EUROGRAPHICS 2012 / P. Cignoni, T. Ertl (Guest Editors) Volume 31 (2012), Number 2 Generalized Swept Mid-structure for Polygonal Models Tobias Martin †1 , Guoning Chen 2 , Suraj Musuvathy 1 , Elaine Cohen 1 and Charles Hansen 1,2 1 School of Computing, University of Utah, USA 2 SCI, University of Utah, USA (a) (b) (c) Choice of Harmonic Function Compute Mid-structure for each Slice Generalized Swept Mid-structure Slice Object Match Mid-structures Figure 1: Pipeline for the Generalized Swept Mid-structure (GSM): (a) User choice of harmonic function. (b) Object is decomposed into (curved) slices, and a medial axis is computed for each slice. (c) Slices are iteratively matched into a GSM (colored surface sheets). Abstract We introduce a novel mid-structure called the generalized swept mid-structure (GSM) of a closed polygonal shape, and a framework to compute it. The GSM contains both curve and surface elements and has consistent sheet-by-sheet topology, versus triangle-by-triangle topology produced by other mid-structure methods. To obtain this structure, a harmonic function, defined on the volume that is enclosed by the surface, is used to decompose the volume into a set of slices. A technique for computing the 1D mid-structures of these slices is introduced. The mid-structures of adjacent slices are then iteratively matched through a boundary similarity computation and triangulated to form the GSM. This structure respects the topology of the input surface model is a hybrid mid-structure representation. The construction and topology of the GSM allows for local and global simplification, used in further applications such as parameterization, volumetric mesh generation and medical applications. 1. Introduction Many applications in the field of computer graphics and visu- alization require interior mid-structures of three dimensional objects that represent their form or shape with lower dimen- sional entities. One dimensional curve skeletons [ATC ∗ 08], and the 3D medial axis [SP08], are such examples that have † martin@cs.utah.edu been used for mesh generation, animation, registration, and segmentation applications. Curve skeletons faithfully repre- sent an object in tubular regions. For more general geom- etry, a medial axis is preferred since it consists of surface sheets [SP08] and they better capture the shape than curve skeletons. However, a medial axis is very sensitive to small changes in shape and it produces nearly degenerate polygons in tubular regions. Our quest for a new type of mid-structure is moti- c  2012 The Author(s) Computer Graphics Forum c  2012 The Eurographics Association and Blackwell Publish- ing Ltd. Published by Blackwell Publishing, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA.