Constraint-based Design of B-spline Surfaces from Curves

dc.contributor.authorMichalik, P.en_US
dc.contributor.authorBruderlin, B. D.en_US
dc.contributor.editorGershon Elber and Nicholas Patrikalakis and Pere Bruneten_US
dc.date.accessioned2016-02-17T18:02:46Z
dc.date.available2016-02-17T18:02:46Z
dc.date.issued2004en_US
dc.description.abstractIn this paper we describe the design of B-spline surface models by means of curves and tangency conditions. The intended application is the conceptual constraint-driven design of surfaces from hand-sketched curves. The solving of generalized curve surface constraints means to find the control points of the surface from one or several curves, incident on the surface, and possibly additional tangency and smoothness conditions. This is accomplished by solving large, and generally under-constrained, and badly conditioned linear systems of equations. For this class of linear systems, no unique solution exists and straight forward methods such as Gaussian elimination, QR-decomposition, or even blindly applied Singular Value Decomposition (SVD) will fail. We propose to use regularization approaches, based on the so-called L-curve. The L-curve, which can be seen as a numerical high frequency filter, helps to determine the regularization parameter such that a numerically stable solution is obtained. Additional smoothness conditions are defined for the surface to filter out aliasing artifacts, which are due to the discrete structure of the piece-wise polynomial structure of the B-spline surface. This leads to a constrained optimization problem, which is solved by Modified Truncated SVD: a L-curve based regularization algorithm which takes into account a user defined smoothing constraint.en_US
dc.description.sectionheadersBoolean Operations and Designen_US
dc.description.seriesinformationSolid Modelingen_US
dc.identifier.doi10.2312/sm.20041392en_US
dc.identifier.isbn3-905673-55-Xen_US
dc.identifier.issn1811-7783en_US
dc.identifier.pages213-223en_US
dc.identifier.urihttps://doi.org/10.2312/sm.20041392en_US
dc.publisherThe Eurographics Associationen_US
dc.subjectI.3.5 [Computer Graphics]en_US
dc.subjectSplinesen_US
dc.subjectG.1.2 [Approximation]en_US
dc.subjectSpline and piecewise polynomial approximationen_US
dc.subjectG.1.3 [Numerical Linear Algebra]en_US
dc.subjectLinear systems (direct and iterative methods)en_US
dc.titleConstraint-based Design of B-spline Surfaces from Curvesen_US
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