Advanced C++ Programming Tutorial 5

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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!


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]
  • Implementing the Matrix by Vector multiplication method 9:21
  • Testing in game.cpp 13:00
  • Implementing basic transformations in Matrix form as static functions 15:16
  • Scaling & Identity Matrices 17:13
  • Flipping the y-axis 18:01
  • Rotation 18:56
  • Testing in game.cpp 21:25
  • 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
  • Implementing a Mat3 class for (3x3) matrices 6:54
  • Implementing a Vec3 class for (3x1) vectors 8:51
  • Test run 10:48
  • 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
  • Design decision: keep working with Vec2, this requires conversion operators to and from Vec3
  • Refactoring the DrawClosedPolygon function in the Graphics class 18:03
  • Refactoring the Drawable class 19:15
  • Refactoring the Entity class 23:22
  • Refactoring the CoordinateTransformer class 24:00
  • 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 *= A yields M=MA, but we need M=AM
  • Recap & key takeaways: math is doable, mind your order of concatenation 32:12
  • Tutorial Roadmap from here on out 34:27


  • GitHub Repo (advmath)
  • Note that the code for this tutorial can be found on the <starfield> branch of the repo not in <master>


None! (or check out 3D Fundamentals you lazy fucks!)

See also