![]() The error (amount of overlap) for each pair will hopefully be reduced after each iteration, and eventually both equations will be simultaneously satisfied. Repeat – iterate– the process of solving both equations a fourth, and maybe a fifth time. Hoping to improve things a bit more, we can solve A vs C a third time, and that will of course force us to solve B vs C a third time too. But don’t give up just yet! Maybe they will overlap a little bit less than the first time. Guess what? solving B vs C will probably make A and C overlap again. But wait… as a result, B vs C overlap again! Should we try solving B vs C a second time…? Nice, A and C no longer overlap, just like the first time we solved A vs C. ![]() We’ll just solve A vs C again and hope for the best. Solving B vs C ruined our initial solution for A vs C, because both adjusted C in different ways and they overlap again! Ok, keep calm. This causes B and C to have their positions slightly adjusted to avoid the collision. However this causes C to sink a little bit deeper into B. This moves both A and C (by calculating penalty forces, impulses, or any other means) so that they no longer overlap each other. This generates two contact constraints, that is, two equations: A vs C and B vs C. Suppose you have two bodies ( A and B) overlapping -colliding- with a third one ( C). The naive iterative solver (which is actually very good). Iterative solvers have a number of advantages that make them widely used for interactive/realtime physics, so we will focus on them. Most literature you can find on the subject is pretty mathy, so I will try to stick to plain english here. Direct solvers are more accurate but slower. ![]() Roughly speaking there are two main categories of solvers: direct and iterative. ![]() And if all we have is just one constraint, finding a body configuration that meets the condition imposed by the constraint is relatively easy.Īs soon as multiple constraints affect the same body, we have multiple equations with shared unknowns that must be simultaneously satisfied. Most constraints used in games (of which collisions are just one kind) involve two bodies: hinges, telescopic joints, ball-and-socket joints, etc. Solve the equation, and you know what to do to enforce the constraint. All kinds of constraints can be, in fact. Solvers are an integral part of any physics engine, so much that oftentimes the term is used to refer to the entire engine.īut why would we want to solve a system of equations, in the first place? Well, as we saw in part #2, a collision between two rigidbodies can be expressed as an equation. The term “solver” in the physics simulation realm usually refers to an algorithm devised to solve (hence their name) a problem, usually expressed as a system of equations. ![]()
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