2D Game Physics Programming (Learn the Theory and the Math Behind 2D Game Physics)

This encyclopedic course, 2D Game Physics Programming, is aimed at a novice and experienced coder auditorium. We will detail the basics of mathematics and the principles behind the physics engines of some of the most popular games. Starting from vectors, matrices, and trigonometry all the way to rigid-body dynamics, collision detection, and constraints, the style of each lecture ensures that the first principles are deeply understood.

The course “2D Game Physics Programming” will allow moving from theory to practice immediately by creating a rather effective 2D physics engine based on C++ language from scratch. With only a code editor and a C++ compiler, you’ll simulate particle physics, use rigid bodies with circle, rectangle and polygon shapes, and create and manage collisions and their resolution. Thus, we shall simplify and explain the different issues in every move while recognizing the basic and fundamental concepts.

This course - 2D Game Physics Programming, is for beginners and even for professional coders in C++. Although it would be helpful to know some prerequisite programming, such as if-else statements and loops, that is not compulsory. Therefore, irrespective of whether you are coming from Java, Python, JavaScript, Swift or any other language, you must be part and parcel of how we take the secret of 2D game physics one formula at a time.

2D Game Physics Programming Table of Contents:

1. Introduction and Motivations: Enter the absorbing universe of the 2D game physics basic and find out the fundamental reasons for learning and applying. Understand the course and ways to benefit from it fully.
2. Vectors: Discover what scalars and vectors are. These are important concepts for physics in games. Utilize the P5. Review the Web Editor with JS to revise the concepts derived in the class. Then, begin coding the vectors by creating the Vec2 class in JavaScript.
3. Vector Operations: Explore the concept of vector operations further, focusing on magnitude, addition, subtraction, and scaling. Reinforce your ideas with examples and quizzes.
4. Dot Product & Cross Product: Dot and cross product are the critical elements of math that one has to apply in physics. Comprehend their uses and know how to apply specific uses in coding.
5. Vectors Normalization: The areas of vector normalization and its importance to computer physics Simulations.
6. Define coding to increase the intelligibility of the normalization method.
7. Vector Transformations: Always be in control of your scalings, translations, and rotations within the vectors. Learn trigonometry and incorporate vector rotation into your program.
8. Vectors in C++: JavaScript to C++ transition, realizing all the peculiarities of the language and its syntactic peculiarities. Start arranging your C++ project on the construction of a physics engine.
9. Starting our C++ Project: Prepare your development environment and the folder structure with the sources for using the physics engine in C++.
10. Particle Physics: First, start developing the fundamentals of your physics engine with particle physics, and learn about velocity, acceleration, and framer rate independence.
11. Simulating Movement: Search for integration techniques that can be used to continuously integrate movement in your physics engine. Explore integration, the mathematics that comes with it, and its use.
12. Applying Forces to Particles: Understand the force that acts on particles and how they move and behave under the forces exerted on them. Application functions must be forced, and various situations must be tried out in code.
13. Drag Force and Friction Force: Based on this, move onto the next level forces, such as drag and friction, which are useful in the physics of movement. Use these forces in your engine and study their impacts.
14. Gravitational Attraction: To create a force of attraction, implement the knowledge of gravitational force onto the objects and apply it to the physics engine.
15. Spring Forces: Understand spring forces in physics and how they can be used in physics simulations. Initiate the application of spring forces and try out various possibilities.
16. Rigid Body Physics: Turn on rigid body physics and learn about moments of inertia and angular motion.
17. It is advised to add primary rigid body mechanics into your engine.
18. Polygons and Vertices: You must extend your physics engine and add polygons and vertices. Identify the difference between the local and global space and perform the necessary functions.
19. Colliding Circles: Understand the collision detection of two geometrical figures, for instance, circles a, and practice detecting collisions before and after they occur.
20. Impulse and Momentum: Know how impulse and momentum work in solving collisions. Apply all these in code for the objects to have personalities that can interact realistically.
21. Colliding Boxes: There is a need to expand collision detection between objects of more complex forms, such as boxes, using an approach like SAT (Separating Axis Theorem).
22. Angular Collision Resolution: If you aim to work with angular motion and solve for collision, then this is a video for you to watch. The algorithms used should be well-directed to result in realistic collision responses.
23. Circle-Polygon Collision: Generalize the algorithms for collision detection to circles and polygons. Incorporate the algorithms for detecting these collisions and ways of handling them.
24. Displaying Textures: Display the textures to improve the appearance of your physics engine. Carry out the additions and changes in loading and rendering textures.
25. The World Class: It is recommended that one ought to organize physics simulation by the provision of a World
26. Class. Initiate other functions that are required for controlling objects and interactions within the world.
27. Engine Collision Instability: There should be changes to stability problems in confrontation resolution algorithms.
28. Research on the possible ways of enhancing the robustness of your physics engine.
29. Constraints: Add constraints to make the objects behave like joints and constraints between them. Learn about various sorts of constraints used in engines and comprehend how to integrate them.
30. Matrices and Systems: Understand matrix selections and products to deal with multiple transformations and systems of equations. You have to put into practice classes and functions needed for matrices manipulations.
31. Distance Constraint: To control the motion of objects in your physics simulation, use distance constraints. To do this, a general knowledge of how constraint-solving works is required.
32. System of Constraints: Generalize the method of constraint solving to incorporate all the constraints within the physics engine. Design sequential algorithms for solving systems of constraints.
33. Penetration Constraint: Penetration constraints help resolve penetration issues between objects. Explicit schemes for counterpenetration and stabilization must be developed.
34. Stack of Boxes: Consider use cases such as placing several boxes one on top of the other and computing the stability issue. Use the principles that would help solve real-world problems connected with multiple objects and constraints.
35. Optimization Options: Explain how you might further optimize your physics needs to enhance the engine's usage. Consider methods such as contact caching and continuous collision detection.
36. Conclusion & Next Steps: Conclude the course and bring the client up to speed about major concepts and terms explored and ideas on further learning and skill enhancement.

Who is this course for?

1. Newbie game developers are enthusiastic about understanding the 2D game physics basics from the ground up.
2. An interesting audience would be programmers who want to advance their knowledge of physics engines.
3. Game developers want to have their separate physics simulations in 

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