There are thousands of articles published on variants of splines, including least squares cubic splines. One of the first least squares articles was de Boor and Rice [1], and a comprehensive explanatory textbook is Dierckx [2]. Unfortunately, every example in the literature and on the web of a least squares cubic spline makes use of B-splines. While B-splines have a certain elegance, they are s...

In this paper a general procedure devoted to trajectory optimization is presented. This procedure is used for optimizing the trajectory of a parallel manipulator named CaPaMan (Cassino Parallel Manipulator) by using a performance criterion that includes the mechanical energy and the total traveling time. The resulting scalar objective function is then minimized. The trajectory is represented by...

We present a second order smooth filling of an n-valent Catmull-Clark spline ring with n biseptic patches. While an underdetermined biseptic solution to this problem has appeared previously, we make several advances in this paper. Most notably, we cast the problem as a constrained minimization and introduce a novel quadratic energy functional whose absolute minimum of zero is achieved for bicub...

This paper examines the role of continuity of the basis in the computation of turbulent flows. We compare standard finite elements and NURBS (non-uniform rational B-splines) discretizations that are employed in Isogeometric Analysis [23]. We make use of quadratic discretizations that are C-continuous across element boundaries in standard finite elements, and C-continuous in the case of NURBS. T...

This paper presents a new method for automatic segmentation of thermographic frontal breast images. First, the method uses a low-pass filter and the topological derivative to get a rough definition of the region of interest (ROI). Then, the previous result is used to initialize the method proposed by Marques. This method uses the adjustment of curves by Quadratic Uniform B-Splines. The efficien...

Normal Doo-Sabin subdivision surfaces are based on uniform quadratic B-splines. This makes it somewhat more difficult to produce an object with sharp creases or corners using normal Doo-Sabin subdivision. Non-Uniform Subdivision Surfaces on the other hand, allow for the possibility of creating an object that will keep specific points sharp based on the knot intervals that a particular edge is a...

The layout of the survey is as follows. After a short discussion of cardinal B-splines, i.e., of B-splines on a uniform knot sequence, in Section 2, B-splines for an arbitrary knot sequence are introduced in Section 3 and shown to be a basis for certain spaces of piecewise polynomial functions. Various simple properties of B-splines are listed in Section 4, and the relationship between a spline...