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- Alireza Entezari, Ramsay Dyer, Torsten Möller
- IEEE Visualization
- 2004

In this paper we derive piecewise linear and piecewise cubic box spline reconstruction filters for data sampled on the body centered cubic (BCC) lattice. We analytically derive a time domain representation of these reconstruction filters and using the Fourier slice-projection theorem we derive their frequency responses. The quality of these filters, when… (More)

- Ramsay Dyer, Hao Zhang, Torsten Möller
- Symposium on Geometry Processing
- 2007

We present algorithms to produce Delaunay meshes from arbitrary triangle meshes by edge flipping and geometrypreserving refinement and prove their correctness. In particular we show that edge flipping serves to reduce mesh surface area, and that a poorly sampled input mesh may yield unflippable edges necessitating refinement to ensure a Delaunay mesh… (More)

- Kai Xu, Hao Zhang, +4 authors Baoquan Chen
- ACM Trans. Graph.
- 2012

We present an algorithm for <i>multi-scale</i> partial intrinsic symmetry detection over 2D and 3D shapes, where the scale of a symmetric region is defined by intrinsic distances between symmetric points over the region. To identify prominent symmetric regions which overlap and vary in form and scale, we decouple scale extraction and symmetry extraction by… (More)

- Hao Zhang, Oliver van Kaick, Ramsay Dyer
- Eurographics
- 2007

Spectral methods for mesh processing and analysis rely on the eigenvalues, eigenvectors, or eigenspace projections derived from appropriately defined mesh operators to carry out desired tasks. Early works in this area can be traced back to the seminal paper by Taubin in 1995, where spectral analysis of mesh geometry based on a combinatorial Laplacian aids… (More)

- Ramsay Dyer, Hao Zhang, Torsten Möller
- Comput. Graph. Forum
- 2008

We develop adaptive sampling criteria which guarantee a topologically faithful mesh and demonstrate an improvement and simplification over earlier results, albeit restricted to 2D surfaces. These sampling criteria are based on functions defined by intrinsic properties of the surface: the strong convexity radius and the injectivity radius. We establish… (More)

- Tamal K. Dey, Ramsay Dyer, Lei Wang
- Computers & Graphics
- 2011

We introduce a surface reconstruction algorithm suitable for large point sets. The algorithm is an octree-based version of the Cocone reconstruction algorithm [4], allowing independent processing of small subsets of the total input point set. When the points are sufficiently sampled from a smooth surface, the global guarantee of topological correctness of… (More)

- Matt Olson, Ramsay Dyer, Hao Zhang, Alla Sheffer
- Computers & Graphics
- 2011

We present an algorithm to compute the silhouette set of a point cloud. Previous methods extract point set silhouettes by thresholding point normals, which can lead to simultaneous overand under-detection of silhouettes. We argue that additional information such as surface curvature is necessary to resolve these issues. To this end, we develop a local… (More)

- Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh
- ArXiv
- 2013

We describe an algorithm to construct an intrinsic Delaunay triangulation of a smooth closed submanifold of Euclidean space. Using results established in a companion paper on the stability of Delaunay triangulations on δ-generic point sets, we establish sampling criteria which ensure that the intrinsic Delaunay complex coincides with the restricted Delaunay… (More)

- Ramsay Dyer, Hao Zhang, Torsten Möller
- Symposium on Solid and Physical Modeling
- 2007

We define a <i>Delaunay mesh</i> to be a manifold triangle mesh whose edges form an <i>intrinsic Delaunay triangulation</i> or <i>iDT</i> of its vertices, where the triangulated domain is the piecewise flat mesh surface. We show that meshes constructed from a smooth surface by taking an iDT or a restricted Delaunay triangulation, do not in general yield a… (More)

- Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh
- Int. J. Comput. Geometry Appl.
- 2013

We introduce a parametrized notion of genericity for Delaunay triangulations which, in particular, implies that the Delaunay simplices of δ-generic point sets are thick. Equipped with this notion, we study the stability of Delaunay triangulations under perturbations of the metric and of the vertex positions. We quantify the magnitude of the perturbations… (More)