Subdivision Surfaces
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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
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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!