Lesson 19 · The convex polygon shape - Build a Physics Engine

The convex polygon shape

The general shape is a convex polygon - a list of corners wound counterclockwise. Today you build it and its bounding box, the foundation for the Separating Axis Theorem later.

The goal

Define a convex polygon by its counterclockwise vertices and compute its bounding box.

Start here - the target

TO DO

Scenario: The bounds of a convex polygon

Givena polygon with vertices {-1, -1}, {1, -1}, {1, 1}, {-1, 1} (a unit square, counterclockwise)

Whenits bounding box is computed

Thenthe box has Min {-1, -1} and Max {1, 1}

Anda triangle {0, 2}, {-1, -1}, {1, -1} has Min {-1, -1} and Max {1, 2}

Background

A convex polygon is the general shape: any triangle, rectangle, pentagon, or tilted box, stored as a list of vertices. Two conventions make the later math clean. First, keep them convex - no dents - because the Separating Axis Theorem you will use for collisions only works on convex shapes. Second, wind them counterclockwise, so that the outward-facing normal of each edge can be computed with a consistent formula in the next chapter.

The bounding box of a polygon is found by sweeping over its vertices and tracking the smallest and largest X and Y seen - the tightest upright rectangle that contains them all. Store the vertices in the shape’s own local space (centered on the origin); the center passed in offsets them into the world, and a later lesson will also rotate them by the body’s angle. For now an unrotated square from {-1, -1} to {1, 1} bounds exactly to itself.

Make it work

type Polygon struct{ Vertices []Vec2 } // counterclockwise, local space
func (p Polygon) Bounds(center Vec2) AABB {
  min, max := p.Vertices[0], p.Vertices[0]
  for _, v := range p.Vertices[1:] {
    // widen min/max to include each vertex (offset by center)
  }
  // return AABB offset by center
}

CheckpointDONE

A convex polygon knows its bounding box. Commit and stop here.