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Subdivision Surfaces: Smooth Limits of Complex Geometry, Exams of Computer Graphics

The concept of subdivision surfaces, a technique used to create smooth curves and surfaces from arbitrary control meshes. Subdivision defines a limit surface as the result of successive refinements, connecting splines and meshes. problems with NURBS patches, the concept of subdivision schemes, and specific examples like Geri's Game from Pixar. It also discusses the classification of subdivision schemes, such as Catmull-Clark and Loop, and their applications.

Typology: Exams

2021/2022

Uploaded on 09/27/2022

kataelin
kataelin 🇬🇧

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Subdivision Surfaces

Geometric ModelingGeometric

Modeling

-^

Sometimes need more than polygon meshes

-^

Sometimes

need more than polygon meshes

  • Smooth surfaces
    • Traditional geometric modeling used NURBS

N

if^

ti^

l B S li

  • Non uniform rational B-Spline– Demo

SubdivisionSubdivision “Subdivision defines a smooth curve or surface asSubdivision defines a smooth curve or surface as

the limit of a sequence of successiverefinements”refinements

Subdivision SurfacesSubdivision

Surfaces

•^

Generalization of

spline

curves / surfaces

•^

Generalization

of spline curves / surfaces

  • Arbitrary control meshes– Successive refinement (subdivision)– Converges to smooth limit surface

g

  • Connection between splines and meshes

5

Example: Geri

’s Game (Pixar)

•^

Subdivision used for

Example: Geri s Game (Pixar) •^

Subdivision

used for

  • Geri’s hands and head – Clothing– Tie and shoes

Example: Geri

’s Game (Pixar)

Example: Geri s Game (Pixar)^ Woody’s hand (NURBS)

Geri’s hand (subdivision) 8

Example: GamesExample:

Games

Supported in hardware in DirectX Supported

in hardware in DirectX 11

10

Subdivision CurvesSubdivision

Curves

Given a control polygon...Given

a control polygon...

...find a smooth curve related to that polygon.

ApproximatingApproximating

ApproximatingApproximating

Splitting step: split each edge in two

ApproximatingApproximating Start over ...Start

over ...

ApproximatingApproximating^ ...splitting......splitting...

ApproximatingApproximating ...and so on......and

so on...

ApproximatingApproximating

If the rule is designed carefully...If

the rule is designed carefully...

... the control polygons will converge to a

smooth limit curve!smooth limit curve!