A new method using the cubic B-spline curves with nominal uniform knot set to parameterize the geometry is proposed to deal with shape optimization problems. In the method, the control points of the B-spline curves are set to be the design variables in the optimization scheme. A knot insertion algorithm has been introduced in order to keep the geometry unchanged whilst increasing the number of ...

The shape reconstruction of a 3D object from its 2D crosssections is important for reproducing it by NC machining or rapid prototyping. In this paper, we present a method of surface approximation to cross-sections with multiple branching problems. In this method, we first decompose each multiple branching problem into a set of single branching problems by providing a set of intermediate contour...

PH curves; B-spline curves; Nodal points; CNC interpolators; Variable feedrate control; Contour error. Abstract This paper presents a C2 Pythagorean-Hodograph (PH) spline curve interpolator for high speed contouring applications. With the knot vector and control points given, the C2 PH quintic spline curve is a ‘‘good’’ interpolant to the nodal points of the cubic B-spline curve, with the same ...

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Characterization of explosive volcanic eruptive processes from interpretation of deposits is a key for assessing volcanic hazard and risk, particularly for infrequent large explosive eruptions and those whose deposits are transient in the geological record. While eruption size-determined by measurement and interpretation of tephra fall deposits-is of particular importance, uncertainties for suc...

In this paper we present a method which tries to automatically represent the designer’s intention while sketching threedimensional curves in a Virtual Reality environment. We translate conceptual sketch strokes into a suitable B-spline representation with a three step method. Firstly a data filter is used to eliminate redundancy and noise in ‘pen’ position recorded by the 3D tracking system. Se...

In this paper, a high-order method for solving the Schrodinger equation is introduced. We apply a compact finite difference approximation for discretizing spatial derivatives and we use the C-cubic spline collocation method for the time integration of the resulting linear system of ordinary differential equations. The proposed method has fourth-order accuracy in both space and time variables. W...

This paper generalizes the classical cubic spline with the construction of the cubic spline coalescence hidden variable fractal interpolation function (CHFIF) through its moments, i.e. its second derivative at the mesh points. The second derivative of a cubic spline CHFIF is a typical fractal function that is self-affine or non-self-affine depending on the parameters of the generalized iterated...

In the present study, we derive a new B-spline technique namely trigonometric B-spline collocation algorithm to solve some initial boundary value problems for the nonlinear Klein-Gordon equation. In order to carry out the time integration with Crank-Nicolson implicit method, the order of the equation is reduced to give a coupled system of nonlinear partial differential equations. The collocatio...