Fast and Stable Evaluation of Box-Splines via the BB-Form (2009)
Minho Kim, Jörg Peters, Direction Matrix Examplep, M M Examplep
◮ Box-splines for generating continuous field from discrete data. Motivation ◮ Box-splines for generating continuous field from discrete data. ◮ Recursive evaluation (de Boor ’93 and Kobbelt...
Data Type General Terms Design (2009)
The Flexible Subdivision Library, FSL, is a policy-based C++ template library for refining geometric meshes. The library is generic and only requires that the underlying mesh data structure provide...
ON THE LOCAL LINEAR INDEPENDENCE OF GENERALIZED SUBDIVISION FUNCTIONS (2009)
Abstract. Characterizing the linear and local linear independence of the functions that span a linear space is a key task if the space is to be used computationally. Given the control net, the...
Ashish Myles, Young In Yeo, Jörg Peters
We convert any quad manifold mesh into an at least C 1 surface consisting of bi-cubic tensor-product splines with localized perturbations of degree bi-5 near non-4-valent vertices. There is one...
Extending Catmull-Clark subdivision and PCCM with polar structures (2009)
Ashish Myles, Kestutis Karčiauskas, Jörg Peters
We complete and bring together two pairs of surface constructions that use polynomial pieces of degree (3,3) to associate a smooth surface with a mesh. The two pairs complement each other in that one...
Simulation for Training With the Autosuture ™ Endo Stitch ™ Device (2008)
Sergei N. Kurenov, Sukitti Punak, Minho Kim, Jörg Peters, Juan C. Cendan, Sergei N. Kurenov, ...
The rapid development and deployment of novel laparoscopic instruments present the surgical educator and trainee with a significant challenge. Several useful instruments have been particularly...
flows using parallel adaptive multigrid techniques (2008)
Sven Groß, Jörg Peters, Volker Reichelt, Arnold Reusken
The DROPS package for numerical simulations of incompressible
Ternary Subdivision for Quadrilateral Meshes (2008)
Tianyun Ni, Ahmad H. Nasri, Jörg Peters
Abstract. A well-documented problem of Catmull and Clark subdivision surfaces is that, in the neighborhood of extraordinary points, the curvature is unbounded and fluctuates. In fact, since one of...
08221 Summary -- Geometric Modeling (2008)
Farin, Gerald, Hahmann, Stefanie, Peters, Jörg, Wang, Wenping
Geometric Modeling is an area drawing from computer science, mathematics, engineering, and the life sciences. It is concerned with the computer representation of objects as diverse as - brain scans -...
08221 Abstracts Collection -- Geometric Modeling (2008)
Farin, Gerald, Hahmann, Stefanie, Peters, Jörg, Wang, Wenping
From May 26 to May 30 2008 the Dagstuhl Seminar 08221 ``Geometric Modeling'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several...
Fast and stable evaluation of box-splines via the BB-form (2008)
To repeatedly evaluate linear combinations of box-splines in a fast and stable way, in particular along knot planes, the box-spline is converted to and tabulated as piecewise polynomial in BB-form...
Constructing C¹ surfaces of arbitrary topology using biquadratic and bicubic splines (2007)
Introduction Two approaches to building smooth free-form surfaces, generalized subdivision and the composition of surfaces from patches, are combined to generalize biquadratic tensor-product...
Interpolation Regions for Convex Cubic Curve Segments (2007)
. Given a family of planar convex cubic curve segments with fixed end points and tangents, subregions of the plane are characterized in which additional points can be interpolated by at least one...
Abstract Patching Catmull-Clark Meshes (2007)
Figure 1: Catmull-Clark subdivision sequence completed as a collection of large Nurbs patches (top five patches are shown). Named after the title, the PCCM transformation is a simple, explicit...
b + Figure 1: (left:) a piecewise bicubic spline surface £. (right:) Zooming in on the sirface envelope of £. The envelope consists of the inner triangulation and outer, matching triangulation. The...
¢ ¡ Free-Form Surfaces of degree (£¥¤§ ¦) (2007)
This paper introduces new techniques for modeling low degree, smooth freeform surfaces of unrestricted patch layout. In particular, surfaces that are ¨� © after reparametrization can be built...
Figure 1: (left:) a piecewise bicubic spline surface. (right of arrow:) Zooming in on the optimized surface enclosure of. The enclosure consists of the inner triangulation and outer, matching...
ATI Research Curved PN Triangles (2007)
Alex Vlachos, Jörg Peters, Chas Boyd, Jason L. Mitchell
quadratically varying normals). To improve the visual quality of existing triangle-based art in realtime entertainment, such as computer games, we propose replacing flat triangles with curved patches...
Contemporary Mathematics (2007)
Smoothness Fairness And, Jörg Peters
This paper surveys the key achievements and outstanding challenges of constructing smooth surfaces for geometric design. The focus here is on explicit methods in parametric form. In particular,...
Threading splines through 3D channels (2007)
Given a polygonal channel between obstacles in the plane or in space, we present an algorithm for generating a parametric spline curve with few pieces that traverses the channel and stays inside....
X.: SLEVEs for planar spline curves (2007)
Given a planar spline curve and local tolerances, a matched pair of polygons is computed that encloses the curve and whose width (distance between corresponding break points) is below the tolerances....
Fast and stable evaluation of box-splines via the Bézier (2007)
To repeatedly evaluate linear combinations of box-splines in a fast and stable way, in particular along knot planes, we convert to and tabulate the box-spline as piecewise polynomials in Bézier...
A realtime GPU subdivision kernel (2005)
Le-jeng Shiue, Ian Jones, Jörg Peters
Figure 1: Catmull-Clark surfaces fully reevaluated (40 patches, depth 5) at 21 fps on an ATi 9700 mobile graphics chip. By organizing the control mesh of subdivision in texture memory so that...
Denisov, Vladimir P, Peters, Jörg, Hörlein, Hans Dietrich, Halle, Bertil
Abstract is not available
Meera Sitharam, Jörg Peters, Yong Zhou
Many geometric constraint solvers use a combinatorial or graph algorithm to generate a decompositionrecombination (DR) plan. A DR plan recursively decomposes the system of polynomial equations into...
U.: Shape characterization of subdivision surfaces – case studies (2004)
K. Karčiauskas, Jörg Peters, U. Reif C
For subdivision surfaces, it is important to characterize local shape near flat spots and points where the surface is not twice continuously differentiable. Applying general principles derived in...
Combining 4- and 3-direction subdivision (2004)
4-3 direction subdivision combines quad and triangle meshes. On quad submeshes it applies a 4-direction alternative to Catmull-Clark subdivision and on triangle submeshes a modification of Loop’s...
Fast iterative solvers for discrete Stokes equations (2004)
Jörg Peters, Volker Reichelt, Arnold Reusken
Abstract. We consider saddle point problems that result from the finite element discretization of stationary and instationary Stokes equations. Three efficient iterative solvers for these problems...
Elimination in generically rigid 3d geometric constraint systems (2004)
Jörg Peters, Meera Sitharam, Yong Zhou, Jianhua Fan
Summary. Modern geometric constraint solvers use combinatorial graph algorithms to recursively decompose the system of polynomial constraint equations into generically rigid subsystems and then solve...
Efficient one-sided linearization of spline geometry (2003)
Abstract. This paper surveys a new, computationally efficient technique for linearizing curved spline geometry, bounding such geometry from one side and constructing curved spline geometry that stays...
On the optimality of piecewise linear max-norm enclosures based on slefes (2003)
Abstract. Subdividable linear efficient function enclosures (Slefes) provide, at low cost, a piecewise linear pair of upper and lower bounds f +, f − , that sandwich a function f on a given...
Optimized refinable enclosures of multivariate polynomial pieces (2002)
¢¡¤ £ An enclosure is a two-sided approximation of a uni- or multivariate function by a pair of typically simpler functions ¦¥¨§ © ���¡��� � £ � such that over the...
Alex Vlachos, Jörg Peters, Chas Boyd, Jason L. Mitchell
quadratically varying normals). To improve the visual quality of existing triangle-based art in realtime entertainment, such as computer games, we propose replacing flat triangles with curved patches...
This chapter covers geometric continuity with emphasis on a constructive definition for piecewise parametrized surfaces. The examples in Section 1 show the need for a notion of continuity different...
Gaussian and mean curvature of subdivision surfaces (2000)
By explicitly deriving the curvature of subdivision surfaces in the extraordinary points, we give an alternative, more direct account of the criteria necessary and sufficient for achieving curvature...
Patching Catmull-Clark meshes (2000)
Named after the title, the PCCM transformation is a simple, explicit algorithm that creates large, smoothly joining bicubic Nurbs patches from a refined Catmull-Clark subdivision mesh. The resulting...
Gaussian and mean curvature of subdivision surfaces (2000)
By explicitly deriving the curvature of subdivision surfaces in the extraordinary points, we give an alternative, more direct account of the criteria necessary and sufficient for achieving curvature...
Higher Order Smooth Patching of Refined Triangulations (2000)
This technical report supplements the paper "Smooth Patching of Refined Triangulations " [3]. That paper gives formulas for smoothly filling -sided holes in a 3-direction box-spline (Loop)...
Smooth patching of refined triangulations (2000)
This paper presents a simple algorithm for associating a smooth, low degree polynomial surface with triangulations whose extraordinary mesh nodes are separated by sufficiently many ordinary, 6-valent...
Smooth Paths In A Polygonal Channel (1999)
David Lutterkort, Jörg Peters, J Org Peters
. We show how to efficiently smooth a polygon with an approximating spline that stays to one side of the polygon. We also show how to find a smooth spline path between two polygons that form a...
Smooth paths in a polygonal channel (1999)
ABSTRACT. We show how to efficiently smooth a polygon with an approximating spline that stays to one side of the polygon. We also show how to find a smooth spline path between two polygons that form...
Pcp2Nurb: smooth free-form surfacing with linearly-trimmed bicubic B-splines (1998)
ing with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works, requires prior specific permission...
The Distance Between A Uniform (B-)spline And Its Control Polygon (1998)
David Lutterkort, Jörg Peters, J Org Peters
. We prove a sharp bound on the distance between a uniform spline and its B{Spline control polygon in terms of the second dierences of the control points. This bound decreases by a factor of 4 under...
The Simplest Subdivision Scheme for Smoothing Polyhedra (1997)
Given a polyhedron, construct a new polyhedron by connecting every edgemidpoint to its four neighboring edge-midpoints. This refinement rule yields a C 1 surface and the surface has a piecewise...
Computing Volumes of Solids Enclosed by Recursive Subdivision Surfaces (1997)
The volume of a solid enclosed by a recursive subdivision surface can be approximated based on the closed-form representation of regular parts of the subdivision surface and a tight estimate of the...
The 42 Equivalence Classes of Quadratic Surfaces in Affine n-Space (1997)
We establish an exhaustive catalogue of 42 equivalence classes of bivariate quadratic surfaces in affine n-space. Here two surfaces belong to the same class if they differ only by zero components or...
Analysis of Algorithms Generalizing B-Spline Subdivision (1997)
A new set of tools for verifying smoothness of surfaces generated by stationary subdivision algorithms is presented. The main challenge here is the verification of injectivity of the characteristic...
The routine Pcp2Nurb is a key building block in overcoming topological constraints in the mathematical modeling of smooth surfaces. On input of a nine-point subnet of a planar-cut polyhedron, this...
Computing Volumes of Solids Enclosed by Recursive Subdivision Surfaces (1997)
The volume of a solid enclosed by a recursive subdivision surface can be approximated based on the closedform representation of regular parts of the subdivision surface and a tight estimate of the...
Computing Volumes of Solids Enclosed by Recursive Subdivision Surfaces (1997)
The volume of a solid enclosed by a recursive subdivision surface can be approximated based on the closed-form representation of regular parts of the subdivision surface and a tight estimate of the...
Smooth Blending of Basic Surfaces using Trivariate Box Splines (1996)
To blend between basic implicitly defined CSG surfaces we propose to use the zero set of a spline in three variables. The resulting blend surface is generically curvature continuous, of algebraic...
The construction of quadratic C¹ surfaces from B-spline control points is generalized to a wider class of control meshes capable of outlining arbitrary free-form surfaces in space. Irregular meshes...
Geometric Constraints for CAGD (1995)
Christoph M. Hoffmann, Jörg Peters
. To enrich the shape vocabulary of mechanical CAD systems, we develop techniques that allow defining free-form curves from geometric constraints. An important aspect of this aproach is the ability...
Biquartic C¹-surface splines over irregular meshes (1995)
Biquartic C, Jörg Peters, Key Words C
C 1 -surface splines define tangent continuous surfaces from control points in the manner of tensor-product (B-)splines, but allow a wider class of control meshes capable of outlining arbitrary...
Curvature Continuous Spline Surfaces Over Irregular Meshes (1994)
. Concepts and techniques for the construction of smooth surfaces over irregular meshes are developed and made concrete by defining C 2 -surface splines. These splines extend the B-spline paradigm...
C² Surfaces Built From Zero Sets of the 7-Direction Box Spline (1994)
. Curvature continuous surfaces can be generated by tracing the zero set of a trivariate box spline of degree four. This box spline is defined by seven directions that form a regular partition of...
Polynomials of total degree d in m variables have a geometrically intuitive representation in the Bernstein-B'ezier form defined over an m-dimensional simplex. The two algorithms given in this...
Smoothing Polyhedra Made Easy (1993)
A mesh of points outlining a surface is polyhedral if all cells are either quadrilateral or planar. A mesh is vertex-degree bounded, if at most four cells meet at every vertex. This paper shows that...
Mineralocorticoid receptor knockout mice: Pathophysiology of Na+ metabolism
Berger, Stefan, Bleich, Markus, Schmid, Wolfgang, Cole, Timothy J., Peters, Jörg, Watanabe, Haruko, ...
Mineralocorticoid receptor (MR)-deficient mice were generated by gene targeting. These animals had a normal prenatal development. During the first week of life, MR-deficient (−/−) mice developed...
Schinke, Martina, Baltatu, Ovidiu, Böhm, Manfred, Peters, Jörg, Rascher, Wolfgang, Bricca, Giampiero, ...
Angiotensin produced systemically or locally in tissues such as the brain plays an important role in the regulation of blood pressure and in the development of hypertension. We have established...
Mineralocorticoid receptor knockout mice: Pathophysiology of Na+ metabolism
Berger, Stefan, Bleich, Markus, Schmid, Wolfgang, Cole, Timothy J., Peters, Jörg, Watanabe, Haruko, ...
Mineralocorticoid receptor (MR)-deficient mice were generated by gene targeting. These animals had a normal prenatal development. During the first week of life, MR-deficient (−/−) mice developed...
Schinke, Martina, Baltatu, Ovidiu, Böhm, Manfred, Peters, Jörg, Rascher, Wolfgang, Bricca, Giampiero, ...
Angiotensin produced systemically or locally in tissues such as the brain plays an important role in the regulation of blood pressure and in the development of hypertension. We have established...
Identifying the Rebound: Theoretical Issues and Empirical. Evidence from a German Household Panel
Manuel Frondel, Jörg Peters, Colin Vance
Using a panel of household travel diary data collected in Germany between 1997 and 2005, this study assesses the effectiveness of fuel efficiency improvements by econometrically estimating the...
Guaranteeing tax reductions and exemptions, the European governments intend to increase the share of biofuels in total EU fuel consumption to 5.75% by 2010. The financial support of this EU objective...
Promoting Biofuels: Implications for Developing Countries
Interest in biofuels is growing worldwide as concerns about the security of energy supply and climate change are moving into the focus of policy makers. With the exception of bioethanol from Brazil,...
Identifying the Rebound - Evidence from a German Household Panel
Manuel Frondel, Jörg Peters, Colin Vance
Using a panel of household travel diary data collected in Germany between 1997 and 2005, this study assesses the effectiveness of fuel efficiency improvements by econometrically estimating the...
Promoting biofuels: Implications for developing countries
Peters, Jörg, Thielmann, Sascha
Interest in biofuels is growing worldwide as concerns about the security of energy supply and climate change are moving into the focus of policy makers. With the exception of bioethanol from Brazil,...
Impact evaluation, ex-ante impact assessment, electricity access, rural development