1. CGDD 4003 THE MATH LECTURE (BOILED DOWN, YET LIGHTLY SALTED)

2. OVERVIEW For 2D games, we use a lot of trigonometry For 3D games, we use a lot of linear algebra and 2D concepts For advanced concepts, we use a lot of calculus and 3D concepts Math is used to: Translate geometry Rotate geometry Scale geometry Calculate light Determine the position of enemies (such as their “AI”) Run physics engines (collisions)

3. TRIG YOU PROBABLY ALREADY KNOW… x (adjacent) y (opposite) h (hypotenuse) θ

4. TRIG YOU PROBABLY KNOW

5. THINGS YOU PROBABLY REMEMBER (REVIEW OF SIN AND COS)

7. ROTATING POINTS IN 2D Note: you may need to add an offset if the origin isn’t (0,0)

8. OTHER TRIG YOU SHOULD KNOW

9. INVERSE TRIG

10. QUESTION How would I describe the 2D difference in location of a player and an enemy? You Nazi-Bear-Zombie

11. QUESTION How would I describe the 2D difference in location of a player and an enemy? (x 1, y 1 ) (x 2, y 2 )

12. QUESTION How would I describe the 2D difference in location of a player and an enemy? (x 1, y 1 ) (x 2, y 2 ) Note: a very useful 2D function is atan2 (y, x) which gives you the angle!

13. 3D STUFF YOU PROBABLY ALREADY KNOW… A 3D point contains x, y and z A vertex is essentially a 3D point An edge connects two vertices Triangles are comprised of 3 vertices Scalar values are just single numbers (e.g. 1, 2, 3) We need to be able to: Translate (move) vertices Rotate vertices Scale vertices

15. OPERATIONS ON VECTORS +=

17. MAGNITUDE AND NORMALIZATION OF VECTORS

18. THE DOT PRODUCT

19. DOT PRODUCT EXAMPLE

20. DOT PRODUCT EXAMPLE 2

21. DOT PRODUCT EXAMPLE 3

22. PROJECTION Can also be used to calculate the projection of one vector onto another Length is:

23. CROSS PRODUCT (AKA THE “VECTOR” PRODUCT)

24. MATRICES

26. A FEW SPECIAL MATRICES (USED FOR ROTATION)

27. MATRIX MULTIPLICATION

32. TRANSLATION Note: the 4 th component must be a 1 for a point, but a 0 if it’s a direction!

33. SCALING

34. LINES

35. DISTANCE OF A POINT TO A LINE

36. PLANES

37. DISTANCE OF POINT TO PLANE

38. INTERSECTION OF A LINE AND PLANE (LAST SLIDE – HURRAY!)