Contacts & Constraints

Your rigid bodies move. They collide. And then, they spasm, jitter, and explode into infinity.

You've mastered the first collision check. You can answer "Are they touching?" But the real question-the one that separates a tech demo from a simulation-is far more severe: "Now that they are touching, what in the world should they do?"

You're told the answer lives in a realm of soul-crushing mathematics: Linear Complementarity Problems, Jacobian matrices, and iterative solvers. That to stack a box on another box without chaos, you must first become an academic researcher.

What if you could cross the chasm from collision detection to stable, convincing simulation in the time it takes to debug one catastrophic failure?

This book is for the engineer, not the spectator. For the developer whose physics engine almost works until things rest, lean, or pile up. For the technical artist tired of slapping "mass" and "friction" values onto objects and praying. For anyone who has seen a perfectly stacked tower in a game and thought, "I need to know how that actually works."

Rigid-body dynamics isn't magic. It's applied justice. It's the system of laws you write for the moment after impact. When two shapes meet, they must negotiate: "You cannot be here. I cannot be there. So we must move, rotate, or push." An LCP is the courtroom where that negotiation is resolved fairly, without energy being created or destroyed.

We move past the abstract academic papers and show you the architect's blueprint:

1. The Contact: The crime scene. (Where, how deep, and at what angle did they penetrate?)

2. The Constraint: The law you will enforce. (Thou shalt not overlap. Thou shalt slide with this friction.)

3. The LCP: The impartial judge. (Find the forces that satisfy all laws simultaneously.)

4. The Integration: The execution of the verdict. (Apply those forces to move bodies correctly.)

That's the entire judicial system of your physical world. Everything else is due process and precedent.

• The Despair: "My boxes stack, then vibrate into the void. My ragdoll's knee spins like a propeller. I have collisions, but I don't have consequences."

• The Revelation: A guided tour through the solver's logic. Suddenly, you're not tweaking mystical damping values-you're presiding over the physics. Contact point by contact point, constraint by constraint, you learn to pass judgments that build a stable world.

Not just a library to call. You will command understanding.

When you finish, you won't see a physics engine as an impenetrable crate of compiled code. You will see a logical, stepwise process you can debug and reason.

The mystification evaporates. What remains is the rigorous, mathematical heart of convincing physical interaction-and you will have just learned how to make it beat.

This book will not shy away from the mathematics. It will translate the mathematics into machinery. It is the master key to the solver's black box. The path to advanced continuous collision, soft bodies, and fluid coupling is arduous. But you will begin that path holding the blueprint to the foundation, not just living in the house.

Stop treating physics as a force of nature. Start understanding it.