search

standupmaths / xmastree2021

Code and coordinates for Matt's 2021 xmas tree
MIT License
129 stars 58 forks source link

Add conic_sections.csv and star_collision.csv #50

Open NicolasVargas11235 opened 2 years ago

NicolasVargas11235 commented 2 years ago

@oliverdunk and @thatmattparker: I have created an animation showing the tree being cut into different conic sections (circle, ellipse, parabola and hyperbola). Each part of the animation is created with the equation of a 3D plane; as the position of the plane varies, each LED position is inserted into the plane equation to determine if that LED lies below or above the plane. In other words, this determines if the LED is turned on or off. To rotate the plane, a sine and cosine factor is added to the Y and X coefficients in the plane equation. This effectively rotates the plane around the Z-axis. The animation is best viewed perpendicular to the Y,Z plane, but can be enjoyed from any angle.

I have also created an animation showing 2 neutron stars colliding into each other, producing a kilonova. This is a tribute to the first neutron star collision detection, back in 2017. Two spheres mapped in 3D space follow a pre-determined curve approximating a decaying orbit. The two jets exploding from the poles are created with growing cylinders along the z-axis. The final part of the explosion is created by mapping a torus, with both in its major and minor radius gradually expanding.

The scripts used the make these CSV files can be found in my public repositories.

d-albrecht commented 2 years ago

The conic sections are a bit low-res (nothing you can change) but still informative. I can't judge the scientific basis of the star collision but it definitely looks pretty.

NicolasVargas11235 commented 2 years ago

UPDATE: I have now also created an animation of the tree split into 5 different segments. The state of the LEDs in each segment is dictated by a travelling sine wave. Each segment begins with a sine wave having a unique phase from all other segment waves. As time passes, the phases of the sine waves are adjusted using the Kuramoto model for coupled oscillator synchronization. By the end of the animation, all segments are in phase with each other and appear to be changing as one whole segment. This was really fun to model! I hope you enjoy. If you want to take a closer look at how the animation was acheived, my c# code will be made available in my public repository.