Math for Game Devs [2022, part 2] solutions for assignments 1-3

Primarily for my students at FutureGames - I will only read chat/superchats during breaks!

[Christopher-D]

My rough timestamps:
7:36 Assignment 1, Radial Trigger
43:07 Assignment 2, Bouncing Lazer/Reflecting Vectors
1:57:39 Rendering Normals that aren't Normalized
2:07:55 Assignment 3a, Transforming Local Space to World Space
2:29:03 Assignment 3b, Transforming World Space to Local Space
2:49:05 Questions

[Hasde_dfs]

This is underrated, you are making tutorials helpful enough to give people a good understanding of a subject while also showing good applications of the concepts, hidden gem.

[michalrv]

For local to world conversion I'm just adding the parent vector to the child vector and I'm getting the correct world coordinates for the child. I'm not quite sure why multiplication is needed here.

[francoperez]

1:17:45
1:22:35 (how to reflect a vector)

[andriypostelzhuk]

Wow! Wait a minute. It's not fair approach to convert from local to world space. I was wondering how is this possible to do with only knowledge of vectors, without matrices. Freya is using Transform position, right, up properties. This properties should use localToWorld matrices under the hood. This is not pure math solution.

[xhivo]

The only reason 3b was easier for me was because they are quite similar probablems and solving 3a quite manually, gave me enough insight to be able to solve 3b with trial and error. The issue here is that I still don't have good intuition on these things. I feel like sllolving more vector problems will help me with that.

[Vuecheap]

why is neccecery to calculate Dot product in worldToLocal function while rel's x and y is already same as local vector ?

[OmerFarukGonen]

3rd assignment were easier than the second.

[mibforunity]

Thank you so much for this great series.

[BomTheJohn]

Where can i download the psd file (or image) of the calculations? I want to use it as a reference.

btw It's a pity that Futuregames' educations are not online. It is impossible for me to go to Sweden to follow the training. Otherwise I would have signed up right away.

[yasasvitennety]

Hey Freya, for question 3a and 3b, I just subtracted the world space position of one point from its parent to get the local space, and added the parent's coordinates to the local space to get the world space. I did that since it's a simple offset calculation. Is my understanding of the problem not correct?

[xhivo]

I managed to do all of them, took all day can't wait to see how you did it.

[glaze]

2:16:47 I wonder if this something specific to game development as i'm not that (I'm just learning math for animations), but I can not figure out what does multiplying the basis vector by the coordinate means

[vima]

Thank you very much Freya! You are the best <3

[musicworld]

hi You can't make a patch for Uncharted game that runs on old graphics

[weltraumimport]

the interactive website doesn't work on the interactive part anymore 😭 i'm using firefox

[kono]

honestly freya's life is my dream life: Game development and math, all while surrounded by adorable cats :3

[MarvinStoker]

Thanks again for sharing knowledge! How many cats you got?

[toby]

yep im offically stupid cause i didnt get assignment 2

[alec_almartson]

Cool video. Thank you for sharing your knowledge.

I love Mathematics.

The beauty of Math, (in my personal opinion), is that it shows you how everything fits, numerically... Existence itself is governed by thousands of variables, equations (Quantum Physics, etc), that are changing and evolving every fraction of second (or frame). When I see something as beautiful as the Sunset, with all its colors... and also I remember that there is a Mathematical Truth like this behind all that, I can't help but believe that God has to exist, because this Work of Art didn't write itself alone, there must be a super Geek Artist behind this... sort of... Amazing & Beautiful Matrix... we live in.