Subdivision Overview Subdivision is a two part process Control Mesh

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Presentation transcript:

Subdivision Overview Subdivision is a two part process Control Mesh Topological Split Averaging Subdivision is a two part process Topological split Local averaging / smoothing

Subdivision Overview Control Mesh Generation 1 Generation 2 Generation 3 Repeated uniform subdivisions of the control mesh converge to the limit surface Stationary schemes (averaging mask does not change) Limit position and normal from eigen-analysis

Bspline Surfaces A single Bspline surface patch is controlled by a regular 4x4 grid of control points

Bspline Surfaces 2 adjacent patches share 12 control points and meet with C2 continuity

Bspline Surfaces Requires regular rectangular (toroidal) control mesh to guarantee continuity (all valence-4 vertices!) Subdivision can be performed by knot insertion (i.e. blossoming)

Catmull-Clark Subdivision Surfaces Smooth surfaces for control meshes of arbitrary topology Closed control mesh  closed limit surface Quad mesh generalization of Bsplines C1 at non-valence-4 vertices, C2 every where else (Bsplines). Sharp corners can be tagged: allows for smooth and sharp features; allows for non-closed meshes.

Catmull-Clark Subdivision Gen 0 Gen 1 Gen 2 Extraordinary vertices are generated by non-valence-4 vertices & faces in the input mesh. No further extraordinary vertices are created after the first generation of subdivision.

Catmull-Clark Averaging Vn0 V20 C10 F10 En0 E40 E30 E20 Fn0 F40 F30 F20 C30 C40 Cn0 C20 NEW EDGE POINTS: NEW FACE POINTS: SMOOTHED VERTICES:

Loop Subdivision Surfaces Gen 0 Gen 1 Gen 2 NEW EDGE POINTS: