle{F_{ten}=\frac{2\pi\left(1.5+0.5\operatorname{random}\left(N_{ten}\right)\right)}{L_{ten}}}$

Desmos JSON

Nerd 🤓

2024/02/26 • 5,106 bytes • 23 expressions • 1 note • 5 folders

> "I'm such a nerd! I can't be free!" 🤓🤓🤓🤓 🤓🤓🤓🤓 🤓🤓🤓🤓 🤓🤓🤓🤓 🤓🤓🤓🤓 🤓🤓🤓🤓 🤓🤓🤓🤓 🤓🤓🤓🤓

Desmos JSON

Pineapple

2024/02/18 • 6,118 bytes • 32 expressions • 2 folders

$\displaystyle{L\left(v\right)=\frac{v}{\operatorname{distance}\left(v,\left(0,0,0\right)\right)}}$

Desmos JSON

Stanford Bunny (Neural Point Cloud)

2024/02/14 • 11,776 bytes • 56 expressions • 5 notes

Finding a way to export compressed point clouds to Desmos, after previously exporting 2D parametric shapes and 3D implicit shapes. This seems to require more parameters with a suboptimal performance compared to implicit shapes. Possibly because surface po...

Desmos JSON

Bowl of Noodles

2024/02/06 • 4,660 bytes • 28 expressions

$\displaystyle{\operatorname{sphere}\left(\left(\left[0.72,0.8\right],\frac{L}{2},h+r_{1}\right),r_{1}\right)}$

Desmos JSON

Neogastropoda

2024/01/15 • 53,560 bytes • 179 expressions • 67 notes • 10 folders • slider animation

"Neogastropoda" by Harry Chen (harry7557558) My artwork attempts to represent five sea snail species under the taxonomic order Neogastropoda. As someone who lived in a coastal town in Southeast China throughout my younger ages, seashells are significant p...

Desmos JSON

Nautilus & Quartz

2024/01/15 • 29,477 bytes • 91 expressions • 47 notes • 7 folders • 1 table

"Nautilus & Quartz" by Harry Chen (harry7557558) My artwork consists of an eye decorated with abstract objects belonging to four classes: a horned nautilus shell, quartz crystals, geometric shapes, and flowers. The objects in decoration are chosen to repr...

Desmos JSON

Banana

2024/01/11 • 2,594 bytes • 9 expressions

$\displaystyle{c_{1}=\operatorname{hsv}\left(55,1,0.9\right)}$

Desmos JSON

Horned Nautilus

2024/01/01 • 2,065 bytes • 8 expressions

$\displaystyle{R\left(u,v\right)=v^{1.2}\left(1-0.35\left|\sin\left(9\pi\ln\left(v\right)\right)\right|^{0.5}\right)\left(1-\frac{\left|u\right|}{\pi}\right)^{4}}$

Desmos JSON

Neural Stanford Bunny

2023/12/26 • 3,831 bytes • 18 expressions • 1 note

Neural Stanford Bunny - Test how fast Desmos can render 3D implicits. Original C++ script that does Adam+BFGS written in 2022 (https://github.com/harry7557558/Graphics/tree/master/fitting/boolean/tanh, low portability warning)

Desmos JSON

Conch on Beach

2023/12/23 • 2,012 bytes • 7 expressions

$\displaystyle{Z\left(u,v\right)=1.2v^{0.7}\left(\sin\left(u\right)N\left(u,v\right)-2.5\right)}$

Desmos JSON

Nautilus Shell Slicing

2023/12/21 • 4,254 bytes • 29 expressions • 1 note

From https://harry7557558.github.io/spirulae/implicit3/ (see examples)

Desmos JSON

Optimal Beam Support Location

2023/06/24 • 7,973 bytes • 36 expressions • 15 notes

Find the optimal locations to support a beam in the middle to minimize overall deflection Motivation: We are building a float with beam supports and plywood, and it needs to hold multiple people in an event. However, when we stand on it, the plywood board...

Desmos JSON

Gamma Function Approximation

2023/03/07 • 2,680 bytes • 18 expressions

$\displaystyle{g_{a0}\left(x\right)=\left\{x>0.5:\exp\left(g_{1}\left(x\right)\right),\frac{\pi}{\sin\left(\pi x\right)\exp\left(g_{1}\left(1-x\right)\right)}\right\}}$

Desmos JSON

UTEA Design

2022/08/23 • 5,882 bytes • 25 expressions • 10 notes • slider animation

This is a design I made for a school project. The goal is to "create a meaningful or eye-catching design using at least three functions, their derivative functions, and their possible integrals." I created a heart (which is possibly the most overused shap...

Desmos JSON

Shortest Spherical Path

2022/08/15 • 8,912 bytes • 37 expressions • 4 notes • 3 folders • slider animation

I have heard that the shortest spherical path an airplane flies from one city to another city looks counter-intuitive on a rectangular map. I try to plot the shortest path between two cities on a rectangular map, and find the highest latitude the plane go...

Desmos JSON

LDS Dependency 3D

2022/07/25 • 5,806 bytes • 25 expressions • 2 notes • 2 folders • 1 table

I think my previous LDS graph (https://www.desmos.com/calculator/zizgz2owda) looks cool, so I want to check what it looks like in 3D.

Desmos JSON

LDS Dependency

2022/07/25 • 3,797 bytes • 13 expressions • 5 notes • 4 folders

My website homepage (https://harry7557558.github.io/) currently uses the base-2 Van der Corput sequence as a quasi-random sequence to generate random quotes and links. While this makes it less likely to generate consecutive same items compared to a regula...

Desmos JSON

Value Noise Distribution

2022/07/17 • 8,794 bytes • 36 expressions • 11 notes • 4 folders

Attempt to produce 1-dimensional noise functions with values uniformly distributed between 0 and 1. The idea is to find the distribution of the value noise and apply its CDF to the range of the function. Basic idea: - Given three uniform random variables...

Desmos JSON

Raymarching Gradient Estimation

2022/06/24 • 15,046 bytes • 62 expressions • 3 notes • 5 folders

Try to develop a fast-converging method for intersecting a ray with an implicit surface. The value of the scalar field along the ray can be viewed as a one-dimensional function, and the problem is to find the first zero of the function with a positive para...

Desmos JSON

Value-Gradient Projection

2022/06/23 • 5,459 bytes • 31 expressions • 1 note • 4 folders

Given v(x) and g(x)=v'(x) at x=-h0 and x=0, project v(x) and g(x) at x=h1. Test a method that expresses the answer as the weighted sum of the givens and finds the coefficients by setting the low-order terms of the series expansion to zero.

Desmos JSON

Bouncing Rigid Body

2022/06/18 • 21,384 bytes • 81 expressions • 23 notes • 6 folders • ticker

Simulating a bouncing rigid body that conserves energy. It has both linear and angular positions and velocities.

$\displaystyle{d_{pCd}\left(r_{0},n\right)=-\frac{2\left(d_{ot}\left(v,n\right)+\omega d_{et}\left(p_{rd}\left(p,\alpha,r_{0}\right),n\right)\right)}{d_{ot2}\left(n\right)+\frac{1}{I}d_{et}\left(p_{rd}\left(p,\alpha,r_{0}\right),n\right)^{2}}}$

Desmos JSON

Action Test

2022/06/14 • 9,244 bytes • 37 expressions • 14 notes • 5 folders • ticker

This is my first time to play with the "action" feature in Desmos. I try to create a bouncing ball with collision response that conserves energy.

Desmos JSON

Tanh Activation Loss Function

2022/04/20 • 6,657 bytes • 26 expressions • 4 notes • 4 folders

Trying to find a loss function for the tanh activation function on a single layer neural network Training data

Desmos JSON

Forest Tutorial

2022/04/19 • 9,883 bytes • 22 expressions • 19 notes • 4 folders

Demonstrate the use of implicit shapes An overview of implicit shapes: - Implicit curve: f(x,y)=g(x,y) (no fill) - Implicit region: f(x,y)<g(x,y) (fill+dashed line), f(x,y)<=g(x,y) (fill+solid line) - Line can be stylized by holding the left icon and chec...

Desmos JSON

Seashells Tutorial

2022/04/19 • 5,832 bytes • 24 expressions • 4 folders • slider animation

$\displaystyle{H_{m}\left(t\right)=\min\left(\max\left(2\cos\left(t+\frac{\pi}{2}\right),0\right),1\right)}$

Desmos JSON

Discord Emoji Complete List

2022/03/15 • 2,895,413 bytes • 7,561 expressions • 3 notes

Discord Emojis Complete List Original graphics by Twemoji - https://twemoji.twitter.com/ Exported to Desmos by harry7557558 - https://github.com/harry7557558/miscellaneous/tree/master/twemoji-to-desmos A summary of the steps to produce this graph: - Sc...

Desmos JSON

Orthogonal linear regression

2022/02/11 • 8,768 bytes • 36 expressions • 9 notes • 6 folders

Compare different ways to fit a straight line to a set of points. Drag the black point to set data The red line (linear regression) doesn't work well for nearly-vertical lines. The blue line sometimes has weird behaviors. The two green lines are identical...

Desmos JSON

3D Parametric Surface Template 3

2022/02/08 • 14,870 bytes • 65 expressions • 18 notes • 8 folders • 1 image

3D Parametric Surface Template 3 - by harry7557558 Improved from version 2 https://www.desmos.com/calculator/ftuogjzprg by using a more efficient way to plot faces.

Desmos JSON

Ammonite

2022/01/09 • 34,882 bytes • 137 expressions • 49 notes • 13 folders • 1 image • slider animation

"Ammonite" by Harry Chen (harry7557558) My artwork is a creature with a spiral shell and tentacles moving underwater. I have been fascinated by objects from the sea, especially the spiral shells of mollusks, so I choose to create an ammonite whose shell c...

Desmos JSON

2022 Firework Animation

2022/01/01 • 6,841 bytes • 28 expressions • 4 folders • slider animation

$\displaystyle{p_{fw3}=0.008c_{fw3}\left(2\pi\cdot\frac{1}{N_{fw3}}\cdot\left[1,2...N_{fw3}\right]\right)}$

Desmos JSON

Random subtraction of two circles #2

2021/12/28 • 3,614 bytes • 27 expressions • 3 notes

$\displaystyle{X_{2}=I_{2inv}\left(I_{1}\cdot\left(2\left\{U<T:\frac{0}{0},\frac{U-T}{1-T}\right\}-1\right)\right)}$

Desmos JSON

Random subtraction of two circles #1

2021/12/28 • 5,826 bytes • 39 expressions • 2 folders

$\displaystyle{I_{1}\left(x\right)=\frac{1}{2}\left(xh_{1}\left(x\right)+r^{2}\arctan\left(\frac{x}{h_{1}\left(x\right)}\right)\right)}$

Desmos JSON

Random points inside union of two circles

2021/12/28 • 3,427 bytes • 25 expressions • 4 notes

$\displaystyle{I_{0}=-\frac{1}{2}\left(cy_{0}+r^{2}\arctan\left(\frac{c}{y_{0}}\right)\right)}$

Desmos JSON

3D Parametric Surface Template 2

2021/12/23 • 17,635 bytes • 79 expressions • 16 notes • 8 folders • 1 image

3D Parametric Surface Template - by harry7557558 Replace the "x_obj", "y_obj", "z_obj" functions in the "Object" folder to graph custom parametric equations. Change the subscript "_obj" to others to display multiple parametric surfaces on the same graph.

Desmos JSON

3D Parametric Surface Template

2021/12/23 • 15,957 bytes • 73 expressions • 9 notes • 8 folders • 1 image

3D Parametric Surface Template - by harry7557558 Replace the "x_obj", "y_obj", "z_obj" functions in the "Object" folder to graph custom parametric equations. Change the subscript "_obj" to others to display multiple parametric surfaces on the same graph.

Desmos JSON

2017 CSMC A6

2021/11/03 • 2,548 bytes • 16 expressions • 1 folder

$\displaystyle{\left(x-3\right)^{2}+\left(y-4\right)^{2}=5^{2}\left\{\frac{x}{6}+\frac{y}{8}\ge1\right\}}$

Desmos JSON

Circle Equidistant Locus

2021/10/17 • 5,363 bytes • 29 expressions • 1 note • 4 folders

Locus points equidistant from two circles

$\displaystyle{\frac{\left(x-x_{0}\right)^{2}}{a_{1}^{2}}+\frac{y^{2}}{a_{1}^{2}-f^{2}}=1}$

Desmos JSON

Cook-Torrance BRDF

2021/10/11 • 12,983 bytes • 58 expressions • 6 notes • 7 folders

$\displaystyle{\Lambda\left(\theta\right)=\frac{\sqrt{1+\alpha^{2}\tan\left(\theta\right)^{2}}-1}{2}}$

Desmos JSON

Henyey-Greenstein importance sampling

2021/10/03 • 6,787 bytes • 31 expressions • 6 notes • 3 folders

$\displaystyle{F_{inv}\left(x\right)=\frac{1}{2g}\left(1+g^{2}-\left(\frac{\left(1-g^{2}\right)}{2g\left(x+\frac{1-g}{2g}\right)}\right)^{2}\right)\left\{0\le x\le1\right\}}$

Desmos JSON

Oren-Nayar BRDF

2021/10/01 • 5,669 bytes • 27 expressions • 4 folders

$\displaystyle{\int_{0}^{2\pi}\int_{0}^{\frac{\pi}{2}}F_{r}\left(u,v\right)\cos\left(v\right)\cdot\sin\left(v\right)dvdu}$

Desmos JSON

Random points inside intersection of two circles

2021/09/12 • 2,842 bytes • 19 expressions • 5 notes

Attempt to generate uniform random samples in the intersection of two circles

$\displaystyle{I\left(x\right)=\frac{1}{2}r^{2}\arcsin\left(\frac{x}{r}\right)+\frac{1}{2}x\sqrt{r^{2}-x^{2}}-cx}$

Desmos JSON

RYB Color Wheel Girl

2021/08/27 • 10,039 bytes • 46 expressions • 5 notes • 4 folders

WebGL version: https://www.shadertoy.com/view/Nd33zB Linear interpolation

Desmos JSON

2D color palette

2021/08/14 • 1,912 bytes • 12 expressions

$\displaystyle{Y=-1+\frac{2}{N}\left(\operatorname{floor}\left(\frac{I}{N}\right)+\frac{1}{2}\right)}$

Desmos JSON

Linear color gradient grapher

2021/08/13 • 2,883 bytes • 13 expressions • 3 notes • 5 folders

$\displaystyle{g\left(t\right)=0.5+0.5\cos\left(2\pi\left(t-\frac{1}{3}\right)\right)}$

Desmos JSON

Titration Curve

2021/03/31 • 2,844 bytes • 14 expressions • 7 notes

pH and H⁺/OH⁻ amounts of the sample, assuming 1L sample

$\displaystyle{a\left(t\right)=\frac{a_{0}+a_{d}\cdot t}{1+t}}$

Desmos JSON

Quadratic Interpolation

2020/12/29 • 4,083 bytes • 16 expressions

$\displaystyle{x=\frac{y_{0}\left(x_{c}^{2}-x_{1}^{2}\right)+y_{c}\left(x_{1}^{2}-x_{0}^{2}\right)+y_{1}\left(x_{0}^{2}-x_{c}^{2}\right)}{2\left(y_{0}\left(x_{c}-x_{1}\right)+y_{c}\left(x_{1}-x_{0}\right)+y_{1}\left(x_{0}-x_{c}\right)\right)}}$

Desmos JSON

Vectorization Test Cases

2020/11/08 • 3,315 bytes • 12 expressions

$\displaystyle{\frac{1}{3}\left(\sin\left(N\left(S\right)t\right),\cos\left(K\left(S\right)t\right)\right)+\left(N\left(S\right),K\left(S\right)\right)}$

Desmos JSON

Epsilon

2020/10/05 • 2,128 bytes • 12 expressions • 3 notes

Machine epsilon demonstration Result may vary by hardware and web browser

Desmos JSON

Torus projection

2020/09/10 • 16,048 bytes • 82 expressions • 7 notes • 6 folders

$\displaystyle{s_{z}\left(n\right)=z_{0}+\frac{n}{D_{z}}\left(z_{1}-z_{0}\right)}$

Desmos JSON

Ellipsoid projection

2020/09/07 • 13,179 bytes • 71 expressions • 5 notes • 4 folders

$\displaystyle{G\left(x,y,z\right)=\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}+\frac{z^{2}}{c^{2}}-1}$

Desmos JSON

Ellipse principal axes

2020/09/07 • 1,536 bytes • 11 expressions

$\displaystyle{P_{1}=\frac{v_{1}}{\operatorname{distance}\left(\left(0,0\right),v_{1}\right)}\sqrt{\frac{1}{\lambda_{1}}}}$

Desmos JSON

Elliptical ring moment of inertia

2020/09/06 • 4,748 bytes • 20 expressions • 1 note • 4 folders

Interactive visualization of the ratio of the moment of inertia of a uniform elliptical ring to its mass

$\displaystyle{r_{e}\left(t\right)=RN\left(t-\frac{1}{N}\operatorname{floor}\left(Nt\right)\right)}$

Desmos JSON

Polynomial trigonometric fit

2020/08/25 • 6,068 bytes • 32 expressions • 3 notes • 6 folders

Multivation: find an approximation of roots of equations in the form P(x)+c1*cos(w*x)+c2*sin(w*x)=0, P(x) is a polynomial with degree no more than 4 that can be solved analytically. Perform Newton's iteration twice on the approximation to solve the equati...

Desmos JSON

damped forced vibration

2020/08/15 • 2,375 bytes • 14 expressions

$\displaystyle{C_{1}=\frac{Fuw}{\left(-mw^{2}+k\right)^{2}+u^{2}w^{2}}+\frac{mg}{k}}$

Desmos JSON

Capacitor Output Voltage

2020/08/13 • 2,315 bytes • 13 expressions • 1 note

Solve http://www.thefouriertransform.com/series/circuitExample.php without Fourier series

Desmos JSON

random vector generator

2020/08/03 • 7,092 bytes • 31 expressions • 7 notes • 6 folders

Generate random vectors in R3

$\displaystyle{Z_{3}\left(t\right)=w_{3}\left(t\right)v_{3}\left(t\right)}$

Desmos JSON

Quadratic Quotient

2020/07/08 • 5,172 bytes • 35 expressions • 2 notes • 4 folders

$\displaystyle{p_{0}=\left(-\frac{1}{2D_{A}}\left(A_{11}u_{0}-A_{01}u_{1}\right),-\frac{1}{2D_{A}}\left(A_{00}u_{1}-A_{01}u_{0}\right)\right)}$

Desmos JSON

Numerical Differentiation Comparison

2020/06/28 • 7,293 bytes • 40 expressions • 6 folders

$\displaystyle{c_{x}=\frac{1}{2h}\left(F\left(x_{0}+h,y_{0}\right)-F\left(x_{0}-h,y_{0}\right)\right)}$

Desmos JSON

Ellipse Distance Lagrangian

2020/06/26 • 4,651 bytes • 19 expressions • 2 notes • 3 folders

$\displaystyle{f_{0}\left(k\right)=\frac{1}{a^{2}}\left(\frac{a^{2}x_{0}}{a^{2}-k}\right)^{2}+\frac{1}{b^{2}}\left(\frac{b^{2}y_{0}}{b^{2}-k}\right)^{2}-1}$

Desmos JSON

Trigonometric Cubic Equation (sin/sinh)

2020/06/20 • 2,731 bytes • 20 expressions • 1 note • 2 folders

Solving general cubic equations using sin/sinh triple angle property

$\displaystyle{\left(u\cdot\sin\left(\frac{1}{3}\arcsin\left(m\cdot q\right)+\frac{2\pi}{3}\right)+f,0\right)}$

Desmos JSON

Trigonometric Cubic Equation

2020/06/19 • 2,534 bytes • 15 expressions • 3 folders

$\displaystyle{\left(\sin\left(\frac{1}{3}\left(\arcsin\left(k\right)+2\pi\right)\right),0\right)}$

Desmos JSON

4th derivative simpson error estimate

2020/05/29 • 807 bytes • 4 expressions

$\displaystyle{f\left(x\right)=\arctan\left(\frac{x^{3}-3x^{2}+2x+1}{2x^{3}+x^{2}-x-2}\right)}$

Desmos JSON

Hitting the Target

2020/05/07 • 2,390 bytes • 17 expressions

$\displaystyle{c\left(h-y\cdot\frac{d}{x}-\frac{1}{2}g\cdot\frac{d^{2}}{x^{2}}\right)<0\left\{x<0\right\}}$

Desmos JSON

solve a*cos(x)+b*sin(x)=c

2020/05/02 • 1,947 bytes • 9 expressions • 4 notes

$\displaystyle{x=\arcsin\left(\frac{a\sqrt{a^{2}+b^{2}-c^{2}}+bc}{b^{2}+a^{2}}\right)}$

Desmos JSON

2D Metaballs - Snowflake

2020/04/18 • 11,071 bytes • 43 expressions • 7 notes • 4 folders

clamp a real number in [0,1]

$\displaystyle{a_{t2}\left(y,x\right)=\arctan\left(\frac{y}{x}\right)+\left\{x>0:\ 0,\ \pi\cdot\operatorname{sign}\left(y\right)\right\}}$

Desmos JSON

2D Metaballs - Coronavirus

2020/04/06 • 11,297 bytes • 46 expressions • 8 notes • 5 folders

Stay Home, Save Lives: Help Stop Coronavirus! (use the following slider to animate)

Desmos JSON

Desmos 3D (Perspective)

2020/04/05 • 12,560 bytes • 41 expressions • 10 notes • 5 folders

3D modeling and animation on Desmos. I decide to keep most of my creation process. These variables control the camera, where the camera is located at d·(cos(rz)cos(rx), sin(rz)cos(rx), sin(rx)).

Desmos JSON

Desmos 3D

2020/04/03 • 14,943 bytes • 68 expressions • 9 notes • 7 folders

3D graphing on Desmos! The following examples demonstrate how to project Planar Implicit Curve, Spacial Parametric Curve, Explicit Surface, Parametric Surface, and Implicit Surface onto a 2D plane. Camera: (cos(rz)cos(rx), sin(rz)cos(rx), sin(rx)).

Desmos JSON

Love Path

2020/04/01 • 1,152 bytes • 2 expressions

$\displaystyle{(0.0184-0.1311\cos(t)-0.03627\sin(t),0.01564+0.0455\cos(t)-0.153\sin(t))}$

Desmos JSON

Offsetting Curves

2020/03/24 • 12,109 bytes • 35 expressions • 8 notes • 9 folders

Offsetting Curves: Useful in CAD and Graphics Design. (And is quite simple)

$\displaystyle{\left(t+o\frac{e^{-t}}{\sqrt{1+e^{-2t}}},\left(e^{-t}-1\right)+o\frac{1}{\sqrt{1+e^{-2t}}}\right)}$

Desmos JSON

Fourier Series

2019/10/24 • 9,745 bytes • 59 expressions • 2 notes • 3 folders • 1 table

Drag the points, see what the graph looks like. Do you understand why most lossy image compression methods doesn't work well for simple illustrations?

Desmos JSON