Difference between revisions of "Advanced C++ Programming Tutorial 5"
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* Translation: why is it a complicated transformation? [https://youtu.be/CS4HQdQnbaA?t=0m14s= 0:14] | * Translation: why is it a complicated transformation? [https://youtu.be/CS4HQdQnbaA?t=0m14s= 0:14] | ||
* Trick: augment the matrix (add an extra dimension) [https://youtu.be/CS4HQdQnbaA?t=3m11s 3:11] | * Trick: augment the matrix (add an extra dimension) [https://youtu.be/CS4HQdQnbaA?t=3m11s 3:11] | ||
| − | * Implementing a <code>Mat3</code> class for (3x3) matrices [https://youtu.be/CS4HQdQnbaA?t=6m54s 6:54] | + | * Coding this into the framweork [https://youtu.be/CS4HQdQnbaA?t=6m54s 6:54] |
| − | * Implementing a <code>Vec3</code> class for (3x1) vectors [https://youtu.be/CS4HQdQnbaA?t=8m51s 8:51] | + | :* Implementing a <code>Mat3</code> class for (3x3) matrices [https://youtu.be/CS4HQdQnbaA?t=6m54s 6:54] |
| − | * [https://youtu.be/CS4HQdQnbaA?t= | + | :* Implementing a <code>Vec3</code> class for (3x1) vectors [https://youtu.be/CS4HQdQnbaA?t=8m51s 8:51] |
| + | :* Test run [https://youtu.be/CS4HQdQnbaA?t=10m48s 10:48] | ||
| + | * The order of applying transformations and its relation to Matrix multiplication (concatenation) [https://youtu.be/CS4HQdQnbaA?t=12m09s 12:09] | ||
| + | :* The order in which you concatenate matrices matters: ABC != CBA | ||
| + | :* The sequence of applying transformations reads from right to left in Matrix multiplication | ||
| + | ::- T = CBA means transformation A is applied first, then B, then C | ||
| + | :* Demo of this principle in debug mode [https://youtu.be/CS4HQdQnbaA?t=14m19s 14:19] | ||
| + | |||
* [https://youtu.be/CS4HQdQnbaA?t=ms :] | * [https://youtu.be/CS4HQdQnbaA?t=ms :] | ||
* [https://youtu.be/CS4HQdQnbaA?t=ms :] | * [https://youtu.be/CS4HQdQnbaA?t=ms :] | ||
Revision as of 15:44, 18 April 2020
Hot take: the Matrix is a mediocre film at best. It's a pretty great way to encode transformations though, so let's matrix it up!
Contents
Topics
Part 1
- Matrix form
- Matrix by vector multiplication
- Matrix encoding of scaling, rotation, and flipping
- Matrix multiplication
- Concatenating matrix transforms
Part 2
- Augmented 3x3 matrix for encoding translations
- Matrix multiplication order matters!
- Porting pipeline to use matrix transforms
- Bug hunting!
Video Timestamp Index
Tutorial 5.1
- Matrices: what are they, what are they good for? 0:44
- Basic Matrix operations: Matrix by Vector multiplication 3:05
- Creating a templated
_Mat2<T>Matrix class 7:16
- Matrix data stored as 2D array
T arr[2][2]
- Matrix data stored as 2D array
- Implementing the Matrix by Vector multiplication method 9:21
- Testing in
game.cpp13:00 - Implementing basic transformations in Matrix form as static functions 15:16
- Testing in
game.cpp21:25 - Basic matrix operations: Matrix multiplication 23:06
- Implementing & testing the Matrix multiplication method 25:52
- Recap: concatenating transformations by multiplying transformation matrices 30:10
- This is the beauty of matrix operations: one single concatenated matrix holds all the transformation information
- Concatenating matrices cuts down the number of vector operations needed at runtime
- What about translation? 31:20
Tutorial 5.2
- Translation: why is it a complicated transformation? 0:14
- Trick: augment the matrix (add an extra dimension) 3:11
- Coding this into the framweork 6:54
- The order of applying transformations and its relation to Matrix multiplication (concatenation) 12:09
- The order in which you concatenate matrices matters: ABC != CBA
- The sequence of applying transformations reads from right to left in Matrix multiplication
- - T = CBA means transformation A is applied first, then B, then C
- Demo of this principle in debug mode 14:19
Links
- GitHub Repo (advmath)
- Note that the code for this tutorial can be found on the <starfield> branch of the repo not in <master>
Homework
None! (or check out 3D Fundamentals you lazy fucks!)
