An arbitrarily shaped but simply connected 3D closed surface can be described by three spherical functions x(θ, φ), y(θ, φ), and z(θ, φ) based on an underlying spherical parameterization (i.e., a bijective mapping between (x, y, z) and (θ, φ)): (A) A sample object surface (i.e., a bowl), (B) its mesh representation, (C) its spherical parameterization, and (D–F) three spherical functions that describe the bowl. Colored dots show the mappings among the object surface, the parameterization, and the three spherical functions.