id 
acadia15_203 
authors 
Ross, Elissa; Hambleton, Daniel 
year 
2015 
title 
Exact FaceOffsetting for Polygonal Meshes 
source 
ACADIA 2105: Computational Ecologies: Design in the Anthropocene [Proceedings of the 35th Annual Conference of the Association for Computer Aided Design in Architecture (ACADIA) ISBN 9780692537268] Cincinnati 1925 October, 2015), pp. 203210 
summary 
Planarfaced mesh surfaces such as triangular meshes are frequently used in an architectural setting. Faceoffsetting operations generate a new mesh whose face planes are parallel and at a fixed distance from the face planes of the original surface. Faceoffsetting is desirable to give thickness or layers to architectural elements. Yet, this operation does not generically preserve the combinatorial structure of the offset mesh. Current approaches to this problem are to restrict the geometry of the original mesh to ensure that the combinatorial structure of the underlying mesh is preserved. We present a general algorithm for faceoffsetting polygonal meshes that places no restriction on the original geometry. The algorithm uses graph duality to describe the range of possible combinatorial outcomes at each vertex of the mesh. This approach allows the designer to specify independent offset distances for each face plane. The algorithm also produces a "perpendicular" structure joining the original mesh with the offset mesh, that consists of only planar elements (i.e. beams). 
keywords 
Mesh offsetting, faceoffsetting, architecture, dual graph, polygonal mesh, triangular mesh 
series 
ACADIA 
type 
normal paper 
email 
elissa.ross@meshconsultants.ca 
full text 
file.pdf (1,405,775 bytes) 
references 
Contenttype: text/plain

Alexandrov, A. D. (2005)
Convex Polyhedra. Springer Monographs in Mathematics
, tr. N. S. Dairbekov, S. S. Kutateladze and A. B. Sossinsky. SpringerVerlag, Berlin




Bobenko, A. I., H. Pottmann, and J. Wallner (2010)
A Curvature Theory for Discrete Surfaces Based on Mesh Parallelity
, Mathematische Annalen, 348(1): 124




Forsyth, M. (1995)
Shelling and offsetting bodies
, Proceedings of the third ACM symposium on Solid modeling and applications, eds. C. Hoffmann and J. Rossignac, 373–381. New York: ACM. DOI 10.1145/218013.218088




Jung, W., H. Shin, and B. K. Choi (2004)
Selfintersection Removal in Triangular Mesh Offsetting
, Computer Aided Design and Applications, 1(14): 477–484




Liu, S. and C. C. Wang (2011)
Fast Intersectionfree Offset Surface Generation from Freeform Models with Triangular Meshes
, IEEE Transactions on Automation Science and Engineering 8(2):347–360




Pottman, H. and J. Wallner (2008)
The Focal Geometry of Circular and Conical Meshes
, Advances in Computational Mathematics 29(3): 249268




Pottmann, H., A. Asperl, M. Hofer, and A. Kilian (2007)
Architectural Geometry
, Exton, Pennsylvania: Bentley Institute Press




Wang, W. and Y. Liu (2010)
A Note on Planar Hexagonal Meshes
, The IMA Volumes in Mathematics and Its Applications, Volume 151: Nonlinear Computational Geometry. eds. I.Z. Emiris, F. Sottile, T. Theobald, 221–233. New York: SpringerVerlag




Wang, W., J. Wallner, and Y. Liu (2007)
An Angle Criterion for Conical Mesh Vertices
, Journal for Geometry and Graphics 11(2): 199208




last changed 
2016/08/05 11:37 
