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- Jens Gravesen, Michael Ungstrup
- Adv. Comput. Math.
- 2002

The paper proposes a rational method to derive fairness measures for surfaces. It works in cases where isophotes, reflection lines, planar intersection curves, or other curves are used to judge the fairness of the surface. The surface fairness measure is derived by demanding that all the given curves should be fair with respect to an appropriate curve… (More)

- Jens Gravesen
- Comput. Geom.
- 1997

- Jens Gravesen, Bert Jüttler, Zbynek Sír
- Computer Aided Geometric Design
- 2008

We analyze the class of surfaces which are equipped with rational support functions. Any rational support function can be decomposed into a symmetric (even) and an antisymmetric (odd) part. We analyze certain geometric properties of surfaces with odd and even rational support functions. In particular it is shown that odd rational support functions… (More)

- Jens Gravesen, Christian Henriksen
- SIAM Review
- 2001

- Jens Gravesen, Anton Evgrafov, Dang-Manh Nguyen, Peter Nørtoft
- MMCS
- 2012

Before isogeometric analysis can be applied to solving a partial differential equation posed over some physical domain, one needs to construct a valid parametrization of the geometry. The accuracy of the analysis is affected by the quality of the parametrization. The challenge of computing and maintaining a valid geometry parametrization is particularly… (More)

The classical invariant theory from the 19th century is used to determine a complete system of 3rd order invariants on a surface in three-space. The invariant ring has 18 generators and the ideal of syzygies has 65 generators. The invariants are expressed as polynomials in the components of the first fundamental form, the second fundamental form and the… (More)

- Zbynek Sír, Jens Gravesen, Bert Jüttler
- Theor. Comput. Sci.
- 2008

This paper studies shapes (curves and surfaces) which can be described by (piecewise) polynomial support functions. The class of these shapes is closed under convolutions, offsetting, rotations and translations. We give a geometric discussion of these shapes and present methods for the approximation of general curves and surfaces by them. Based on the rich… (More)

- Henrik Almegaard, Anne Bagger, Jens Gravesen, Bert Jüttler, Zbynek Sír
- IMA Conference on the Mathematics of Surfaces
- 2007

Given a smooth surface patch we construct an approximating piecewise linear structure. More precisely, we produce a mesh for which virtually all vertices have valency three. We present two methods for the construction of meshes whose facets are tangent to the original surface. These two methods can deal with elliptic and hyperbolic surfaces, respectively.… (More)

- Peter Nørtoft Nielsen, Allan Roulund Gersborg, Jens Gravesen, Niels Leergaard, Allan Roulund Gersborgb, Jens Gravesena
- 2011

This paper deals with isogeometric analysis of the 2-dimensional, steady state, incompressible Navier-Stokes equation subjected to Dirichlet boundary conditions. We present a detailed description of the numerical method used to solve the boundary value problem. Numerical infsup stability tests for the simplified Stokes problem confirm the existence of many… (More)

Robust and efficient methods for dealing with offset curves and surfaces are one of the major challenges in Computer Aided Design. Offset to (piecewise) rational curves and surfaces (i.e., NURBS) are not rational and need to be approximated. Also, singularities and self–intersections can easily be generated and have to be dealt with [Mae]. Certain subsets… (More)