Curve network interpolation by C 1 quadratic B-spline surfaces

Abstract

Please cite this article in press as: Dagnino, C., et al. Curve network interpolation by C 1 quadratic B-spline surfaces. Comput. Aided Geom. Des. (2015), http://dx. Highlights• Interpolation of a B-spline curve network by a surface based on C 1 quadratic B-splines on criss-cross triangulations.• Proof of the existence and uniqueness of the surface and constructive algorithm for its generation.• Numerical and graphical results and comparisons with other spline methods. AbstractIn this paper we investigate the problem of interpolating a B-spline curve network, in order to create a surface satisfying such a constraint and defined by blending functions spanning the space of bivariate C 1 quadratic splines on criss-cross triangulations. We prove the existence and uniqueness of the surface, providing a constructive algorithm for its generation. We also present numerical and graphical results and comparisons with other methods.

Quadratic B-Spline Surfaces with Free Parameters for the Interpolation of Curve Networks

“…with m ≥ R and n ≥ S, respectively. As in [10] (Chapter 10) and in [15], here we suggest the following compatibility conditions to be satisfied by (1):…”

“…Starting from a so called minimal configuration [15], where a C 1 quadratic B-spline curve network is interpolated by a quadratic B-spline surface, whose knots match the curve network knots, we consider a more general approach by introducing some free parameters that provide some degree of freedom in the surface shape and that are obtained by letting some surface knots not satisfying such a match. This means that some surface knots are not network knots.…”

Bayesian curved lane estimation for autonomous driving

“…For curved lane detection, others works used more complex models such as B-Splines, parabolas, and hyperbolas Jung and Kelber (2005); Khalifa et al (2010); Timar and Alagoz (2010). Bezier curves Cimurs et al (2017) and B-Splines Li et al (2017b) are considered as relevant methods for curved lines detection, and have been configured to overcome the disadvantages of curves interpolation Dagnino et al (2015) that suffer from two main drawbacks: i) the curve is defined by a polynomial whereas it is often more interesting to have a parametric representation, and ii) high computational cost since the polynomial degree increases in proportion to the number of control points. For the same model that uses the B-splines method, the authors in Faizal and Mansor (2009); Wang et al (1999) proposed an algorithm based on the B-Snake technique.…”

Quasi-Interpolation Operators for Bivariate Quintic Spline Spaces and Their Applications

“…In 1975, Wang [5] established the so-called "smoothing cofactor-conformality method" to study the general theory on multivariate splines for any partition by using the methods of function theory and algebraic geometry. Splines have been widely applied to fields such as function approximation and numerical analysis, computer geometry, computer aided geometric design, image processing, and so on [6][7][8][9][10][11][12]. In fact, spline functions have become a fundamental tool in these fields.…”