game.github.io

WebGL RTX

• language: HTML,CSS,JavaScript,glsl
• web app list: https://jeffreymaomao.github.io/game.github.io/GRraytrace/index.html
• web : kerr BH
• web : Schwarzschild BH
• web : Flat BH

Black Hole Ray Tracing

• language: HTML,CSS,JavaScript
• ODE solver: Classical 4-stage Runge-Kutta method
• web app: https://jeffreymaomao.github.io/game.github.io/GRraytrace/index.html

Visualization of the motion of photon near by Schwarzschild black hole in 3D space, where all the photons are shooting from the camera to image plane. Here I using p5.js to render the 3D space. Using Schwarzschild metirc derive the Gravitational lensing formula

$$\cfrac{d^2u}{d\phi^2}-u = \cfrac{3GM}{c^2}u^2,\quad u=\cfrac{1}{r},$$

where the intial value is given by $u_0\left(\phi=0\right) = 1/b$. However, the photon from camera to every pixel of image have a included angle $\phi_0$, the path should be rotate by this angle to visualize this scene.

Gravitational Lensing game

• language: HTML,CSS,JavaScript
• ODE solver: Classical 4-stage Runge-Kutta method
• web app: https://jeffreymaomao.github.io/game.github.io/GRlensing/index.html

Visualization of the motion of photon near by Schwarzschild black hole. Using Schwarzschild metirc derive the Gravitational lensing formula

$$\cfrac{d^2u}{d\phi^2}-u = \cfrac{3GM}{c^2}u^2,\quad u=\cfrac{1}{r},$$

which is a non-linear ODE, and I using Classical 4-stage Runge-Kutta method to solve every photon shoot from right hand side to left hand side.

Notice that near $2.6,R_s$ is photon sphere, and the solution may easily diverge. ($R_s$ is the Schwarzschild Radius).

$$R_s = \cfrac{2GM}{c^2}$$

General Relativity Precession

• language: HTML,CSS,JavaScript/Python
• ODE solver: 1~4 stage Runge-Kutta method
• web app: https://jeffreymaomao.github.io/game.github.io/GRprecession/webGRorbit/main.html
• python app: https://jeffreymaomao.github.io/game.github.io/GRprecession/pyGRorbit/

When a planet comes into close proximity with a compact object, its orbit begins to precess, a phenomenon which can be explained by the principles of General Relativity. In the course "General Physics Experiment (I)" that I took in the second semester of sophomore year, we need to make a final project. Our group chose this phenomenon to simulate, using Python's package called VPython that we learn in this course. However, it is not convenient for those who don't have Python, also using python can not customize the UI (User Interface). After the course, I rewrite all the project into web app, so user may start this app only click the url.

In this project, the motion of planet si descibed by

$$\cfrac{d^2\vec{r}^2}{dt^2} = \cfrac{GM}{r^2}\left(1+\cfrac{6L^2}{m^2r^2c^2}\right),$$

where $\vec{r}$ is the position vector of planet, $G$ is gravitational constant, $c$ is speed of light, $M$ is the mass of compact start, $L$ is the angular momentum of compact star and $m$ is the mass of planet.

Dragable balls game

• language: HTML,CSS,JavaScript
• ODE solver: Euler method
• web app: https://jeffreymaomao.github.io/game.github.io/dragBall/index.html

In the course "General Physics Experiment (II)" that I took in the first semester of the junior year, we need to make a simple game that user can manipulate the position and motion of the ball by drag it. Therefore I wrote this simple game using some web language. In the web app, every ball following the motion described by $$\displaystyle \cfrac{d^2\vec{r}}{dt^2} = -\cfrac{b}{m} \cfrac{d\vec{r}}{dt}, \quad b>0,$$ where $\vec{r}$ is the postion vector of the ball, $m$ is the mass of the ball and $b$ is drag coefficient.

Running game

• language: HTML,CSS,JavaScript
• web app: https://jeffreymaomao.github.io/game.github.io/running/main.html

In the course "Introduction to Game Design" that I took in the second semester of my sophomore year, we need to make a final project with a simple game. The language we use in the course is Lua. However, making a web app is more convenient for user, I wrote this simple game using some web language.