Smooth surface reconstruction via natural neighbour interpolation of distance functions

Boissonnat, Jean‐Daniel; Cazals, Frédéric

doi:10.1016/s0925-7721(01)00048-7

Cited by 197 publications

(159 citation statements)

References 11 publications

Supporting

Mentioning

157

Contrasting

Unclassified

Order By: Relevance

“…Several results were obtained in this framework, some of the earliest of which pertaining the medial axis are due to Amenta, Bern, and Eppstein [2], and Boissonnat and Cazals [5], each establishing that a subset of the Voronoi vertices in the Voronoi diagram of the sample points lie close to the medial axis. Later, Amenta, Choi, and Kolluri [3] designed an algorithm that computes an approximation of the medial axis, in shape of a cell complex, that is provably homotopy equivalent to the medial axis of the shape, provided that that shape boundary is sampled densely enough.…”

Section: Introductionmentioning

confidence: 99%

Medial Axis Approximation and Unstable Flow Complex

Giesen

Ramos

Sadri

2008

Int. J. Comput. Geom. Appl.

View full text Add to dashboard Cite

The medial axis of a shape is known to carry a lot of information about it. In particular a recent result of Lieutier establishes that every bounded open subset of R n has the same homotopy type as its medial axis. In this paper we provide an algorithm that, given a sufficiently dense but not necessarily uniform sample from the surface of a shape with smooth boundary, computes a core for its medial axis approximation, in form of a piecewise linear cell complex, that captures the topology of the medial axis of the shape. We also provide a natural method to freely augment this core in order to enhance it geometrically all the while maintaining its topological guarantees. The definition of the core and its extension method are based on the steepest ascent flow induced by the distance function to the sample. We also provide a geometric guarantee on the closeness of the core and the actual medial axis.

show abstract

Section: Introductionmentioning

confidence: 99%

Medial Axis Approximation and Unstable Flow Complex

Giesen

Ramos

Sadri

2008

Int. J. Comput. Geom. Appl.

View full text Add to dashboard Cite

show abstract

“…For example, in the study of dynamical systems, the quasiperiodic and chaotic orbits can be automatically recognized from sample points in the phase portraits if automatic shape recognition can be performed; see [23]. To this end one may try reconstruction algorithms for curves [2, I l, 17] and for surfaces [1,3,6,8,12,18]. Unfortunately, these reconstruction algorithms are of no use if the dimension of the shape is not determined a priori.…”

Section: Introductionmentioning

confidence: 99%

Shape Dimension and Approximation from Samples

Dey¹,

Giesen²,

Goswami³

et al. 2003

Discrete and Computational Geometry

View full text Add to dashboard Cite

There are many scientific and engineering applications where an automatic detection of shape dimension from sample data is necessary. Topological dimensions of shapes constitute an important global feature of them. We present a Voronoi based dimension detection algorithm that assigns a dimension to a sample point which is the topological dimension of the manifold it belongs to, Based on this dimension detection, we also present an algorithm to approximate shapes of arbitrary dimension from their samples. Our empirical results with data sets in three dimensions support our theory.

show abstract

“…33 Centrifugal forces do not significantly affect the flow in this vascular compartment, where the motion is quasi-independent on the vessel geometry.…”

Section: Quasi-steady Flowmentioning

confidence: 90%

“…Delaunay tetrahedralization algorithms first generate 3D triangulation over a point cloud and then extract a bounded surface triangulation from this set of tetrahedra using suitable topological and geometrical criteria [33].…”

Section: Image-based Computational Modelmentioning

confidence: 99%

Biofluid Flow and Heat Transfer

Thiriet¹,

Sheu²,

Garon³

2016

Handbook of Fluid Dynamics, Second Edition

View full text Add to dashboard Cite

2nd EditionInternational audienceMajor moving biological fluids, or biofluids, are blood and air that cooperate to bring oxygento the body’s cells and eliminate carbon dioxide produced by these cells. Blood is conveyed ina closed network composed of 2 circuits in series — the systemic and pulmonary circulation—, each constituted by arteries, capillaries, and veins, under the synchronized action of theleft and right cardiac pumps, respectively. Air is successively inhaled from and exhaled to theatmosphere through the airway openings (nose and/or mouth). In the head, blood generatesthe cerebrospinal fluid in choroid plexi of all compartments of the ventricular system andreceives it in arachnoid villi. Other biofluids are either secreted, such as bile from the liverand breast milk that both transport released substances with specific tasks, or excreted,such as urine from kidneys or sweat from skin glands that both convey useless materials andwaste produced by the cell metabolism. In addition to the convective transport, peristalsis,which results from the radial contraction and relaxation of mural smooth muscles, propelsthe content of the lumen of the muscular bioconduit (e.g., digestive tract) in an anterogradedirection.Blood circulation and air flow in the respiratory tract are widely explored because oftheir vital functions. Note that inhaled air is transported through the respiratory tract bytwo processes: convection down to bronchioles and diffusion down to pulmonary alveoli.1Furthermore, investigations of these physiological flows in deformable bioconduits give riseto models such as the Starling resistance that themselves become object of new study fieldsin physics and mechanics (e.g., collapsible tubes) as well as of new developments in math-ematical modeling and scientific computing. Whereas fluid–structure interaction problemsin aeronautics and civil engineering deal with materials of distinct properties, blood streamand vessel wall correspond to two domains of nearly equal physical properties, as both bloodand vessels have densities close to that of water. New processing strategies must then beconceived

show abstract

Smooth surface reconstruction via natural neighbour interpolation of distance functions

Cited by 197 publications

References 11 publications

Medial Axis Approximation and Unstable Flow Complex

Medial Axis Approximation and Unstable Flow Complex

Shape Dimension and Approximation from Samples

Biofluid Flow and Heat Transfer

Contact Info

Product

Resources

About