Lesson 35 · Positional correction - Build a Physics Engine

Positional correction

Impulses fix velocities but leave bodies slightly sunk into each other, and that error accumulates. Today you push overlapping bodies apart directly, with a slop margin so resting stacks stay calm.

The goal

Move two overlapping bodies apart along the normal by a fraction of the penetration, ignoring a small slop.

Start here - the target

TO DO

Scenario: Nudging sunk bodies apart

Givenbody A at {0, 0} and body B at {1.5, 0}, both inverse mass 1, a manifold with normal {1, 0} and penetration 0.5 (slop 0.05, correction 40 percent)

Whenpositional correction is applied

ThenA moves to {-0.09, 0} and B moves to {1.59, 0}

Andif the penetration is only 0.03 (below the slop) neither body moves

Background

The velocity solver stops bodies approaching, but it never removes the overlap that has already happened, so bodies gradually sink into each other and into the floor. The fix is positional correction: move the two bodies apart along the contact normal by a fraction of the penetration, split by inverse mass just like an impulse (a static body, inverse mass zero, stays put and the dynamic one takes the whole move).

Two constants keep it stable. The slop is a small penetration you deliberately tolerate - correcting all the way to zero every frame makes resting stacks vibrate, so overlaps below the slop are left alone (which is why penetration 0.03 produces no motion here). The percent corrects only a fraction each frame, easing the error out over several steps instead of snapping and overshooting. With penetration 0.5, slop 0.05, and 40 percent split two ways, each body moves 0.09. This runs after the velocity resolve, every contact, every frame.

Make it work

const slop, percent = 0.05, 0.4
func CorrectPositions(a, b *Body, m Manifold) {
  // scalar = max(penetration - slop, 0) * percent / (imA + imB)
  corr := math.Max(m.Penetration-slop, 0) * percent / (a.InvMass + b.InvMass)
  push := Scale(m.Normal, corr)
  a.Position = Sub(a.Position, Scale(push, a.InvMass))
  b.Position = Add(b.Position, Scale(push, b.InvMass))
}

CheckpointDONE

Overlapping bodies are nudged apart along the normal, with a slop margin. Commit and stop here.