complex geometry with detail in scale (instancing)

volumetric shape (fury dog)

shape of protein is important characteristics

Explicit Encoding: all points are given directly (easy to find all points, relatively easy to check point belonging, hard to check 3D relation)

triangle meshes

polygon mesh

point cloud

subdivision surfaces

NURBS

Implicit Encoding (decision problem): find the best way to encode functions (hard to find all points, easy to check point belonging, easy to check 3D relation)

level set

algebraic surface

L-system

constructive solid geometry

blobby surfaces

fractals

Implicit Encoding

Algebraic Surfaces: surface is a zero set of polynomial in x, y, z.

very hard to come up with polynomial encoding with shapes in mind

Constructive Solid Geometry: building complicated shapes using boolean operations