Implicit Objects in Computer Graphics

Velho, Luiz; Gomes, Jonas; Figueiredo, Luiz Henrique de

doi:10.1007/b97350

Cited by 45 publications

(30 citation statements)

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“…One way around the problem is to locally refine the grid size. This is not new and is actually the way the digitization of implicit curves and surfaces have been done most of the time [1,2,[4][5][6][7][8][9]. Our aim is to explore such subdivision methods for surfaces in dimension n. …”

Section: Discussion Conclusion and Perspectivesmentioning

confidence: 99%

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Implicit Digital Surfaces in Arbitrary Dimensions

Toutant

Andrès

Largeteau-Skapin

et al. 2014

Advanced Information Systems Engineering

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Abstract. In this paper we introduce a notion of digital implicit surface in arbitrary dimensions. The digital implicit surface is the result of a morphology inspired digitization of an implicit surface {x ∈ R n : f (x) = 0} which is the boundary of a given closed subset ofUnder some constraints, the digital implicit surface has some interesting properties, such as k-tunnel freeness, and can be analytically characterized.

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Section: Discussion Conclusion and Perspectivesmentioning

confidence: 99%

“…In computer graphics, implicit surfaces {x ∈ R n : f (x) = 0} play a fundamental role because of their powerful expressiveness for modeling and their ability to describe general closed manifolds [1,2]. It is a very convenient way to define surfaces or more generally isosurfaces.…”

Section: Introductionmentioning

confidence: 99%

Implicit Digital Surfaces in Arbitrary Dimensions

Toutant

Andrès

Largeteau-Skapin

et al. 2014

Advanced Information Systems Engineering

View full text Add to dashboard Cite

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“…[35]), which offers various advantages for surface fitting. The most important ones are the nonexistence of the parameterization problem, repairing capabilities of incomplete data and simple operations of shape editing.…”

Section: Surface Fittingmentioning

confidence: 99%

Robust fitting of implicitly defined surfaces using Gauss–Newton-type techniques

Aigner

Jüttler

2009

Vis Comput

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We describe Gauss-Newton type methods for fitting implicitly defined curves and surfaces to given unorganized data points. The methods are suitable not only for leastsquares approximation, but they can also deal with general error functions, such as approximations to the ℓ 1 or ℓ ∞ norm of the vector of residuals. Two different definitions of the residuals will be discussed, which lead to two different classes of methods: direct methods and data-based ones. In addition we discuss the continuous versions of the methods, which furnish geometric interpretations as evolution processes.It is shown that the data-based methods -which are less costly, as they work without the computation of the closest points -can efficiently deal with error functions that are adapted to noisy and uncertain data. In addition, we observe that the interpretation as evolution process allows to deal with the issues of regularization and with additional constraints.

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“…Implicitly defined surfaces offer various advantages, such as the nonexistence of the parameterization problem for scattered data fitting, repairing capabilities of incomplete data, and simple operations of shape editing [33].…”

Section: Introductionmentioning

confidence: 99%

Modeling and 3D object reconstruction by implicitly defined surfaces with sharp features

Song

Jüttler

2009

Computers & Graphics

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We propose a new method for describing sharp features (i.e., edges and vertices) of implicitly defined surfaces. We consider an initial implicitly defined surface, which is represented as the zero set of a C 1 smooth scalar field with non-vanishing gradients. In order to represent sharp edges and vertices, this surface is augmented by adding new types of implicit representations, called edge descriptors and vertex descriptors. They are defined with the help of the distance field of edge curves. In our implementation, we use circular splines to describe these edge curves, since they support a fast and non-iterative closest point computation.After adding the edge and vertex descriptors to the initial scalar field, the zero set of the augmented function contains the sharp features. We apply the new representation to surface modelling by implicitly defined surfaces with sharp features and to object reconstruction. In the latter case we describe an algorithm for detecting the sharp curves and vertices of a shape which is given by an unorganized point cloud, which are then approximated by circular splines, in order to define the edge and vertex descriptors.

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Implicit Objects in Computer Graphics

Cited by 45 publications

References 0 publications

Implicit Digital Surfaces in Arbitrary Dimensions

Implicit Digital Surfaces in Arbitrary Dimensions

Robust fitting of implicitly defined surfaces using Gauss–Newton-type techniques

Modeling and 3D object reconstruction by implicitly defined surfaces with sharp features

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