2021-11-05

[public] 6.31K views, 13.5K likes, 7.00 dislikes audio only

Reducible

In this video, we start with an interesting animation of blobby objects which we introduce as metaballs. There's a lot of surprisingly intricate ideas behind making these objects render on a screen. We'll see how folks in computer graphics attempted to solve this problem through a really elegant algorithm called marching squares. Marching squares is a really powerful algorithm that allows you to render any implicit function. But what's even more impressive in my opinion is the many clever shifts in perspective that allowed a vague problems such as this one to be transformed into a clear, well-defined, and solvable problem.

0:00 Introduction

3:29 Circles and Ellipses

4:57 Defining the Problem

6:00 A Guessing Game

8:29 Contours around Two Points

10:35 Sampling The Space

12:32 Breaking Down Cases

15:00 A Clever Optimization

17:20 How Marching Squares Works

18:59 Parallel Marching Squares

20:21 How Do Metaballs Work?

24:59 Marching Cubes

25:58 Some Parting Thoughts

References/Additional Resources:

http://jamie-wong.com/2014/08/19/metaballs-and-marching-squares/ - the initial inspiration for the framework of this video, great introduction to metaballs and how they can be rendered using marching squares.

http://www.geisswerks.com/ryan/BLOBS/blobs.html - great resource on implementing metaballs and some of the physics inspirations behind implicit functions

Original Marching cubes paper: https://www.researchgate.net/publication/202232897_Marching_Cubes_A_High_Resolution_3D_Surface_Construction_Algorithm

Sebastian Lague Video on Marching Cubes:

/youtube/video/M3iI2l0ltbE

Further reading on polynomial approximations of metaball implicit functions:

https://www.researchgate.net/publication/242914163_Data_Structure_for_Soft_Objects

Implementation Help for Marching Cubes

http://paulbourke.net/geometry/implicitsurf/

Excellent lecture by Casey Muratori about Marching Cubes: https://www.youtube.com/watch?v=SDS5gLSiLg0&t=978s

https://courses.lumenlearning.com/physics/chapter/19-4-equipotential-lines/ - some of the physics behind equipotential lines in electric fields

Support: https://www.patreon.com/reducible

Twitter: https://twitter.com/Reducible20

This video wouldn't be possible without the open source library manim created by 3blue1brown and maintained by Manim Community.

The Manim Community Developers. (2021). Manim – Mathematical Animation Framework (Version v0.11.0) [Computer software]. https://www.manim.community/

Here is link to the repository that contains the code used to generate the animations in this video: https://github.com/nipunramk/Reducible

All music in the video is from Aakash Gandhi