Smooth subdivision of tetrahedral meshes

Schaefer, Scott; Hakenberg, Jan; Warren, Joe

doi:10.1145/1057432.1057452

Cited by 32 publications

(24 citation statements)

References 8 publications

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“…where F(S d ) and {∆x} are the points and volumes of the finite-element approximation to S 3 , based on a recursive tetrahedral-octahedral subdivision method [19].…”

Section: First-ordermentioning

confidence: 99%

Tracking the spin on a ping pong ball with the quaternion Bingham filter

Glover

Kaelbling

2014

2014 IEEE International Conference on Robotics and Automation (ICRA)

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“…where F(S d ) and {∆x} are the points and volumes of the finite-element approximation to S 3 , based on a recursive tetrahedral-octahedral subdivision method [19].…”

Section: First-ordermentioning

confidence: 99%

Tracking the spin on a ping pong ball with the quaternion Bingham filter

Glover

Kaelbling

2014

2014 IEEE International Conference on Robotics and Automation (ICRA)

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“…To improve FEM, a large amount of research has been conducted for the discretization of the input object (e.g., (Shewchuk, 1998) or (Schaefer et al, 2004)), and for accelerating the computation. To reduce the heavy computation cost of FEM, adaptive subdivision approaches (e.g., (Debunne et al, 2001;Grinspun et al, 2002;Dequidt et al, 2005)) are usually used.…”

Section: Related Workmentioning

confidence: 99%

Adaptively Simulating Inhomogeneous Elastic Deformation

Imai

Yue

Chen

et al. 2013

Proceedings of the International Conference on Computer Graphics Theory and Applications and International Conference on Inform

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Abstract:In this paper, we present an adaptive approach for simulating elastic deformation of homogeneous and inhomogeneous objects based on continuum mechanics. In typical adaptive simulation approaches, the deforming elastic object is usually subdivided to form a tree structure on the fly. However, they are not directly applicable for inhomogeneous elastic deformation, since the elasticity matrix, which describes the stiffness, of each element in each resolution is difficult to estimate at runtime. Furthermore, as most multi-resolution approaches, it is usually required that the stiffness of the object should either be uniform all throughout its body or consist of a collection of uniform parts, otherwise the elasticity matrices for the elements in coarse levels cannot be determined. Hence, we propose a bottom-up sampling approach to estimate the elasticity matrices for all elements in all levels based on a given stiffness function. Moreover, the subdivision process is also moved to the off-line preprocessing stage with the elasticity matrix estimation to reduce the runtime computational cost while achieving the adaptive simulation by adaptively selecting the simulation level on the fly. Therefore, we can efficiently simulate the deformation of an elastic object even with spatially varying stiffness.

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“…For modeling anatomical structures in 3D, we consider the tetrahedral subdivision scheme of Schaeffer et al [21]. Given an initial mesh consisting of tetrahedral cells of arbitrary topology (Fig.…”

Section: Atlas Representationmentioning

confidence: 99%

Automated, Foot-Bone Registration Using Subdivision-Embedded Atlases for Spatial Mapping of Bone Mineral Density

Liu¹,

Commean²,

Hildebolt³

et al. 2012

J Digit Imaging

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We present an atlas-based registration method for bones segmented from quantitative computed tomography (QCT) scans, with the goal of mapping their interior bone mineral densities (BMDs) volumetrically. We introduce a new type of deformable atlas, called subdivision-embedded atlas, which consists of a control grid represented as a tetrahedral subdivision mesh and a template bone surface embedded within the grid. Compared to a typical latticebased deformation grid, the subdivision control grid possesses a relatively small degree of freedom tailored to the shape of the bone, which allows efficient fitting onto subjects. Compared with previous subdivision atlases, the novelty of our atlas lies in the addition of the embedded template surface, which further increases the accuracy of the fitting. Using this new atlas representation, we developed an efficient and fully automated pipeline for registering atlases of 12 tarsal and metatarsal bones to a segmented QCT scan of a human foot. Our evaluation shows that the mapping of BMD enabled by the registration is consistent for bones in repeated scans, and the regional BMD automatically computed from the mapping is not significantly different from expert annotations. The results suggest that our improved subdivision-based registration method is a reliable, efficient way to replace manual labor for measuring regional BMD in foot bones in QCT scans.

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Smooth subdivision of tetrahedral meshes

Cited by 32 publications

References 8 publications

Tracking the spin on a ping pong ball with the quaternion Bingham filter

Tracking the spin on a ping pong ball with the quaternion Bingham filter

Adaptively Simulating Inhomogeneous Elastic Deformation

Automated, Foot-Bone Registration Using Subdivision-Embedded Atlases for Spatial Mapping of Bone Mineral Density

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