TY - JOUR
T1 - Multi-degree reduction of Bézier curves using reparameterization
AU - Chen, Xiao-Diao
AU - Ma, Weiyin
AU - Paul, Jean-Claude
PY - 2011/2
Y1 - 2011/2
N2 - L2-norms are often used in the multi-degree reduction problem of Bzier curves or surfaces. Conventional methods on curve cases are to minimize ∫01∥A(t)-C(t)∥2dt, where C(t) and A(t) are the given curve and the approximation curve, respectively. A much better solution is to minimize ∫01∥A(φ(t))- C(t)∥2dt, where A(φ(t)) is the closest point to point C(t), that produces a similar effect as that of the Hausdorff distance. This paper uses a piecewise linear function L(t) instead of t to approximate the function φ(t) for a constrained multi-degree reduction of Bzier curves. Numerical examples show that this new reparameterization-based method has a much better approximation effect under Hausdorff distance than those of previous methods. © 2010 Elsevier Ltd. All rights reserved.
AB - L2-norms are often used in the multi-degree reduction problem of Bzier curves or surfaces. Conventional methods on curve cases are to minimize ∫01∥A(t)-C(t)∥2dt, where C(t) and A(t) are the given curve and the approximation curve, respectively. A much better solution is to minimize ∫01∥A(φ(t))- C(t)∥2dt, where A(φ(t)) is the closest point to point C(t), that produces a similar effect as that of the Hausdorff distance. This paper uses a piecewise linear function L(t) instead of t to approximate the function φ(t) for a constrained multi-degree reduction of Bzier curves. Numerical examples show that this new reparameterization-based method has a much better approximation effect under Hausdorff distance than those of previous methods. © 2010 Elsevier Ltd. All rights reserved.
KW - Bzier curves
KW - L2-norm
KW - Multi degree reduction
KW - Reparameterization
UR - http://www.scopus.com/inward/record.url?scp=78651237601&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-78651237601&origin=recordpage
U2 - 10.1016/j.cad.2010.11.001
DO - 10.1016/j.cad.2010.11.001
M3 - 21_Publication in refereed journal
VL - 43
SP - 161
EP - 169
JO - CAD Computer Aided Design
JF - CAD Computer Aided Design
SN - 0010-4485
IS - 2
ER -