Difference between revisions of "Advanced C++ Programming Tutorial 5"
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:* Be careful with Matrix multiplication operators: using the overloaded <code>operator*=()</code> is risky: | :* Be careful with Matrix multiplication operators: using the overloaded <code>operator*=()</code> is risky: | ||
:: <code>M *= A</code> yields M=MA, but we need M=AM | :: <code>M *= A</code> yields M=MA, but we need M=AM | ||
| − | * | + | * Recap & key takeaways: math is doable, mind your order of concatenation [https://youtu.be/CS4HQdQnbaA?t=32m12s 32:12] |
| − | + | * Tutorial Roadmap from here on out [https://youtu.be/CS4HQdQnbaA?t=34m27s 34:27] | |
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| − | * [https://youtu.be/CS4HQdQnbaA?t= | + | |
== Links == | == Links == | ||
Revision as of 16:05, 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
- Matrix augmentation is not just a hack, it falls in the domain of Projective Geometry 15:29
- Fix up the Starfield rendering pipeline 16:31
- Debugging session: the wrong order of transformations can mess you up 24:51
- Be careful with Matrix multiplication operators: using the overloaded
operator*=()is risky:
-
M *= Ayields M=MA, but we need M=AM
- Be careful with Matrix multiplication operators: using the overloaded
- Recap & key takeaways: math is doable, mind your order of concatenation 32:12
- Tutorial Roadmap from here on out 34:27
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!)
