On the Computation of Nonlinear Spline Functions

Malcolm, Michael A.

doi:10.1137/0714017

Cited by 55 publications

(15 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This approach introduced a free parameter which could not be consistently determined. (6) We considered but did not implement nonlinear splines [24]. Although these splines produce differentiable curvatures, there is no guarantee that there exists such a spline through a given set of points and, if such a spline does exist, there is no guarantee that it is unique.…”

Section: (3)mentioning

confidence: 99%

Surface tension and viscosity with lagrangian hydrodynamics on a triangular mesh

Fyfe

Oran

Fritts

1988

Journal of Computational Physics

114

View full text Add to dashboard Cite

Section: (3)mentioning

confidence: 99%

Surface tension and viscosity with lagrangian hydrodynamics on a triangular mesh

Fyfe

Oran

Fritts

1988

Journal of Computational Physics

114

View full text Add to dashboard Cite

“…Our algorithm to construct the surfaces is based on discrete data. This has been proven to be especially well suited for the construction of nonlinear splines [13]. The idea behind the construction process is to design an algorithm that creates meshes with subdivision connectivity composed of regular patches.…”

Section: Introductionmentioning

confidence: 99%

Generating fair meshes with G/sup 1/ boundary conditions

Schneider

Kobbelt

2000

Proceedings Geometric Modeling and Processing 2000. Theory and Applications

View full text Add to dashboard Cite

In this paper we present a new algorithm to create fair discrete surfaces satisfying prescribed ½ boundary constraints. All surfaces are built by discretizing a partial differential equation based on pure geometric intrinsics. The construction scheme is designed to produce meshes that are partitioned into regular domains. Using this knowledge in advance we can develop a fast iterative algorithm resulting in surfaces of high aesthetic quality that have no local mean curvature extrema in the interior.

show abstract

“…This is clone by checking for each zero of ( 40) which of the two 1>:i-values according to (17) in fact provides K~ = 20". Thus the roots are divided in two groups one for each objective function.…”

mentioning

confidence: 99%

A univariate method for plane elastic curves

Brunnett

Wendt

1997

Computer Aided Geometric Design

View full text Add to dashboard Cite

The problem to interpolate Hermite-type data (i.e. two points with attached tangent vectors) with elastic curves of prescribed tension is known to have multiple solutions. A method is presented that finds all solutions of length not exceeding one period of its curvature function. The algorithm is based on algebraic relations between discrete curvature information which allow to transform the problem into a univariate one. The method operates with curves that by construction partially interpolat~ the given data. Hereby the objective function of the problem is drastically simplified. A bound on the maximum curvature value is established that provides an interval containing all solutions.

show abstract

On the Computation of Nonlinear Spline Functions

Cited by 55 publications

References 7 publications

Surface tension and viscosity with lagrangian hydrodynamics on a triangular mesh

Surface tension and viscosity with lagrangian hydrodynamics on a triangular mesh

Generating fair meshes with G/sup 1/ boundary conditions

A univariate method for plane elastic curves

Contact Info

Product

Resources

About