Subdivision Overview Control Mesh Topological Split Subdivision is
Subdivision Overview Control Mesh Topological Split • Subdivision is a two part process – Topological split – Local averaging / smoothing Averaging
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 4 x 4 grid of control points
Bspline Surfaces • 2 adjacent patches share 12 control points and meet with C 2 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 – C 1 at non-valence-4 vertices, – C 2 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 C 20 C 30 V 3 0 F 2 0 F 3 V 4 NEW EDGE POINTS: 0 0 F 4 0 V 2 0 E 3 0 E 4 0 V 0 0 C 10 F 1 0 E 1 0 V 1 0 NEW FACE POINTS: En 0 Fn 0 C 40 Vn 0 Cn 0 SMOOTHED VERTICES:
Loop Subdivision Surfaces Gen 0 NEW EDGE POINTS: Gen 1 Gen 2
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