TY - JOUR
T1 - Spline curve approximation and design by optimal control over the knots
AU - Goldenthal, R.
AU - Bercovier, M.
PY - 2004
Y1 - 2004
N2 - In [1] Optimal Control methods over re-parametrization for curve and surface design were introduced. The advantage of Optimal Control over Global Minimization such as in [16] is that it can handle both approximation and interpolation. Moreover a cost function is introduced to implement a design objective (shortest curve, smoothest one etc...). The present work introduces the Optimal Control over the knot vectors of non-uniform B-Splines. Violation of Schoenberg-Whitney condition is dealt naturally within the Optimal Control framework. A geometric description of the resulting null space is provided as well.
AB - In [1] Optimal Control methods over re-parametrization for curve and surface design were introduced. The advantage of Optimal Control over Global Minimization such as in [16] is that it can handle both approximation and interpolation. Moreover a cost function is introduced to implement a design objective (shortest curve, smoothest one etc...). The present work introduces the Optimal Control over the knot vectors of non-uniform B-Splines. Violation of Schoenberg-Whitney condition is dealt naturally within the Optimal Control framework. A geometric description of the resulting null space is provided as well.
KW - Curve fitting
KW - Interpolation
KW - Knot vector placement
KW - Optimal control
KW - Schoenberg-whitney condition
UR - http://www.scopus.com/inward/record.url?scp=2542491275&partnerID=8YFLogxK
U2 - 10.1007/s00607-003-0046-y
DO - 10.1007/s00607-003-0046-y
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AN - SCOPUS:2542491275
SN - 0010-485X
VL - 72
SP - 53
EP - 64
JO - Computing (Vienna/New York)
JF - Computing (Vienna/New York)
IS - 1-2
ER -