English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT
  On Generalized Barycentric Coordinates and Their Applications in Geometric Modeling

Langer, T. (2008). On Generalized Barycentric Coordinates and Their Applications in Geometric Modeling. PhD Thesis, Universität des Saarlandes, Saarbrücken.

Item is

Files

show Files
hide Files
:
Dissertation_2646_Lang_Thor_2008.pdf (Any fulltext), 9MB
 
File Permalink:
-
Name:
Dissertation_2646_Lang_Thor_2008.pdf
Description:
-
OA-Status:
Visibility:
Restricted (Max Planck Institute for Informatics, MSIN; )
MIME-Type / Checksum:
application/pdf
Technical Metadata:
Copyright Date:
-
Copyright Info:
-
License:
-

Locators

show

Creators

show
hide
 Creators:
Langer, Torsten1, 2, Author           
Weikert3, Advisor
Seidel, Hans-Peter1, Referee                 
Affiliations:
1Computer Graphics, MPI for Informatics, Max Planck Society, ou_40047              
2International Max Planck Research School, MPI for Informatics, Max Planck Society, Campus E1 4, 66123 Saarbrücken, DE, ou_1116551              
3External Organizations, ou_persistent22              

Content

show
hide
Free keywords: -
 Abstract: Generalized barycentric coordinate systems allow us to express the position of a point in space with respect to a given polygon or higher dimensional polytope. In such a system, a coordinate exists for each vertex of the polytope such that its vertices are represented by unit vectors $\vect{e}_i$ (where the coordinate associated with the respective vertex is 1, and all other coordinates are 0). Coordinates thus have a geometric meaning, which allows for the simplification of a number of tasks in geometry processing. Coordinate systems with respect to triangles have been around since the 19\textsuperscript{th} century, and have since been generalized; however, all of them have certain drawbacks, and are often restricted to special types of polytopes. We eliminate most of these restrictions and introduce a definition for 3D mean value coordinates that is valid for arbitrary polyhedra in $\realspace{3}$, with a straightforward generalization to higher dimensions. Furthermore, we extend the notion of barycentric coordinates in such a way as to allow Hermite interpolation and investigate the capabilities of generalized barycentric coordinates for constructing generalized B\'ezier surfaces. Finally, we show that barycentric coordinates can be used to obtain a novel formula for curvature computation on surfaces.

Details

show
hide
Language(s): eng - English
 Dates: 2009-03-032008-12-182008
 Publication Status: Issued
 Pages: -
 Publishing info: Saarbrücken : Universität des Saarlandes
 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 428319
Other: Local-ID: C125756E0038A185-BFAF8554E927CBB8C125752400480229-Langer08
 Degree: PhD

Event

show

Legal Case

show

Project information

show

Source

show