Two‐dimensional Potential Fields for Advanced Implicit Modeling Operators

Barthe, Loïc; Dodgson, Neil A.; Sabin, Malcolm; Wyvill, Brian; Gaildrat, Véronique

doi:10.1111/1467-8659.t01-1-00643

Cited by 39 publications

(67 citation statements)

References 36 publications

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“…When m = 1, it boils down to a simple sum, as the popular operator of Blinn [3], whose continuous extension by Bloomenthal et al [23] yielded to convolution implicit surfaces. While several new composition operators [24,25,26] and composition concepts [27,28] are introduced for field functions with global support, operators for compactly supported fields received less attention until the last decade. Hsu et al [13] improved the control of the blending size using adequate transfer functions modifying the slope of the composed field functions.…”

Section: Related Workmentioning

confidence: 99%

Adequate inner bound for geometric modeling with compact field functions

Canezin¹,

Guennebaud²,

Barthe³

2013

Computers & Graphics

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Recent advances in implicit surface modeling now provide highly controllable blending effects. These effects rely on the field functions of R 3 → R in which the implicit surfaces are defined. In these fields, there is an outside part in which blending is defined and an inside part. The implicit surface is the interface between these two parts. As recent operators often focus on blending, most efforts have been made on the outer part of field functions and little attention has been paid on the inner part. Yet, the inner fields are important as soon as difference and intersection operators are used. This makes its quality as crucial as the quality of the outside.In this paper, we analyze these shortcomings, and deduce new constraints on field functions such that differences and intersections can be seamlessly applied without introducing discontinuities or field distortions. In particular, we show how to adapt state of the art gradient-based union and blending operators to our new constraints. Our approach enables a precise control of the shape of both the inner or outer field boundaries. We also introduce a new set of asymmetric operators tailored for the modeling of fine details while preserving the integrity of the resulting fields.

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Section: Related Workmentioning

confidence: 99%

Adequate inner bound for geometric modeling with compact field functions

Canezin¹,

Guennebaud²,

Barthe³

2013

Computers & Graphics

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“…Moreover, it is easily possible to combine implicitly defined surfaces in various ways, e.g., by blending them together or by Boolean operations (CSG), see e.g. [4,15,23].…”

Section: Related Workmentioning

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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“…The superelliptic approximations of min / max [18] do not describe exact set-theoretic operations and suit only for blending. The elliptic approximation of min / max by Barthe et al [24] is designed initially for blending and the error of the distance function grows infinitely far from the boundary.…”

Section: Distance Function Constructionmentioning

confidence: 99%

“…This bad behavior can cause unexpected results when later operations are applied. The idea developed here is inspired by the work of Barthe et al [24] and consists in replacing the sharp corners in the graphs of min and max (see Fig. 1, left, for the case of the union of two half-planes f 1 (x, y) = x ≥ 0 and f 2 (x, y) = y ≥ 0), by bounded circular approximations (see Fig.…”

Section: Smooth Function Approximation For Set-theoretic Operationsmentioning

confidence: 99%

Web-based Constructive Shape Modeling Using Real Distance Functions

Fayolle

Sliwa

Goto³

et al. 2005

IEICE Transactions on Information and Systems

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Abstract:We present an approach and a web-based system implementation for modeling shapes using real distance functions. The system consists of an applet supporting the HyperFun modeling language. The applet is extended with primitives defined by Euclidean distance from a point to the surface of the shape. Set-theoretic operations (union, intersection, difference) that provide an approximation of the Euclidean distance to a shape built in a constructive way are introduced. Such operations have a controllable bounded error of the exact Euclidean distance to the shape and preserve C 1 continuity of the overall function, which is an important condition for further operations and applications. The proposed system should help model various shapes, store them in a concise form, and exchange them easily between different entities on a network. The applet offers also the possibility to export the models defined in the HyperFun language to other formats for raytracing or rapid prototyping. Department of Digital Media Faculty of Computer and Information SciencesHosei University 3-7-2 Kajino-cho, Koganei-shi Tokyo 184-8584 Japan SummaryWe present an approach and a web-based system implementation for modeling shapes using real distance functions. The system consists of an applet supporting the HyperFun modeling language. The applet is extended with primitives defined by Euclidean distance from a point to the surface of the shape. Set-theoretic operations (union, intersection, difference) that provide an approximation of the Euclidean distance to a shape built in a constructive way are introduced. Such operations have a controllable bounded error of the exact Euclidean distance to the shape and preserve C 1 continuity of the overall function, which is an important condition for further operations and applications. The proposed system should help model various shapes, store them in a concise form, and exchange them easily between different entities on a network. The applet offers also the possibility to export the models defined in the HyperFun language to other formats for raytracing or rapid prototyping.

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Two‐dimensional Potential Fields for Advanced Implicit Modeling Operators

Cited by 39 publications

References 36 publications

Adequate inner bound for geometric modeling with compact field functions

Adequate inner bound for geometric modeling with compact field functions

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

Web-based Constructive Shape Modeling Using Real Distance Functions

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