## Differential Equations & Linear Algebra

Jerry Farlow, James E. Hall, Beverly H. West

Mentioned 1

For sophomore-level courses in Differential Equations and Linear Algebra. Extensively rewritten throughout, the Second Edition of this flexible text features a seamless integration of linear algebra into the discipline of differential equations. Abundant computer graphics, IDE interactive illustration software, and well-thought-out problem sets make it an excellent choice for either the combination DE/LA course or pure differential equations courses. The authors' consistent, reader-friendly presentation encourages students to think both quantitatively and qualitatively when approaching differential equations -- and reinforces concepts using similar methods to solve various systems (algebraic, differential, and iterative).

It was possible to smash those cars into pieces and even split them. While thinking about it, how did they do it? What were the basic algorithms they used? Anyone knows?

All I remember the game had a quite springy feel and that it ran well on pentium 2. Also it weren't looking like accurate at all, just fun. It was fun to scrap those cars.

I guess it was some kind of spring physics combined with some vertex collision and transformation algorithms. Could you supply me with details?

Video games physics are based on Newton's Laws of Motion.

• Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.
• The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma. Acceleration and force are vectors (as indicated by their symbols being displayed in slant bold font); in this law the direction of the force vector is the same as the direction of the acceleration vector.
• For every action there is an equal and opposite reaction.

Source

Video games physics are designed to look and feel fun, not to be 100% realistic. A mantra in graphics is If it looks good, it is good.

An undergraduate class in classical physics and differential equations will give you the tools necessary to understand some of the basic models used in video games.

Some good books to check out are:

The questioner also asked about deforming body physics. Mesh deformation is a complex subject. Some modern (i.e. more recent than Carmageddon) approaches to mesh deformation include Mesh Deformation by solving Laplace's equation with fast linear algebra solvers, such as Multigrid. The references in that paper serve as a good launching point to learn more about physics-based mesh deformation.

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