A Swift Introduction to Projective Geometric Algebra
This video is an introduction to Projective Geometric Algebra, which is a flavor of geometric algebra that allows for manipulating objects like points, lines, and planes, including operations like meets, joins, projections, and rigid transformations. This is done by treating lines/planes as their own linear space and doing geometric algebra on it. PGA provides a simple and powerful framework to do dimension-independent geometry.
In case you were curious, this is finally the big project I’ve been teasing several times on my channel. It’s also my #SoME3 submission.
Here’s my video on the linear space of lines:
In case you don’t really know anything about geometric algebra, here are three videos of mine that I would suggest:
(My original introduction)
(The addendum to the introduction)
(The general definition of all of the operations used in this video)
Here are some links to other introductions of PGA that might be useful/interesting:
(The first resource that I saw that takes the “Rigid Transformations“ approach to PGA)
(A playlist that covers PGA in a similar manner to the previous video but goes in more detail, and it culminates in describing rigid body dynamics)
(One of the first sources to describe PGA, and it uses projective geometry)
I would link to sources for the applications shown at the end, but you can find sources for most of them at , so you can just go there instead.
The notes got too big to fit in the description, so I moved them to a pinned comment.
Discord:
Patreon:
Patreon Supporters:
Christoph Kovacs
David Johnston
Jason Killian
LoganMP
p11
Richard Penner
Rosario
trb
Sections:
00:00 Introduction
02:15 The Linear Space of Lines
07:04 Basic Definition of 2D PGA
09:43 2D PGA Bivectors/2D Meets
13:47 2D PGA Points
14:57 More 2D Meets
16:15 2D Joins
17:50 2D Inner Product
19:35 2D Projections
21:51 2D Reflections
24:16 2D Rigid Transformations
26:27 2D Rigid Transformations on Points
28:03 2D Bivector Exponentials
31:16 2D Rigid Transformations Without PGA
32:54 2D Summary
33:27 3D Introduction
36:13 The Linear Space of Planes
37:32 Basic Definition of 3D PGA
38:07 3D PGA Bivectors and Trivectors
41:08 3D Meets
42:30 3D Joins
43:59 3D Inner Product
47:03 3D Projections
49:00 3D Rigid Transformations
49:46 3D Summary
50:25 nD PGA
50:54 Demonstration
52:10 Applications
1 view
483
110
1 month ago 00:02:32 4
26 ноября 2024 г.
1 month ago 00:00:00 1
La puntata più difficile - TeleRagione
1 month ago 00:36:53 1
Roberto Germano: Oxhy un’altra economia
2 months ago 00:59:24 1
Владимир Боглаев. “Ну если ВСЕ молчат, ТО Я СКАЖУ.“
2 months ago 00:05:38 1
Elezione Trump: subito 4 fatti positivi. Il programma Trump. Mons. Viganò: battuta d’arresto per NWO
2 months ago 02:23:35 1
Le plus grand come-back de l’histoire politique américaine ! | En direct avec Idriss Aberkane
2 months ago 00:11:19 1
В упор из танков и РПГ: Разгром огромной колонны РФ под Угледаром
2 months ago 00:44:11 1
Политик из США Пинкус. Сенсация от Ермака, переговоры Зеленского с Путиным, что спасет Украину
2 months ago 00:31:10 1
Riassunto di Kazan
2 months ago 00:04:46 1
Fab - All Good Things (Come to an End) [Nelly Furtado cover]
2 months ago 00:25:20 1
Visa and Swift Don’t Work in Russia. This Is What They Use Instead
2 months ago 00:03:25 1
This Age of Z Origins Hack/Mod is INSANE! How I Got Unlimited AOZ Coins & Gold - Android & iOS
2 months ago 00:55:56 1
In memoria di un grande italiano - TeleRagione
2 months ago 00:19:09 1
The Cult Of Taylor Swift
2 months ago 00:15:48 11
Kickstart 2 By Nicky Romero And Cableguys Review And Demo (Plus A Giveaway!!!)
2 months ago 00:28:22 12
Harmonica Blues by Indiara Sfair - Parte 2 - (@IndiaraSfair)
2 months ago 00:43:33 1
Роберт Адамс - Три мудрости. Сатсанг | Аудиокнигa | Адвайта | NikOsho
2 months ago 00:38:01 1
МЕДИАФРЕНИЯ-106. ИЗДЕРЖКИ УСТАЛОСТИ ЛЖИ
2 months ago 00:01:56 25
Shri Damodarashtakam - Pop Version | SUNIDHI AL RADHA #bhajan #devotionalsongs #krishnabhajan
2 months ago 00:02:16 1
WYR GEMI - Juno
2 months ago 00:00:00 1
BRICS VS OCCIDENT : COMPRENDRE LE CHANGEMENT RADICAL DU MONDE | FRÉDÉRIC MOURAUD | GPTV
2 months ago 00:45:39 1
Владимир Боглаев на канале Точка сборки: Фиатные деньги- инструмент оккупации.
2 months ago 01:02:47 1
URGENT🚨 POUTINE : LE MONDE MULTIPOLAIRE EST UNE RÉALITÉ, LA SOUVERAINETÉ DE LA RUSSIE RETROUVÉE !!!
2 months ago 00:04:47 1
ATTENZIONE !!!!CITTADINO DEL MALI OSPITATO IN ITALIA CHE CHIEDE DI ITALIANI