A discrete approach to knot removal and degree reduction algorithms for splines
Algorithms for approximation
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Scientific and Statistical Computing
On generalized cross validation for tensor smoothing splines
SIAM Journal on Scientific and Statistical Computing
ACM Transactions on Graphics (TOG)
Integrating products of B-splines
SIAM Journal on Scientific and Statistical Computing
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
The modified truncated SVD method for regularization in general form
SIAM Journal on Scientific and Statistical Computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Functional composition algorithms via blossoming
ACM Transactions on Graphics (TOG)
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
The NURBS book
Sparse Multifrontal Rank Revealing QR Factorization
SIAM Journal on Matrix Analysis and Applications
Applied numerical linear algebra
Applied numerical linear algebra
Filleting and rounding using trimmed tensor product surfaces
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Sketch- and constraint-based design of B-spline surfaces
Proceedings of the seventh ACM symposium on Solid modeling and applications
A Constraint-Based Method for Sculpting Free-Form Surfaces
Geometric Modelling
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In 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.