Convex hull

A convex hull is "the smallest convex set that contains" a shape (Wikipedia: Convex hull). Picture "the shape enclosed by a rubber band stretched around" an object (Wikipedia: Convex hull); in 3D, shrink-wrap. Every dent, hole and opening in the original is filled in.

In game art, convex hulls matter because physics engines handle convex shapes far more cheaply and reliably than arbitrary triangle meshes. They are the usual building block for collision meshes that need a tighter fit than a box.

#Convex and concave

A shape is convex when a straight line between any two points inside it stays inside. A box, a sphere, a wedge and a pyramid are convex. An L-shape, an arch, a cup or a hollow box are concave. Godot's documentation states the rule: "a convex shape can only accurately represent a shape that doesn't have any concave angles (a pyramid is convex, but a hollow box is concave)" (Godot Engine documentation: Node type customization using name suffixes).

#Convex shapes in game engines

• Godot says convex collision shapes "can result in better performance" than triangle meshes for simple enough meshes, but are "generally not suited for level geometry" because of the concavity rule (Godot Engine documentation: Node type customization using name suffixes).
• Unity's Mesh Collider has a Convex option, which lets the collider "collide with other mesh colliders"; convex mesh colliders "are limited to 255 triangles" (Unity Manual: Mesh collider component reference).
• For moving objects, Unity notes that primitive colliders "can be more efficient because they offer more stability and better-performing physics simulation" (Unity Manual: Mesh collider component reference), so a convex hull is often the step between a box and an exact mesh.

#Convex decomposition

Concave objects need several hulls. Splitting a mesh into convex parts is called convex decomposition. You can do it by hand, which gives the most control, or with a tool.

V-HACD is an open-source library that "decomposes a 3D surface into a set of 'near' convex parts" (GitHub: V-HACD: Volumetric Hierarchical Approximate…). Its documentation explains the motivation: a single convex hull approximates a concave shape poorly and causes false collisions, so a decomposition gives more accurate shapes while staying fast enough for real time (GitHub: V-HACD: Volumetric Hierarchical Approximate…). Its default target of 32 hulls is, in its author's words, "often way too high" (GitHub: V-HACD: Volumetric Hierarchical Approximate…). The project is now archived, and its page recommends CoACD for new work (GitHub: V-HACD: Volumetric Hierarchical Approximate…).

Godot's -convcolonly import suffix builds collision "using convex decomposition" (Godot Engine documentation: Node type customization using name suffixes). Unreal's FBX import and Static Mesh Editor options are covered in collision meshes.

#Related terms

collision meshes · player collision capsule · manifold and non-manifold geometry · polygon and triangle budgets

#Further reading and watching