TY - JOUR

T1 - Blending based corner cutting subdivision scheme for nets of curves

AU - Conti, Costanza

AU - Dyn, Nira

PY - 2010/5

Y1 - 2010/5

N2 - We present a new subdivision scheme (BCC-algorithm) for constructing a surface from an initial net of 3D curves, by repeated refinements of nets of curves. This algorithm improves a subdivision scheme for nets of curves (BC-algorithm), proposed in a previous paper, which generalizes the well known Chaikin subdivision scheme refining control points. While the BC-algorithm generates continuous surfaces, the BCC-algorithm generates C1 surfaces. This is achieved by a corner cutting step following each refinement step of the BC-algorithm. The analysis of convergence, smoothness and approximation order of the BCC-algorithm is based on its proximity to the tensor-product Chaikin scheme. A short discussion of boundary rules for the BCC-algorithm is also included. Several numerical examples, illustrating the operation of the BCC-algorithm, with and without boundary rules, are presented. In the examples the advantage of the BCC-algorithm over the tensor-product Chaikin algorithm is evident.

AB - We present a new subdivision scheme (BCC-algorithm) for constructing a surface from an initial net of 3D curves, by repeated refinements of nets of curves. This algorithm improves a subdivision scheme for nets of curves (BC-algorithm), proposed in a previous paper, which generalizes the well known Chaikin subdivision scheme refining control points. While the BC-algorithm generates continuous surfaces, the BCC-algorithm generates C1 surfaces. This is achieved by a corner cutting step following each refinement step of the BC-algorithm. The analysis of convergence, smoothness and approximation order of the BCC-algorithm is based on its proximity to the tensor-product Chaikin scheme. A short discussion of boundary rules for the BCC-algorithm is also included. Several numerical examples, illustrating the operation of the BCC-algorithm, with and without boundary rules, are presented. In the examples the advantage of the BCC-algorithm over the tensor-product Chaikin algorithm is evident.

KW - Chaikin scheme

KW - Coons transfinite interpolation

KW - Corner cutting

KW - Proximity

KW - Subdivision scheme for nets of curves

UR - http://www.scopus.com/inward/record.url?scp=77949918551&partnerID=8YFLogxK

U2 - 10.1016/j.cagd.2009.12.006

DO - 10.1016/j.cagd.2009.12.006

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AN - SCOPUS:77949918551

VL - 27

SP - 340

EP - 358

JO - Computer Aided Geometric Design

JF - Computer Aided Geometric Design

SN - 0167-8396

IS - 4

ER -