1,454 research outputs found
A tension approach to controlling the shape of cubic spline surfaces on FVS triangulations
We propose a parametric tensioned version of the FVS macro-element to control the shape of the composite surface and remove artificial oscillations, bumps and other undesired behaviour. In particular, this approach is applied to C1 cubic spline surfaces over a four-directional mesh produced by two-stage scattered data fitting methods
Shape Preserving Spline Interpolation
A rational spline solution to the problem of shape preserving interpolation is discussed. The rational spline is represented in terms of first derivative values at the knots and provides an alternative to the spline-under-tension. The idea of making the shape control parameters dependent on the first derivative unknowns is then explored. The monotonic or convex shape of the interpolation data can then be preserved automatically through the solution of the resulting non-linear consistency equations of the spline
Generalized quadratic B-splines generated by Merrien subdivision algorithm and some applications
A new global basis of B-splines is defined in the space of generalized
quadratic splines (GQS) generated by Merrien subdivision algorithm. Then,
refinement equations for these B-splines and the associated corner-cutting
algorithm are given. Afterwards, several applications are presented. First a
global construction of monotonic and/or convex generalized splines
interpolating monotonic and/or convex data. Second, convergence of sequences of
control polygons to the graph of a GQS. Finally, a Lagrange interpolant and a
quasi-interpolant which are exact on the space of affine polynomials and whose
infinite norms are uniformly bounded independently of the partition.Comment: 2004-1
Convexity preserving interpolatory subdivision with conic precision
The paper is concerned with the problem of shape preserving interpolatory
subdivision. For arbitrarily spaced, planar input data an efficient non-linear
subdivision algorithm is presented that results in limit curves,
reproduces conic sections and respects the convexity properties of the initial
data. Significant numerical examples illustrate the effectiveness of the
proposed method
Investigations into the shape-preserving interpolants using symbolic computation
Shape representation is a central issue in computer graphics and computer-aided geometric design. Many physical phenomena involve curves and surfaces that are monotone (in some directions) or are convex. The corresponding representation problem is given some monotone or convex data, and a monotone or convex interpolant is found. Standard interpolants need not be monotone or convex even though they may match monotone or convex data. Most of the methods of investigation of this problem involve the utilization of quadratic splines or Hermite polynomials. In this investigation, a similar approach is adopted. These methods require derivative information at the given data points. The key to the problem is the selection of the derivative values to be assigned to the given data points. Schemes for choosing derivatives were examined. Along the way, fitting given data points by a conic section has also been investigated as part of the effort to study shape-preserving quadratic splines
Totally positive refinable functions with general dilation M
We construct a new class of approximating functions that are M-refinable and provide shape preserving approximations. The refinable functions in the class are smooth, compactly supported, centrally symmetric and totally positive. Moreover, their refinable masks are associated with convergent subdivision schemes. The presence of one or more shape parameters gives a great flexibility in the applications. Some examples for dilation M=4and M=5are also given
Polynomial cubic splines with tension properties
In this paper we present a new class of spline functions with tension properties. These splines are composed by polynomial cubic pieces and therefore are conformal to the standard, NURBS based CAD/CAM systems
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