This short paper describes our five submissions to the 2012 edition of the MIREX Symbolic Melodic Similarity task. All five submissions rely on a geometric model that represents melodies as spline curves in the pitch-time plane. The similarity between two melodies is then computed with a sequence alignment algorithm between sequences of spline spans: the more similar the shape of the curves, th...

We present a full pipeline for computing the medial axis transform of an arbitrary 2D shape. The instability of the medial axis transform is overcome by a pruning algorithm guided by a user-defined Hausdorff distance threshold. The stable medial axis transform is then approximated by spline curves in 3D to produce a smooth and compact representation. These spline curves are computed by minimizi...

We study the problem of computing a planar curve, restricted to lie between two given polygonal chains, such that the integral of the square of arc-length derivative of curvature along the curve is minimized. We introduce the Minimum Variation B-spline problem which is a linearly constrained optimization problem over curves defined by Bspline functions only. An empirical investigation indicates...

This paper describes the development of a regular hull meshing code using cubic B-Spline curves. The discretization procedure begins by definition curves over stations, bow and stern contours plan lines. Thus, new knots are created applying an equal spaced subdivision on defined B-spline Then, these transversal space knots, longitudinal subdivided into equally too. Subsequently, knots. Finally,...

A new class of spline curves in polar coordinates has been presented in 12] and independently considered in 3]. These are rational trigonometric curves in Cartesian coordinates and can be represented as NURBS. From the relationship existing with the correspondent curves in Cartesian coordinates an alternative way to derive some useful tools for modelling splines in polar coordinates has been pr...

This is an intuitive description of some of the parametric spline formulations that are most prevalent in computer graphics. The intent is to provide a "high-level". descriptive presentation rather than a detailed, rigorous one. The specific teChniques discussed are piecewise Hermite interpolation. spline interpolation. B6zier curves. Bsplines. Beta-splines. and rational splines. The topics of ...

The matrix forms for curves and surfaces were largely promoted in CAD/CAM. In this paper we have presented two matrix representation formulations for arbitrary degree NURBS curves and surfaces explicitly other than recursively. The two approaches are derived from the computation of divided difference and the Marsden identity respectively. The explicit coefficient matrix of B-spline with equally...

In this work we bring together classical mechanism theory with recent works in the area of Computer Aided Geometric Design(CAGD) of rational motions as well as curve approximation techniques in CAGD to study the problem of mechanism motion approximation from a computational geometric viewpoint. We present a framework for approximating algebraic motions of spherical mechanisms with rational B-Sp...

A constructive approach is adopted to build B-spline like basis for cubic spline curves with a more general continuity than beta-continuity. This method provides not only a large variety of very interesting shape controls like biased, point, and interval tensions but, as a special case, also recovers a number of spline methods like nu-spline of Nielson[9], beta-splines[1], gamma-splines of Boeh...

Freeform features (FFF) manipulation is an emerging research area in geometric modelling field, which aims to develop innovative shape modification paradigms, more focused on global shape than on local curve modification. A major hindrance to FFF is given by locality properties of spline curves features representation, which forces designers to apply a direct control points manipulation, where ...