Lars Linsen, Hartmut Prautzsch
Free form surfaces are commonly represented by triangular or quadrilateral meshes. Often these meshes are obtained from unorganized point sets sampled from some object’s surface. We show that local...
Parametrizations for Triangular G k Spline Surfaces (2008)
Hartmut Prautzsch, Georg Umlauf
In this article, we present regularly parametrized Gk free-form spline surfaces that extend box and half-box splines over regular triangular grids. The polynomial degree of these splines is max{4k +...
Alfred A. Schmitt, Jan S. Bender, Hartmut Prautzsch
First, we will provide a short introduction to the impulse-based method for dynamic simulation. Till now, impulses were frequently used to resolve collisions between rigid bodies. In the last years,...
Alfred A. Schmitt, Jan S. Bender, Hartmut Prautzsch
Impulse-based dynamic simulation using the iterative method results in relatively simple algorithms which are easy to implement. However, two important theoretical questions have so far still...
Alfred A. Schmitt, Jan S. Bender, Hartmut Prautzsch
First, we will provide a short introduction to the impulse-based method for dynamic simulation. Till now, impulses were frequently used to resolve collisions between rigid bodies. In the last years,...
Alfred A. Schmitt, Jan S. Bender, Hartmut Prautzsch
Impulse-based dynamic simulation using the iterative method results in relatively simple algorithms which are easy to implement. However, two important theoretical questions have so far still...
Circle and Sphere as rational splines (2008)
Claudia Bangert And, Claudia Bangert, Hartmut Prautzsch
A simple method is given to construct periodic spline representations forcircles.
Subdivision Scheme For, Hartmut Prautzsch, Georg Umlauf
this article we improve the butterfly and Loop's algorithm. As a result we obtain subdivision algorithms for triangular nets which can be used to generate G -andG - surfaces, respectively
A New ApproachtoTchebycheffian B-Splines (2008)
Daniel Bister And, Daniel Bister, Hartmut Prautzsch
Originally,Tchebycheffian B-splines have been defined by generalized divided differences. In this paper, we define Tchebycheffian B-splines byintegration. Based upon this definition, all basic...
Wolfgang Boehm And, Wolfgang Boehm, Hartmut Prautzsch
The following recalls the facts and terminology mostly used in Geometry.Itmayserve also as a first introduction to geometric tools, for more in depth coverage see the list of references, in...
B-Splines with Arbitrary Connection Matrices (2008)
We consider a space of Chebyshev splines whose left and right derivatives satisfy linear constraints that are given by arbitrary non-singular connection matrices. We show that for almost all knot...
Lars Linsen Hartmut, Hartmut Prautzsch
Free form surfaces are commonly represented by triangular or quadrilateral meshes. Often these meshes are obtained from unorganized point sets sampled from some object's surface.
Multivariate Splines with Convex B-Patch Control Nets are Convex (2008)
Hartmut Prautzsch, Fakultat Fur Informatik
In this paper results from a forthcoming paper are presented concerning the convexity of multivariate spline functions built from B-patches. Conditions are given under which it is possible todefi a...
A G¹ and a G²-subdivision scheme for triangular nets (2007)
Hartmut Prautzsch, Georg Umlauf
In this article we improve the butterfly and Loop's algorithm. As a result we obtain subdivision algorithms for triangular nets which can be used to generate G¹- and G²-surfaces, respectively.
Marco Paluszny, Hartmut Prautzsch, Martin Schafer, Facultad De Ciencias
In this paper we consider corner cutting and convexity preserving interpolatory refinement schemes in the plane and on the sphere. Using well-known facts from projective geometry we present a unified...
Triangular G²-Splines (2007)
Hartmut Prautzsch, Georg Umlauf
. We introduce curvature continuous regular free-form surfaces with triangular control nets. These surfaces are composed of quartic box spline surfaces and are piecewise polynomial multisided patches...
Circle and Sphere as rational splines (2007)
Claudia Bangert, Hartmut Prautzsch
A simple method is given to construct periodic spline representations for circles. These are n-times differentiable and of minimal degree. Further, the extension to spheres is discussed. Keywords...
Wolfgang Boehm, Hartmut Prautzsch
The following recalls the facts and terminology mostly used in Geometry. It may serve also as a rst introduction to geometric tools, for more in depth coverage see the list of references, in...
Lars Linsen, Hartmut Prautzsch
Free form surfaces are commonly represented by triangular or quadrilateral meshes. Often these meshes are obtained from unorganized point sets sampled from some object's surface. We show that...
Umlauf, Georg, Prautzsch, Hartmut
In this paper a new approach is presented to construct piecewise polynomial G^k-surfaces of arbitrary topology and smoothness order k>= 1 of degree O(k). This approach generalizes some results...
Iterative mesh generation for FE-computations on free form surfaces (2007)
Kobbelt, Leif, Hesse, Torsten, Prautzsch, Hartmut, Schweizerhof, Karl
Métodos de Bézier y B-splines (2005)
Paluszny, Marco, Prautzsch, Hartmut, Boehm, Wolfgang
Este libro provee una base sólida para la teoría de curvas de Bézier y B-spline, revelando su elegante estructura matemática. En el texto se hace énfasis en las nociones centrales del Diseño...
Hartmut Prautzsch, Wolfgang Boehm
e 1: Bivariate box splines over the triangular grid. These box splines are normalized such that which can easily be verified for k = s and further by induction over k. Namely tv k )dtdx = tv k )dxdt...
Local versus global triangulations (2001)
Lars Linsen, Hartmut Prautzsch
Free form surfaces are commonly represented by triangular or quadrilateral meshes. Often these meshes are obtained from unorganized point sets sampled from some object's surface. We show that...
Prautzsch, Hartmut, Umlauf, Georg
We introduce curvature continuous regular free-form surfaces with triangular control nets. These surfaces are composed of quartic box spline surfaces and are piecewise polynomial multisided patches...
Claudia Bangert, Hartmut Prautzsch
In this paper we will present a geometric approach to piecewise quadric C
Claudia Bangert, Hartmut Prautzsch
this paper is to derive their quadric splines solely geometrically in projective space. The geometric approach has several benefits. It provides a geometric meaning for certain parameters chosen to...
A Geometric Criterion for the Convexityof (1999)
Claudia Bangert, Hartmut Prautzsch
We derive a geometric criterion for the convexityofPowell-Sabin interpolants and presentamultivariate generalization.
Claudia Bangert Hartmut, Hartmut Prautzsch
this paper is to derive their quadric splines solely geometrically in projective space. The geometric approach has several benefits. It provides a geometric meaning for certain parameters chosen to...
Analysis of Csupra(k)-subdivision surfaces at extraordinary points (1998)
This paper gives an analysis of surfaces generated by subdividing control nets of arbitrary topology. We assume that the underlying subdivision algorithm is stationary on the regular parts of the...
Claudia Bangert, Hartmut Prautzsch, Fakultat Fur Informatik
In this paper we will present a geometric approach to piecewise quadric C 1 -interpolants constructed algebraically by Dahmen in 1989. These piecewise quadrics interpolate the vertices of a...
A G²-subdivision algorithm (1998)
Hartmut Prautzsch, Georg Umlauf
In this paper we present a method to optimize the smoothness order of subdivision algorithms generating surfaces of arbitrary topology. In particular we construct a subdivision algorithm with some...
Improved Triangular Subdivision Schemes (1998)
Hartmut Prautzsch, Georg Umlauf
In this article we improve the butterfly and Loop's algorithm. As a result we obtain subdivision algorithms for triangular nets which can be used to generate G 1 - and G 2 - surfaces,...
Claudia Bangert, Hartmut Prautzsch, Fakultat Fur Informatik
We derive a geometric criterion for the convexity of Powell-Sabin interpolants and present a multivariate generalization.
A G 2 {subdivision algorithm 1 (1998)
Subdivision Algorithm Hartmut, Hartmut Prautzsch, Georg Umlauf
In this paper we present a method to optimize the smoothness order of subdivision algorithms generating surfaces of arbitrary topology. In particular we construct a subdivision algorithm with some...
Iterative mesh generation for FE-computations on free form surfaces. (1997)
Kobbelt, Leif, Hesse, Torsten, Prautzsch, Hartmut, Schweizerhof, Karl
Iterative Mesh Generation for FE-computation on Free Form Surfaces (1997)
Leif Kobbelt, Torsten Hesse, Hartmut Prautzsch, Karl Schweizerhof
We present an interpolatory subdivision scheme to generate adaptiely refined quadrilateral meshes which approximate a smooth surface of arbitrary topology. The described method significantly differs...
A New Approach to Tchebycheffian B-Splines (1997)
Daniel Bister, Hartmut Prautzsch
. Originally, Tchebycheffian B-splines have been defined by generalized divided differences. In this paper, we define Tchebycheffian B-splines by integration. Based upon this definition, all basic...
Necessary Conditions for Subdivision Surfaces (1997)
Hartmut Prautzsch, Ulrich Reif
Subdivision surfaces are considered which consist of tri- or quadrilateral patches in a mostly regular arrangement with finitely many irregularities. A sharp estimate on the lowest possible degree of...
Hartmut Prautzsch, Georg Umlauf
this paper, where we introduce box and half-box spline surfaces with multiple extraordinary control points
Analysis of C<sup>k</sup>-subdivision surfaces at extraordinary points (1995)
Subdivision Surfaces, Hartmut Prautzsch
This paper gives an analysis of surfaces generated by subdividing control nets of arbitrary topology. We assume that the underlying subdivision algorithm is stationary on the regular parts of the...
Subdivision Surfaces At, Hartmut Prautzsch
This paper gives an analysis of surfaces generated by subdividing control nets of arbitrary topology. We assume that the underlying subdivision algorithm is stationary on the regular parts of the...
The Location of the Control Points in the Case of Box Splines (1986)
In this paper a theorem of Greville (1967) for univariate splines is carried over to multivariate box splines; namely, it is shown how the vector-valued function s(x)=x can expressed in terms...