half-space methodsolid representation is based

Question

Half-space Method

Solid representation is based fundamentally on the notion that a physical object divides an n-dimensional space Eⁿ into two regions: interior and exterior, separated by object boundaries. In terms of above notion, a solid model of an object is defined mathematically as a point set S in 3-D Euclidean space (E³). 

Suppose a surface divides the whole of three-dimensional space into two distinct regions. Each such region is called a "half-space". This does NOT imply that they are equal in volume. One possible surface is the sphere denoted by the equation 

                                 X * X + Y * Y + Z * Z = 1