LIVE coding a simple raytracer, without error messaging...
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Music by Terminal Sound System

Writing a basic raytracer

The maths behind rounding procedural shapes with SDFs. 
Support this channel: https://www.patreon.com/inigoquilez

Tutorials on maths , art, SDFs and computer graphics: http://iquilezles.org

Donate: http://paypal.me/inigoquilez
Subscribe: https://www.youtube.com/c/inigoquilez
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Soundtrack by Khrome:  https://www.facebook.com/KhromeMusic

Rounding Corners in SDFs

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:
https://www.youtube.com/watch?v=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

How Computers Draw Weird Shapes (Marching Squares)

We had a fun 3-hour discussion covering some of the basics of how a video game draws pixels on the screen, when it's a 3D renderer. There's a lot more to know than this, but it's a start!

How 3D video games do graphics.

Bézier curves - how do they do?

They're used for animation, text rendering, and all sorts of curved shapes! But how do they actually work? well, like, that's what the video is about, so, watch it to find out etc!!


• Lots of love to
💛 Jazz "queenjazz" Mickle for making the music ❱ https://queenjazz.bandcamp.com/
💙 Grant "3Blue1Brown" Sanderson for pushing me to finally do this ❱ https://youtube.com/3blue1brown
🐦 Pomax for their wonderful writeup on Bézier curves ❱ https://pomax.github.io/bezierinfo
🐈 Thor the cat for.. hanging out.. when I was trying to record audio with no interruptions
🇫🇷 French subtitles by @damqui on Twitter

• How was this video made?
🔨 Created in the Unity game engine
⭕ Using Shapes, my vector graphics plugin ❱ https://u3d.as/1W37
📈 Using Mathfs, my math library ❱ https://github.com/FreyaHolmer/Mathfs
...along with a bunch of hacky, partially broken, procedural animation tools I made specifically for this video

• Did you know that "osculating" isn't pronounced that way?
✅ yes I do now in fact please stop commenting on it ;-; ❱ https://twitter.com/FreyaHolmer/status/1429472399389507591

• Links
💖 Patreon ❱ https://www.patreon.com/acegikmo
🐦 Twitter ❱ https://twitter.com/FreyaHolmer
📺 Twitch ❱ https://www.twitch.tv/acegikmo
💬 Discord ❱ https://discord.gg/v5VWuga
🌸 Instagram ❱ https://instagram.com/freya_holmer

00:00 Intro
01:06 Use Cases of Bézier Curves
01:56 Lerp
02:34 Quadratic Béziers
03:07 Cubic Béziers
03:57 De Casteljau's Algorithm
04:25 Bernstein Polynomial Form
06:18 1st Derivative (Velocity)
07:31 Tangents & Normals
08:03 2nd Derivative (Acceleration)
08:31 3rd Derivative (Jerk/Jolt)
09:07 Curvature
11:05 Bounding Box
14:14 Arc Length
15:07 Arc Length Parameterization & Uniform Animation
19:13 Outro
19:54 Credits
23:57 Thor helping me record this at 2am

The Beauty of Bézier Curves

Welcome to my three part lecture on shader coding for game devs 💖 I hope you'll find this useful in your game dev journey!

If you are enjoying this series, please consider supporting me on Patreon!
🧡 https://www.patreon.com/acegikmo

00:00:00 - What are shaders?
00:03:00 - Case study/screenshots from FFXIV, Overwatch & more
00:37:42 - The Structure of a Shader
00:42:49 - Vertex shader
00:47:09 - Fragment shader
00:49:32 - Shader vs Material
00:51:29 - A first look at shader code
01:02:17 - Vertex Normals
01:06:17 - Interpolators
01:15:59 - Data types (fixed vs half vs float)
01:21:32 - Fragment shader output
01:24:31 - Swizzling
01:33:48 - Passing data from vertex shader to fragment shader
01:42:04 - Space transformation w. Matrices
01:47:07 - UV coordinates & manipulation
01:53:34 - Gradients
02:01:06 - Values outside of 0 to 1
02:09:20 - Triangle waves using math
02:12:04 - Preprocessor constants
02:25:28 - Pattern manipulation
02:31:48 - Blending Modes
02:39:42 - Depth buffer & depth testing (ZTest)
02:56:40 - Waves, ripples & vertex offsetting
03:12:07 - Textures
03:20:33 - World space coordinates
03:28:04 - Texture masking
03:37:33 - Isotropic mip maps
03:42:17 - Anisotropic mip maps
03:44:36 - Point vs bilinear vs trilinear filtering
03:49:54 - Final questions

Project Download & Assignments: https://docs.google.com/document/d/1h_7O9n5-q8Kb-rhnMJyF4Tab6i3lH97E4Ykn7tsP-zc

Originally streamed as a course for students at http://futuregames.se/, who were super kind to let me both stream this live as well as upload it here! so massive thanks to the people at FutureGames!!

💖 Patreon ❱ https://www.patreon.com/acegikmo
🐦 Twitter ❱ https://twitter.com/FreyaHolmer
📺 Twitch ❱ https://www.twitch.tv/acegikmo
💬 Discord ❱ https://discord.gg/v5VWuga
🌸 Instagram ❱ https://instagram.com/freya_holmer

✫ Video Production by Higher Vision:
➥ https://twitter.com/HigherVision1
➤ Edited by Stelly: https://twitter.com/stelly47050876

Shader Basics, Blending & Textures • Shaders for Game Devs [Part 1]

Welcome to the first episode in a series on creating a simple character in Blender. (http://blender.org)

Download reference images:
http://i.imgur.com/7LPDejZ.jpg (front)
http://i.imgur.com/Bjfeafn.jpg (side)

Download blender file:
http://www.blendswap.com/blends/view/77613

If you're struggling with this tutorial, try this series instead: https://youtu.be/ocLZNRasU64?list=PLFt_AvWsXl0djuNM22htmz3BUtHHtOh7v

FAQ:
Q: My background images won't show up after dragging them in.
A: Ensure that your view is properly aligned (press 1 on numpad to set view from front). You also need to be in orthographic (as opposed to perspective) view. You can toggle between ortho and perspective with 5 on the numpad. If, for whatever reason, simply dragging the images in does not work for you, you can also add them manually by pressing 'n' to open the properties panel, navigating to the 'Background Images' section near the bottom, and pressing "Add Image".

Q: Pressing the numbers only changes frame/layer.
A: You need to press the numbers on the numpad (as opposed to the top row of numbers). If your keyboard does not have a numpad, go into preferences and in the input tab check 'emulate numpad'.

If you'd like to support these videos, you can make a recurring monthly donation (cancellable at any time) through Patreon: http://bit.ly/sebPatreon
Or a once-off donation through PayPal:
http://bit.ly/SupportGamedevTutorials

Blender Character Creation: Modelling

Painting a cute little flower with mathematical formulas in Google Sheets.
Support this channel by subscribing or on Patreon: https://www.patreon.com/inigoquilez

Google Document with the flower: https://docs.google.com/spreadsheets/d/1zPtl4DpFRb-RANetrK4RrgSH-nuttDo6FdSgNiViKic/edit?usp=sharing
Tutorials on maths , art, SDFs and computer graphics: http://iquilezles.org


Donate: http://paypal.me/inigoquilez
Subscribe: https://www.youtube.com/c/inigoquilez
Support: https://www.patreon.com/inigoquilez
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Soundtrack by Khrome:  https://www.facebook.com/KhromeMusic