Sphere tracing: a geometric method for the antialiased ray tracing of implicit surfaces

Hart, John C.

doi:10.1007/s003710050084

Cited by 335 publications

(233 citation statements)

References 41 publications

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“…One can safely march this distance within a single step along the ray without penetrating a surface. This technique is called sphere tracing [4], and accelerates ray marching significantly. When the distance is below a certain threshold, x is considered to be a surface point.…”

Section: Ray Marchingmentioning

confidence: 99%

“…Thus, ray marching is often used to render implicit surfaces directly, where possible intersections are determined by marching along a ray in small steps until a surface is hit. Sphere tracing [4] speeds up ray marching significantly, but requires distance surfaces [1], implicitly described by functions that return a measurement or bound of the geometric distance, instead of a generic algebraic distance.…”

Section: Introductionmentioning

confidence: 99%

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Interactive modeling of implicit surfaces using a direct visualization approach with signed distance functions

Reiner

Mückl

Dachsbacher

2011

Computers & Graphics

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Modeling appealing virtual scenes is an elaborate and time-consuming task, requiring not only training and experience, but also powerful modeling tools providing the desired functionality to the user. In this paper, we describe a modeling approach using signed distance functions as an underlying representation for objects, handling both conventional and complex surface manipulations. Scenes defined by signed distance functions can be stored compactly and rendered directly in real-time using sphere tracing. Hence, we are capable of providing an interactive application with immediate visual feedback for the artist, which is a crucial factor for the modeling process. Moreover, dealing with underlying mathematical operations is not necessary on the user level. We show that fundamental aspects of traditional modeling can be directly transferred to this novel kind of environment, resulting in an intuitive application behavior, and describe modeling operations which naturally benefit from implicit representations. We show modeling examples where signed distance functions are superior to explicit representations, but discuss the limitations of this approach as well.

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Section: Ray Marchingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Interactive modeling of implicit surfaces using a direct visualization approach with signed distance functions

Reiner

Mückl

Dachsbacher

2011

Computers & Graphics

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“…Sphere tracing was introduced in [Har93] to ray trace implicit surfaces and applied to height field ray tracing in [Don05]. It uses a distance map and an iterative algorithm in order to always find the first hit.…”

Section: Sphere Tracingmentioning

confidence: 99%

Displacement Mapping on the GPU — State of the Art

Szirmay‐Kalos¹,

Umenhoffer²

2008

Computer Graphics Forum

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“…Distance based models are in fact extremely useful in many applications such as: constant-radius offsetting and blending operations [4], surface metamorphosis and smoothing [5], object reconstruction from a set of crosssections [6], rendering with sphere tracing [7], generation of skeletal shape representation [8], heterogeneous object modeling [9], and others.…”

Section: Introductionmentioning

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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Sphere tracing: a geometric method for the antialiased ray tracing of implicit surfaces

Cited by 335 publications

References 41 publications

Interactive modeling of implicit surfaces using a direct visualization approach with signed distance functions

Interactive modeling of implicit surfaces using a direct visualization approach with signed distance functions

Displacement Mapping on the GPU — State of the Art

Web-based Constructive Shape Modeling Using Real Distance Functions

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