Lesson 40 · The world and its step - Build a Physics Engine

The world and its step

A world is a bag of bodies with gravity, stepped forward together. Today you build the World and its first step, integrating every body under gravity.

The goal

Build a World that holds bodies and gravity and integrates every dynamic body one step.

Start here - the target

TO DO

Scenario: Stepping a world under gravity

Givena world with gravity {0, -10} holding a dynamic body (mass 1) at {0, 0} and a static body at {5, 0}

Whenthe world is stepped with dt = 1

Thenthe dynamic body is at velocity {0, -10}, position {0, -10} and the static body is unchanged at {5, 0}

Andgravity accelerates every dynamic body equally regardless of mass

Background

The World is the top-level object a user of the engine actually holds: a list of bodies and a global gravity. Its Step advances the whole simulation by one fixed dt, and today that means the integration loop from chapter two, now run over every body. Applying gravity as a weight force mass * gravity means the mass cancels when you divide by it to get acceleration, so every dynamic body falls at the same rate gravity - which is why a feather and an anvil drop together in a vacuum.

Static bodies are skipped entirely, so the ground stays put while everything else falls onto it. This is the walking skeleton of the engine: from here, each remaining lesson slots one more stage into Step - finding contacts, then resolving them - until a full frame runs. Right now stepping the world just drops its bodies, but that is already a runnable simulation you can print frame by frame.

Make it work

type World struct {
  Bodies  []*Body
  Gravity Vec2
}
func (w *World) Step(dt float64) {
  for _, b := range w.Bodies {
    if b.InvMass == 0 { continue } // statics never integrate
    b.ApplyForce(Scale(w.Gravity, b.Mass)) // weight = m * g, so accel = g
    b.Acceleration = b.accelerationFromForce()
    b.Integrate(dt)
    b.ClearForces()
  }
}

CheckpointDONE

A world steps all its dynamic bodies forward under gravity. Commit and stop here.