Advanced C++ Programming Tutorial 4

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Why don't you sit on this and rotate? Oh you don't know how? Well allow me to elucidate. Srsly tho, rotation math is pretty damn important shit, so pay attention.


Part 1

  • Angles, degrees, radians, and π
  • Sine, cosine, and the unit circle
  • Arcsin, arccos

Part 2

  • Derivation of rotation formula: arcsin/arccos
  • Angle sum theorem (trig identity)
  • Derivation of rotation formula: angle sum theorem
  • Derivation of rotation formula: vector derivation
  • Using rotation to solve A3 homework (rotate to get plank normal)

Part 3

  • Vec2 rotation functions
  • Basic rotation of model
  • Implementing rotation into Drawable pipeline
  • Optimizing pipeline for rotation

Notes / Errata

  • In Tutorial 4.3, on screen the return statement is missing from the star generation code as shown on screen. It is added off screen.
  • The code for the animation (either end of 4.3 or end of homework), there is a member variable for time that is not initialized. This can cause sporatic problems, especially in debug mode (it often works fine in release, just depends on what happens to be in that spot in memory). This is fixed in a future video.

Video Timestamp Index

Tutorial 4.1

  • Proper definition of an angle 0:55
  • Visualization in a Unit Circle 2:00
  • Pi and its relation to a circle 5:05
  • Radians vs. Degrees 7:14
  • Trigonometry, meaning of cos & sin: from angles to coordinates 9:20
  • arcsin & arccos: from coordinates to angles 13:29
  • Extension to general (non-unit) circles 16:15
  • Rotation: the most important transformation in 3D computer graphics 18:38
  • Understanding the Star vertices generation algorithm 19:28
  • SOH-CAH-TOA 22:56

Tutorial 4.2

  • How to rotate an arbitrary point anywhere in the 2D coordinate system: three derivations 0:38
  • Derivation 1: Basic, naive SOH-CAH-TOA application 1:03
  • Derivation 2: Using Trigonometric Identities: Angle sum & difference identities 3:52
  • Derivation 3: Chili's intuitive vector derivation using the unit circle 8:56
  • Getting 2D vector normals using rotation; clockwise 90 degrees rotation 15:55

Tutorial 4.3

  • Coding a rotating star in the center of the screen 0:20
  • Clean up the solution: create new branch starfield, cherry-pick changes made in later commits in the dev branch 6:05
  • Add the Rotation transformation to the Drawable class 8:28
  • Note: rotation doesn't affect scaling; the order of these transformations doesn't matter
  • BUT: rotation DOES affect translation; the order matters: rotate first, then translate
  • Include Rotation into the Polyline rendering algorithm 10:40
  • Test drive: rotate the stars in the starfield 11:53
  • Include rotation dynamics in the Update(dt) function of the StarBro subclass 13:53
  • Optimizing the Rotation transformation calculations by avoiding unnecessary cos & sin calculations 15:38
  • Homework assignment: enable camera rotation 17:45


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


Implement rotation of the camera in the world using keyboard controls (Q and E keys for rotation).

See also