# Tightening: curvature-limiting morphological simplification

@inproceedings{Williams2005TighteningCM, title={Tightening: curvature-limiting morphological simplification}, author={Jason Williams and Jarek Rossignac}, booktitle={SPM '05}, year={2005} }

Given a planar set S of arbitrary topology and a radius r, we show how to construct an r-tightening of S, which is a set whose boundary has a radius of curvature everywhere greater than or equal to r and which only differs from S in a morphologically-defined tolerance zone we call the mortar. The mortar consists of the thin or highly curved parts of S, such as corners, gaps, and small connected components, while the boundary of a tightening consists of minimum-length loops through the mortar…

## 22 Citations

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- Mathematics, Computer ScienceDGCI
- 2011

Three different formulations of variable distance offsetting for planar shapes: orthogonal, radial, and ball are compared and compatibility conditions that specify when a shape is the offset of another are discussed.

b-morphs between b-compatible curves in the plane

- Mathematics, Computer ScienceSymposium on Solid and Physical Modeling
- 2009

This work defines b-compatibility for planar curves and proposes three ball morphing techniques (b-morphs) between pairs of b-compatible curves, finding that the Linear b-morph has consistently the shortest travel distance and that the Circular b- morph has the least amount of distortion.

Ball-Map: Homeomorphism between Compatible Surfaces

- Mathematics, Computer ScienceInt. J. Comput. Geom. Appl.
- 2010

The proposed ball-map is an excellent map for transferring parameterizations and textures between ball compatible curves or surfaces, and it is shown that, when S and S′ are Ck (n - 1)-manifolds in ℝn, BMS,S′ is a Ck-1 diffeomorphism and defines a CK-1 ambient isotopy that smoothly morphs between S to S′.

Shape complexity

- Computer ScienceThe Visual Computer
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This work discusses several complexity measures and the corresponding complexity reduction techniques and describes how the footprint and ease of use of a data structure, or the storage size of a compressed model, vary as a function of accuracy.

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- Computer ScienceNPAR
- 2008

A method for generating expressive stencils from polygonal meshes or images that makes use of multiple metrics to measure the appropriateness of connections between unstable stencil regions and chooses a best fit connection that maintains both structural integrity and local shape information.

Lattice Cleaving: A Multimaterial Tetrahedral Meshing Algorithm with Guarantees

- Computer Science, MedicineIEEE Transactions on Visualization and Computer Graphics
- 2014

This work introduces a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials and provides proofs showing that both element quality and geometric fidelity are bounded using this approach.

Dynamic particles for adaptive sampling of implicit surfaces

- Mathematics
- 2008

A ubiquitous requirement in many mathematical and computational problems is a set of well-placed point samples. For producing very even distributions of samples across complex surfaces, a dynamic…

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- Computer Science, MedicineIPMI
- 2007

A new method for constructing compact statistical point-based models of ensembles of similar shapes that does not rely on any specific surface parameterization, applicable to a wider range of problems than existing methods, including nonmanifold surfaces and objects of arbitrary topology.

Particle-based Sampling and Meshing of Surfaces in Multimaterial Volumes

- Computer Science, MedicineIEEE Transactions on Visualization and Computer Graphics
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This paper proposes a strategy for sampling and meshing multimaterial volumes using dynamic particle systems, including a novel, differentiable representation of the material junctions that allows the particle system to explicitly sample corners, edges, and surfaces of material intersections.

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- 2012

Generating accurate volume meshes from segmented image volumes is important in certain medical applications. One application is finite element analysis (FEA) for orthopaedic pre-operative planning.…

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