triangles - are they for you? find out in this angular journey through trigonometry

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

00:00:00 - Intro
00:01:10 - Asgmt. 4 solution (Bouncing laser)
00:09:36 - Asgmt. 5 solution (Mesh surface area)
00:30:28 - Asgmt. 6 solution (The turret)
00:44:31 - Angles
00:50:43 - Radians
01:01:47 - Cosine & sine
01:20:14 - Tangent
01:47:24 - Angle to vector
01:51:17 - Vector to angle
02:04:07 - Angle between vectors
02:25:31 - Questions 
02:31:46 - Solving triangles
02:38:48 - Camera FoV example in unity
02:52:19 - Determinant

Assignments:
Asgmt. 7 (Regular Polygons)
Asgmt. 8 (Adaptive FoV)
https://docs.google.com/document/d/1Nou1ZAbNOkELggW9YqZ9LTRIW9Hc-isUpURbQ8gjiMM

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!!

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

Trigonometry • Math for Game Devs [Part 3]

How to derive formula of the SDF of a Line Segment, a common shape in procedural modeling.
Support this channel: https://www.patreon.com/inigoquilez

Tutorials on maths , art, SDFs and computer graphics: http://iquilezles.org. The article that includes information about the Elongation operator is here (half way down the article): https://iquilezles.org/articles/distfunctions

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Soundtrack by Khrome:  https://www.facebook.com/KhromeMusic

0:00 Introduction
0:32 Math derivation
5:38 Implementation
6:12 Interpretation as Elongation 
6:53 End

The SDF of a Line Segment

It's true, so why so many wrong proofs?

There are many incorrect proofs that .999... = 1 on YouTube and elsewhere. In this video we see why all those proofs are wrong, and then demystify what is actually meant when a mathematician says .999... = 1 and I explain why it is actually true. Did your favorite math creator make one of these mistakes?

*Title only applies before the first viewing of this video and only to people who have not studied real analysis.

― mCoding with James Murphy (https://mcoding.io)

References on the standard definition of decimals and repeating decimals (please read if you are confused or unsure about the standard notation):
https://www.math.utah.edu/~bertram/courses/4030/Reals.pdf
https://people.math.sc.edu/filaseta/gradcourses/Math785/Math785Notes1.pdf
https://www.ndsu.edu/pubweb/~comez/Decimal%20expansion.pdf
http://kevincarmody.com/math/repeatingdecimals.pdf
https://amsi.org.au/teacher_modules/pdfs/Real_numbers.pdf

SUPPORT ME ⭐
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Every PROOF you've seen that .999... = 1 is WRONG

Exploring some common math that game developers use, let's look at linear interpolation and apply it to everything.

GLSL Course: https://simondev.teachable.com/p/glsl-shaders-from-scratch

Support me on Patreon: https://www.patreon.com/simondevyt

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Twitter: https://twitter.com/iced_coffee_dev
Instagram: https://www.instagram.com/beer_and_code/

In this video, I cover lerp, also known as mix in GLSL, a common mathematical function used in game dev. It's extremely versatile, and we'll go through basic uses, as well as some problems and how to overcome them.

Some easing functions to try out:
https://easings.net/
https://iquilezles.org/articles/functions/

An In-Depth look at Lerp, Smoothstep, and Shaping Functions

Support Primer on Patreon: https://www.patreon.com/primerlearning
Check out 3Blue1Brown: https://www.youtube.com/c/3blue1brown

Books that inspired this video and have more information:
- The Selfish Gene, Richard Dawkins, https://amzn.to/2LpffQl
- An Introduction to Behavioral Ecology, https://amzn.to/2YspPQz
(If you decide to buy one of these books, doing so through one of these links helps support the channel)

Thanks to supporters on Patreon, especially:
Vladimir Duchenchuk, Victor Anne, Noah Healy, Zachariah Richard Fournier, Patrick Gorrell, Jordan Scales, Jacob Maes, Kairui Wang, Josh Levent, StackAbuse.com, Marcial Abrahantes, Feimeng Zheng, Eric Helps, Sean Barker, Leonardo Kluppel, Tamas Gombkoto, Ben Kamens, Ben Komalo, Victor Moisescu, Alexander Mahone, Bjarke, Aurélien Géron, Daniel Giavedoni, Jeff, Jason Prado, Ryan Mahuron, Laura Picard, Anselm Eickhoff, Christy Serbus, 3blue1brown, Paul Straw, Roy Steves, Max Kaye, Elliot Press, ThePotatoGuy, Kevin Holesh, Talon Howitt, Mitchell Douglass, Sam Van Cise, Rikard Eide, Garrett F, Brian, Daniel Schramm, Wyatt Nelson, Mr_Chimick 

For discussion and updates
- Discord: https://discord.gg/NbruaNW
- Reddit: r/primerlearning
- Twitter: @primerlearning
- Facebook: facebook.com/primerlearning

Streaming myself working on these monstrosities:
- Twitch: https://www.twitch.tv/primerjustin

This video is presented under a Creative Commons Attribution-NonCommercial-ShareAlike License. More at:
https://creativecommons.org/licenses/by-nc-sa/4.0/

Made with Blender and python. 
- Github: https://github.com/Helpsypoo/primer

The music is "A Song of Doves and Hawks" donated by Mathieu Keith. For business inquiries: mathieu.keith@gmail.com

Several other inputs into the graphics are from public domain contributions to blendswap.com

Simulating the Evolution of Aggression

There is an interactive simulation: https://labs.minutelabs.io/evolution-simulator
And an overview video of that simulator: https://youtu.be/6nMo8T3T0L4

A few places to learn more about evolution and natural selection:
https://evolution.berkeley.edu/evolibrary/misconceptions_faq.php
https://www.khanacademy.org/science/biology/her
Any intro biology text you might have access to.

Special thanks to supporters on Patreon, especially:
Jordan Scales
Eric Helps
Ben Kamens
Ben Komalo
Christy Serbus
Sean Barker

Support Primer on Patreon: 
https://www.patreon.com/primerlearning

For discussion and updates
- Discord: https://discord.gg/NbruaNW
- Reddit: r/primerlearning
- Twitter: @primerlearning
- Facebook: facebook.com/primerlearning

Streaming myself working on these monstrosities:
- Twitch: https://www.twitch.tv/primerjustin

This video is presented under a Creative Commons Attribution-NonCommercial-ShareAlike License. More at:
https://creativecommons.org/licenses/by-nc-sa/4.0/

Made with Blender and python. 
Github: https://github.com/Helpsypoo/primer

The music is "Investigations" by Kevin MacLeod, distributed under a CC-BY license via incompetech.com.

Several other inputs into the graphics are from public domain contributions to https://www.blendswap.com.

Simulating Natural Selection

Today we are painting a landscape using mathematics.
Support this channel: https://www.patreon.com/inigoquilez
Buy this painting in a metal, canvas or photographic paper print: https://www.redbubble.com/shop/ap/39843511

This is the link to the real-time rendering code (that you can edit yourself live) for the painting: https://www.shadertoy.com/view/4ttSWf

Music by Bent Stamnes (https://twitter.com/gloom303).

Donate: http://paypal.me/inigoquilez
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Support: https://www.patreon.com/inigoquilez
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0:00 Intro
0:48 Basic Polynomial Surface (Noise)
4:12 Fractal Surface (FBM)
6:28 Key Lighting
9:15 Atmospheric Coloring
11:00 Composition and Cliffs
12:28 Light Direction
13:53 Sky
15:42 Fill Lighting
17:42 Grass
18:31 Tree Sculpting
23:53 A Story of Painting with Maths professionally
24:52 Tree  Lighting and Coloring
29:48 Highlights
32:05 Color Touchups
34:48 Clouds
40:32 Conclusion

Related articles I wrote:
* Fractal Noise Summation, also known as FBM: https://iquilezles.org/articles/fbm
* Raymarching terrains: https://iquilezles.org/articles/terrainmarching
* Rendering SDFs: https://iquilezles.org/articles/raymarchingdf
* Derivatives of Noise: https://iquilezles.org/articles/morenoise
* SDF of an Ellipsoid: https://iquilezles.org/articles/ellipsoids
* SDF Gradient: https://iquilezles.org/articles/normalsSDF
* Soft Shadows: https://iquilezles.org/articles/rmshadows

Painting a Landscape with Maths

More than you ever wanted to know about Hamilton's rule:
https://users.ox.ac.uk/~grafen/cv/oseb.pdf

For discussion and updates
- Twitter: @primerlearning
- Discord: https://discord.gg/NbruaNW
- Reddit: r/primerlearning

Plush blobs and other merch: https://store.dftba.com/collections/primer
Support these videos on Patreon: https://www.patreon.com/primerlearning

This video is presented under a Creative Commons Attribution-NonCommercial-ShareAlike License. More at:
https://creativecommons.org/licenses/by-nc-sa/4.0/

Made with Unity and Manim
https://github.com/Helpsypoo/PrimerUnity
https://www.manim.community

Music by Mathieu Keith. For business inquiries: mathieu.keith@gmail.com

Several other inputs into the graphics are from public domain contributions to blendswap.com

Made possible by support through Patreon:
abledbody
Alba Caparros-Roissard
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Angela Tam
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Ben Kamens
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Jeff
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Matt Welke
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