Results 1 
5 of
5
Drawing graphs with glee
, 2007
"... Abstract. This paper describes novel methods we developed to lay out graphs using Sugiyama’s scheme [16] in a tool named GLEE. The main contributions are: a heuristic for creating a graph layout with a given aspect ratio, an efficient method of edgecrossings counting while performing adjacent verte ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
Abstract. This paper describes novel methods we developed to lay out graphs using Sugiyama’s scheme [16] in a tool named GLEE. The main contributions are: a heuristic for creating a graph layout with a given aspect ratio, an efficient method of edgecrossings counting while performing adjacent vertex swaps, and a simple and fast spline routing algorithm. 1
Fitting curves and surfaces to point clouds in the presence of obstacles. Computer Aided Geometric Design 26
, 2009
"... of obstacles ..."
Constrained curve fitting on manifolds
 COMPUTERAIDED DESIGN
, 2008
"... When designing curves on surfaces the need arises to approximate a given noisy target shape by a smooth fitting shape. We discuss the problem of fitting a Bspline curve to a point cloud by squared distance minimization in the case that both, the point cloud and the fitting curve, are constrained to ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
When designing curves on surfaces the need arises to approximate a given noisy target shape by a smooth fitting shape. We discuss the problem of fitting a Bspline curve to a point cloud by squared distance minimization in the case that both, the point cloud and the fitting curve, are constrained to lie on a smooth manifold. The onmanifold constraint is included by using the first fundamental form of the surface for squared distance computations between the point cloud and the fitting curve. For the solution we employ a constrained optimization algorithm that allows us to include further constraints such as onesided fitting or surface regions that have to be avoided by the fitting curve. We illustrate the effectiveness of our algorithm at hand of several examples showing different applications.
Constrained Optimization with EnergyMinimizing Curves and Curve Networks — A Survey
"... We survey recent research results in constrained optimization with curves and curve networks. The addressed topics include constrained variational curve and curve network design, variational motion design, and guaranteed error bound approximation of point cloud data with curve networks. The main the ..."
Abstract
 Add to MetaCart
We survey recent research results in constrained optimization with curves and curve networks. The addressed topics include constrained variational curve and curve network design, variational motion design, and guaranteed error bound approximation of point cloud data with curve networks. The main theoretic results are summarized with a focus on geometric solutions of the studied problems. A variety of applications is outlined including obstacle avoiding rigid body motion design and smoothing of digital terrain elevation data.
Fitting Bspline Curves to Point Clouds in the Presence of Obstacles
"... We consider the computation of an approximating curve to fit a given set of points. Such a curve fitting is a common problem in CAGD and we review three different approaches based upon minimization of the squared distance function: the point distance, tangent distance and squared distance error term ..."
Abstract
 Add to MetaCart
We consider the computation of an approximating curve to fit a given set of points. Such a curve fitting is a common problem in CAGD and we review three different approaches based upon minimization of the squared distance function: the point distance, tangent distance and squared distance error term. We enhance the classic setup comprising a point cloud and an approximating BSpline curve by obstacles a final solution must not penetrate. Two algorithms for solving the emerging constrained optimization problems are presented and used to enclose point clouds from inside as well as from outside and to avoid arbitrary smooth bounded obstacles. Moreover, approximations of guaranteed quality and shaking objects are examined within this context. In a next step, we extend our work and study the curve fitting problem on parametrized surfaces. The approximation is still performed in the two dimensional parameter space while geometric properties of the manifold enter the computation at the same time. Additionally, we use this new error term to approximate the borders of point clouds on manifolds. Finally, as a minimization of the squared distance function