Lesson 01 · A 2D vector you can add - Build a Physics Engine

A 2D vector you can add

A physics engine is arithmetic on 2D vectors, so that is where everything begins. Today you build the Vec2 type and its first operation, addition, so every later lesson has positions and velocities to work with.

The goal

Create a Vec2 value type with X and Y components and an addition that sums them componentwise.

Start here - the target

TO DO

Scenario: Adding two 2D vectors

Giventhe vectors {1, 2} and {3, 4}

Whenthey are added

Thenthe result is {4, 6}

AndAdd({-1, 5}, {2, -3}) is {1, 2}

Background

Every quantity in a physics engine - a position, a velocity, a force, a contact normal - is a 2D vector: a pair of numbers you can do arithmetic on. Before any of the interesting motion or collision code can exist, that value type has to exist, along with the operations that combine vectors. The most basic of those is addition, which sums the two components independently: moving a point by an offset, or combining two velocities, is just adding vectors.

Use plain float64 components so results stay exact for the clean inputs the specs use. Keep Add a pure function that returns a brand-new Vec2 rather than mutating its inputs - the rest of the engine leans on vectors being simple, copyable values, and that convention starts today.

Make it work

// the value type every position, velocity, and force will be
type Vec2 struct{ X, Y float64 }
// componentwise sum, returns a new vector
func Add(a, b Vec2) Vec2 {
  return Vec2{ /* X + X, Y + Y */ }
}

CheckpointDONE

You have a Vec2 type and can add two of them. Commit and stop here.