Lecture_008_Introduction_to_Geometry

Encodings of Geometry

Challenges: can't find the best representation

• curved vs. not curved geometry

• simulate dynamic cloth, changing over time

• fluid droplets merge

• 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

Blending Irregular Shape with Distance Function

Blobby Surfaces: blend surfaces together

Explicit Encoding