Lesson 22 · Circle versus circle - Build a Physics Engine

Circle versus circle

Collision detection has to answer two things at once - are these touching, and if so which way and how deep? Today you build the contact manifold and the simplest test, circle versus circle.

The goal

Detect overlap between two circles and return a contact manifold with the normal and penetration depth.

Start here - the target

TO DO

Scenario: Two circles overlapping

Givena circle of radius 1 at {0, 0} and a circle of radius 1 at {1.5, 0}

Whenthey are tested for collision

Thenthey collide with normal {1, 0} and penetration 0.5

Andradius-1 circles at {0, 0} and {3, 0} do not collide, and two coincident circles report normal {1, 0} with penetration 2

Background

Every collision test in the engine returns the same little package of facts, the contact manifold: did the shapes overlap, and if so, the normal (the unit direction to separate them, pointing from A toward B) and the penetration (how far they overlap along that normal). Resolution consumes exactly these two numbers, so getting the manifold right is the whole game.

Circle versus circle is the cleanest case. Measure the distance between centers; if it is less than the sum of the radii they overlap, the penetration is that shortfall, and the normal is the direction from one center to the other. Pin the edges: circles just touching or fully apart do not collide, and two circles at the exact same point have no real direction - guard that zero distance and return a fixed fallback normal {1, 0} so the manifold is never poisoned by a divide by zero. That coincident case is rare but real, and handling it now keeps the resolver safe.

Make it work

type Manifold struct {
  Collision   bool
  Normal      Vec2    // unit vector from A toward B
  Penetration float64 // overlap depth
}
func CircleVsCircle(ca Vec2, ra float64, cb Vec2, rb float64) Manifold {
  d := Sub(cb, ca)
  dist := Length(d)
  if dist >= ra+rb { return Manifold{} } // no overlap
  // normal from A to B (guard dist==0), penetration = (ra+rb) - dist
}

CheckpointDONE

Two circles report whether, how deep, and in which direction they collide. Commit and stop here.