Mathematical Representation of Half-space Method:

Half-spaces form a basic representation system for bounded solids. Through combining half spaces (by using set operations) in a building block fashion, several solids may be constructed. Normally Half-spaces are unbounded geometric entities; each one divides the representation space in two infinite portions, one filled along with material and the other empty. Surfaces may be considered half-space boundaries and half-spaces may be considered directed surfaces.

A half-space is described as a regular point set in E³ as:

H = {P : P ∈ = E³   and f (P) < 0}

Here P is a point in E³ and f (P) = 0 described the surface equation of the half-space boundaries. Half-space may be combined together using set operations to make complex objects.