TY - JOUR
T1 - Loop subdivision surfaces interpolating B-spline curves
AU - Ma, Weiyin
AU - Wang, Huawei
PY - 2009/11
Y1 - 2009/11
N2 - This paper presents a novel method for defining a Loop subdivision surface interpolating a set of popularly-used cubic B-spline curves. Although any curve on a Loop surface corresponding to a regular edge path is usually a piecewise quartic polynomial curve, it is found that the curve can be reduced to a single cubic B-spline curve under certain constraints of the local control vertices. Given a set of cubic B-spline curves, it is therefore possible to define a Loop surface interpolating the input curves by enforcing the interpolation constraints. In order to produce a surface of local or global fair effect, an energy-based optimization scheme is used to update the control vertices of the Loop surface subjecting to curve interpolation constraints, and the resulting surface will exactly interpolate the given curves. In addition to curve interpolation, other linear constraints can also be conveniently incorporated. Because both Loop subdivision surfaces and cubic B-spline curves are popularly used in engineering applications, the curve interpolation method proposed in this paper offers an attractive and essential modeling tool for computer-aided design. © 2009 Elsevier Ltd. All rights reserved.
AB - This paper presents a novel method for defining a Loop subdivision surface interpolating a set of popularly-used cubic B-spline curves. Although any curve on a Loop surface corresponding to a regular edge path is usually a piecewise quartic polynomial curve, it is found that the curve can be reduced to a single cubic B-spline curve under certain constraints of the local control vertices. Given a set of cubic B-spline curves, it is therefore possible to define a Loop surface interpolating the input curves by enforcing the interpolation constraints. In order to produce a surface of local or global fair effect, an energy-based optimization scheme is used to update the control vertices of the Loop surface subjecting to curve interpolation constraints, and the resulting surface will exactly interpolate the given curves. In addition to curve interpolation, other linear constraints can also be conveniently incorporated. Because both Loop subdivision surfaces and cubic B-spline curves are popularly used in engineering applications, the curve interpolation method proposed in this paper offers an attractive and essential modeling tool for computer-aided design. © 2009 Elsevier Ltd. All rights reserved.
KW - Cubic B-spline curve
KW - Curve-based surface design
KW - Loop subdivision surface
KW - Minimum energy surface
KW - Surface interpolation
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U2 - 10.1016/j.cad.2009.03.011
DO - 10.1016/j.cad.2009.03.011
M3 - 21_Publication in refereed journal
VL - 41
SP - 801
EP - 811
JO - CAD Computer Aided Design
JF - CAD Computer Aided Design
SN - 0010-4485
IS - 11
ER -