Implicit surfaces that interpolate

Turk, Greg; Dinh, Huong Quynh; O’Brien, James F.; Yngve, Gary

doi:10.1109/sma.2001.923376

Cited by 58 publications

(67 citation statements)

References 19 publications

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“…In this paper, we will adopt the notations presented by Turk et al [12]. The scattered data interpolation problem in 3D can be stated as follows: given n distinct points fc 1 ; c 2 ; y; c n g in R 3 and their associated real values fh 1 ; h 2 ; y; h n g; find a smooth unknown function f ðrÞ such that f ðc i Þ ¼ h i ; i ¼ 1; 2; y; n: The smoothness of f ðrÞ is measured by minimizing the energy functional…”

Section: Interpolating Implicit Surface Based On Radial Basis Functionsmentioning

confidence: 99%

“…where o j are real-valued weights, f are radial basis functions, and PðrÞ is a one-degree polynomial accounting for the linear and constant portions of f [12]. Choosing PðrÞ as a linear polynomial can ensure that the resulting surface is affine invariant to the input scattered points.…”

Section: Interpolating Implicit Surface Based On Radial Basis Functionsmentioning

confidence: 99%

“…In this paper, we adopt triharmonic spline fðrÞ ¼ jrj 3 for 3D interpolation as in [12]. The interpolant then becomes:…”

Section: Interpolating Implicit Surface Based On Radial Basis Functionsmentioning

confidence: 99%

“…We use two types of constraints: boundary constraints and normal constraints, as introduced by Turk et al [12]. The vertices of the mesh form a set of boundary constraints where the implicit function takes on zero, and the normals form a set of normal constraints where the function takes on one.…”

Section: Interpolating Implicit Surface Based On Radial Basis Functionsmentioning

confidence: 99%

“…Later, Turk et al used an interpolating implicit surface as a shape transformation tool [8], both shape interpolation and feature specification are elegantly incorporated in one concise scattered data interpolation model. In addition to shape blending and surface reconstruction [8][9][10], interpolating implicit surfaces are also gaining acceptance in computer assisted surgical planning [11], complex surface modeling [12], mesh repairing [13] and sketching [14].…”

Section: Introductionmentioning

confidence: 99%

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Subdivision interpolating implicit surfaces

Jin

Sun

Peng

2003

Computers & Graphics

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Interpolating implicit surfaces using radial basis functions can directly specify surface points and surface normals with closed form solutions, so they are elegantly used in surface reconstruction and shape morphing. This paper presents subdivision interpolating implicit surfaces, a new progressive subdivision tessellation scheme for interpolating implicit surfaces controlled by a triangular mesh with arbitrary topology. We use a recursive polyhedral subdivision scheme to subdivide the control triangular mesh, and the new generated vertices are mapped to the implicit surface using Newton iteration. A multiresolution surface representation is automatically built with the proposed approach. Based on this approach, a newly surface modeling tool with more flexible control is developed by blending the interpolating subdivision surfaces with the subdivision interpolating implicit surfaces. r

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Section: Interpolating Implicit Surface Based On Radial Basis Functionsmentioning

confidence: 99%

Section: Interpolating Implicit Surface Based On Radial Basis Functionsmentioning

confidence: 99%

“…In this paper, we adopt triharmonic spline fðrÞ ¼ jrj 3 for 3D interpolation as in [12]. The interpolant then becomes:…”

Section: Interpolating Implicit Surface Based On Radial Basis Functionsmentioning

confidence: 99%

Section: Interpolating Implicit Surface Based On Radial Basis Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Subdivision interpolating implicit surfaces

Jin

Sun

Peng

2003

Computers & Graphics

View full text Add to dashboard Cite

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Reconstruction of shape and its effect on flow in arterial conduits

Gambaruto

Peiró

Doorly

et al. 2007

Numerical Methods in Fluids

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SUMMARYThe geometry of arterial conduits derived from in vivo image data is subject to acquisition and reconstruction errors. This results in a degree of uncertainty in defining the bounding geometry for a patient-specific anatomical conduit. In applying computational fluid dynamics to model the flow in specific anatomical configurations, the effect of the uncertainty in boundary definition should be considered, particularly if the objective is to extract quantitative measures of the local haemodynamics.Taking an example of a bypass graft configuration, we examine the effects of image threshold, surface smoothing and semi-idealization on the modelled geometry and the resulting flow. Procedures for reconstruction from medical images are outlined and applied with different parameter values within the image uncertainty range to create alternative models from the same data set.Methods to characterize the flow structure and wall shear stress (WSS) are introduced and used to provide quantitative comparison of the different haemodynamic environments associated with the varying model geometries. Comparable effects on the WSS distribution are found to occur with progressively increased surface smoothing and semi-idealization of the geometry by elliptical section fitting. Significant differences in WSS correspond to different threshold choices.

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High‐order algorithms for vascular flow modelling

Peiró

Giordana

Griffith

et al. 2002

Numerical Methods in Fluids

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This paper presents the development of spectral/hp high‐order elements for vascular flows with particular attention to surface reconstruction and high‐order mesh generation. Using ideas from computer visualization we apply a technique of constructing smooth implicit functions to reconstruct incomplete sectional imaging data from magnetic resonance imaging. Using this as a starting point we outline techniques to discretize and computationally solve the Newtonian flow within these geometries using high‐order spectral/hp element methods. Finally we demonstrate the application of these ideas to anatomically correct and model distal bypass grafts. Copyright © 2002 John Wiley & Sons, Ltd.

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Implicit surfaces that interpolate

Abstract: Abstract

Cited by 58 publications

References 19 publications

Subdivision interpolating implicit surfaces

Subdivision interpolating implicit surfaces

Reconstruction of shape and its effect on flow in arterial conduits

High‐order algorithms for vascular flow modelling

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