We consider a problem of designing optimal smoothing spline curves using normalized uniform B-splines as basis functions. Assuming that the data for smoothing is obtained by sampling some curve with noises, an expression for optimal curves is derived when the number of data becomes infinity. It is then shown that, under certain condition, optimal smoothing splines converge to this curve as the ...

Construction of spline surfaces from given boundary curves is one of the classical problems in computer aided geometric design, which regains much attention in isogeometric analysis in recent years and is called domain parameterization. However, for most of the state-of-the-art parameterization methods, the rank of the spline parameterization is usually large, which results in higher computatio...

This paper focuses on interpolating vertices and normal vectors of a closed quad-dominant mesh1 G2continuously using regular Coons B-spline surfaces, which are popular in industrial CAD/CAM systems. We first decompose all non-quadrangular facets into quadrilaterals. The tangential and second-order derivative vectors are then estimated on each vertex of the quads. A least-square adjustment algor...

Recently, Runions and Samavati [7] proposed Partion of Unity Parametrics (PUPs), a generalization of NURBS which replaces B-spline basis functions with arbitrary Weight-Functions (WFs) while preserving affine invariance. A key problem identified by Runions and Samavati was the identification of classes of weight-functions which are well-suited to geometric modeling. In this paper, we propose a ...

We present an efficient geometric algorithm for conic spline curve fitting and fairing through conic arc scaling. Given a set of planar points, we first construct a tangent continuous conic spline by interpolating the points with a quadratic Bézier spline curve or fitting the data with a smooth arc spline. The arc spline can be represented as a piecewise quadratic rational Bézier spline curve. ...

Non-uniform basis functions for construction of interpolating and approximating spline curves and surfaces are presented. The construction is based on the theory of B-splines and enables a continuous change from interpolation to approximation of given data. It is also possible to change the tension of the curves and surfaces.

Given an m-dimensional surface Φ in R, we characterize parametric curves in Φ, which interpolate or approximate a sequence of given points p i ∈ Φ and minimize a given energy functional. As energy functionals we study familiar functionals from spline theory, which are linear combinations of L norms of certain derivatives. The characterization of the solution curves is similar to the well-known ...

Pen-input is not a new means for CAD designers, in particular, in the concept design phase. Meanwhile, B-Splines are well known curve and surface design tool in 3D shape modeling in the final modeling stages in which neat curves and surfaces should be produced. In this paper, an intuitive B-Spline design method that can be used for the CAD systems both in conceptual modeling phase and in later ...

This paper discusses a design methodology of cooperative path planning for dynamical multi-agent systems with spatial and temporal constraints. The cooperative behavior of the multi-agent systems is specified in terms of the objective function in an optimization formulation. The path of achieving cooperative tasks is then generated by the optimization formulation constructed based on a differen...

Tubular splines are like the usual spline curves, but have thickness, i.e. locally look like circular cones. They are constructed with pieces of indefinitely differentiable surfaces whose profiles are circles, which are joined together with a prescribed degree of smoothness. We consider splines constructed joining together pieces of canal surfaces bounded by circles. A canal surface is determin...