A discrete methodology for controlling the sign of curvature and torsion for NURBS

This paper develops a discrete methodology for approximating the so-called convex domain of a NURBS curve, namely the domain in the ambient space, where a user-specified control point is free to move so that the curvature and torsion retains its sign along the NURBS parametric domain of definition. The methodology provides a monotonic sequence of convex polyhedra, converging from the interior to the convex domain. If the latter is non-empty, a simple algorithm is proposed, that yields a sequence of polytopes converging uniformly to the restriction of the convex domain to any user-specified bounding box. The algorithm is illustrated for a pair of planar and a spatial Bézier configuration

Ship-hull shape optimization with a T-spline based BEM-isogeometric solver

In this work, we present a ship-hull optimization process combining a T-spline based parametric ship-hull model and an Isogeometric Analysis (IGA) hydrodynamic solver for the calculation of ship wave resistance. The surface representation of the ship-hull instances comprise one cubic T-spline with extraordinary points, ensuring C2 continuity everywhere except for the vicinity of extraordinary points where G1 continuity is achieved. The employed solver for ship wave resistance is based on the Neumann-Kelvin formulation of the problem, where the resulting Boundary Integral Equation is numerically solved using a higher order collocated Boundary Element Method which adopts the IGA concept and the T-spline representation for the ship-hull surface. The hydrodynamic solver along with the ship parametric model are subsequently integrated within an appropriate optimization environment for local and global ship-hull optimizations against the criterion of minimum resistance

Wave-resistance computation via CFD and IGA-BEM solvers : a comparative study

This paper delivers a preliminary comparative study on the computation of wave resistance via a commercial CFD solver (STAR-CCM+®) versus an in-house developed IGA-BEM solver for a pair of hulls, namely the parabolic Wigley hull and the KRISO container ship (KCS). The CFD solver combines a VOF (Volume Of Fluid) free-surface modelling technique with alternative turbulence models, while the IGA-BEM solver adopts an inviscid flow model that combines the Boundary Element approach (BEM) with Isogeometric Analysis (IGA) using T-splines or NURBS. IGA is a novel and expanding concept, introduced by Hughes and his collaborators (Hughes et al, 2005), aiming to intrinsically integrate CAD with Analysis by communicating the CAD model of the geometry (the wetted ship hull in our case) to the solver without any approximation

Sectional-Curvature Preserving Skinning Surfaces

: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : -11. Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : -22. A family of skinning interpolants : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : -63. Sectional-curvature preserving (scp) skinning interpolants : : : : : : : : : : : : : : : : : -114. An automatic algorithm for constructing scp skinning interpolants : : : : : : : : : -195. Numerical results : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : -23REFERENCES : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : -26FIGURES Abstract. In this work we develop a method for constructing sectional-curvature preserving (scp) C 2 - continuous surfaces, ..

Convexity Conditions for Parametric Tensor-Product B-spline Surfaces

This paper provides four alternative sufficient condition-sets, ensuring that a patch of a parametric tensor-product B-spline surface is locally convex. These conditions are at most tri-quadratic with respect to the control points of the surface

A Quadratic-Programming Method for Removing Shape-Failures from Tensor-Product B-spline Surfaces

We first study the effect caused, on the local shape of a tensor-product B-spline surface, by the movement of a subset of its control net. We then propose two (2) discrete approaches for removing shape failures from such surfaces, without altering them more than is needed. The second approach is a simple Quadratic-Programming method, that is suitable for restoring the shape of almost shape-preserving tensorproduct B-spline surfaces. The performance of this method is tested and discussed for three industrial surfaces

Spatial Shape-Preserving Interpolation Using Nu-Splines

Introduction Shape-preserving interpolation, via functional, as well as parametric splines, can be regarded as a well studied topic for the planar case. Indeed, there exists an abundance of papers, that provide schemes for constructing monotonicity- and/or convexitypreserving planar splines. On the contrary, the literature on shape-preserving interpolation in the three-dimensional space is apparently limited. This may be partially attributed to the fact that, introducing and validating a notion of shape-preserving interpolation in 3D is not as straightforward as it is in 2D. As a consequence, the first relevant papers in the literature have been devoted to introducing and investigating alternative notions of shape-preserving spatial interpolation, such as the inflection count of a curve in Good- 218 M. I. Karavelas, P. D. Kaklis / Shape-preserving interpolation using -splines man [4] and the shape properties o

Planar C 2 cubic spline interpolation under geometric boundary conditions

Abstract This paper deals with the problem of C 2 cubic spline interpolation under geometric boundary conditions, that is, fixing the unit-tangent vector and the curvature at the end points of a planar point-set. The solvability of the resulting non-linear problem, which is equivalent to a quadratic system with respect to the lengths of the boundary tangent vectors, is exhaustively studied, leading to necessary and sufficient conditions for all possible boundarydata configurations. A robust scheme for the numerical solution of the quadratic system is presented, and the use of the new boundary conditions is illustrated in the context of three examples