Heterogeneous material modeling with distance fields

Biswas, Arpan; Shapiro, Vadim; Tsukanov, Igor

doi:10.1016/j.cagd.2003.08.002

Cited by 138 publications

(102 citation statements)

References 22 publications

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“…A heterogeneous construct is defined as an object with spatially varying material composition, as opposed to objects designed and manufactured out of a single material with constant properties [14]. Relevant work within the field of HOM was previously demonstrated that aims to better represent such constructs [12,14,22,23,24]. A range of mathematical models exists that achieve heterogeneous object representations [8,10,12,14,24,25,26,27,28].…”

Section: Heterogeneous Object Modeling (Hom)mentioning

confidence: 99%

“…Relevant work within the field of HOM was previously demonstrated that aims to better represent such constructs [12,14,22,23,24]. A range of mathematical models exists that achieve heterogeneous object representations [8,10,12,14,24,25,26,27,28]. These representations are generally classified under one of these three categories: evaluated models, unevaluated models and composite models [14].…”

Section: Heterogeneous Object Modeling (Hom)mentioning

confidence: 99%

“…Conventional computeraided design (CAD) tools can enable and support the manipulation of geometric and topologic virtual constructs. However, they generally lack the means to embed material data within virtual model constructs [12,13] mostly since such tools typically assume material homogeneity [12]. The field of Heterogeneous Object Modeling (HOM) addresses the growing demands for computational tools that embed material data [14] and enable the design of functionally graded structures.…”

mentioning

confidence: 99%

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Flow-based fabrication: An integrated computational workflow for design and digital additive manufacturing of multifunctional heterogeneously structured objects

Duro-Royo

Mogas-Soldevila

Oxman

2015

Computer-Aided Design

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Structural hierarchy and material organization in design are traditionally achieved by combining discrete homogeneous parts into functional assemblies where the shape or surface is the determining factor in achieving function. In contrast, biological structures express higher levels of functionality on a finer scale through volumetric cellular constructs that are heterogeneous and complex. Despite recent advancements in additive manufacturing of functionally graded materials, the limitations associated with computational design and digital fabrication of heterogeneous materials and structures frame and limit further progress. Conventional computer-aided design tools typically contain geometric and topologic data of virtual constructs, but lack robust means to integrate material composition properties within virtual models. We present a seamless computational workflow for the design and direct digital fabrication of multi-material and multi-scale structured objects. The workflow encodes for and integrates domainspecific meta-data relating to local, regional and global feature resolution of heterogeneous material organizations. We focus on water-based materials and demonstrate our approach by additively manufacturing diverse constructs associating shape-informing variable flow rates and material properties to mesh-free geometric primitives. The proposed workflow enables virtual-to-physical control of constructs where structural, mechanical and optical gradients are achieved through a seamless design-to-fabrication tool with localized control. An enabling technology combining a robotic arm and a multi-syringe multi nozzle deposition system is presented. Proposed methodology is implemented and full-scale demonstrations are included.

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Section: Heterogeneous Object Modeling (Hom)mentioning

confidence: 99%

Section: Heterogeneous Object Modeling (Hom)mentioning

confidence: 99%

mentioning

confidence: 99%

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Flow-based fabrication: An integrated computational workflow for design and digital additive manufacturing of multifunctional heterogeneously structured objects

Duro-Royo

Mogas-Soldevila

Oxman

2015

Computer-Aided Design

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“…Each primitive of this object is defined by Euclidean distance, and the set-theoretic operations are defined using SARDF operations. Therefore, the distance field of the object gives an accurate approximation to the exact Euclidean distance function and can be used in further applications such as heterogeneous object modeling [30], [9]. …”

Section: Cad Objectmentioning

confidence: 99%

“…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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Geometric Modeling of Complex Shapes and Engineering Artifacts

Wolter¹,

Peinecke²,

Reuter³

2004

Encyclopedia of Computational Mechanics

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A geometric model of an object -in most cases being a subset of the three dimensional space -can be used to better understand the object's structure or behaviour. Therefore data such as the geometry, the topology and other application specific data have to be represented by the model. With the help of a computer it is possible to manipulate, process or display these data. We will discuss different approaches for representing such an object: Volume based representations describe the object in a direct way, whereas boundary representations describe the object indirectly by specifying its boundary. A variety of different surface patches can be used to model the object's boundary. For many applications it is sufficient to know only the boundary of an object. For special objects explicit or implicit mathematical representations can easily be given. An explicit representation is a map from a known parameter space e.g. the unit cube to 3D-space. Implicit representations are equations or relations such as the set of zeros of a functional with three unknowns. These can be very efficient in special cases. As an example of volume based representations we will give a brief overview of the voxel representation. We also show how the boundary of complex objects can be assembled by simpler parts e.g. surface patches. These come in a variety of forms: planar polygons, parametric surfaces, especially spline surfaces and trimmed surfaces, multiresolutionally represented surfaces, e.g. wavelet-based surfaces. In a boundary representation only the boundary of a solid is described. This is usually done by describing the boundary as a collection of surface patches attached to each other at outer edges. Simple objects constructed via any of the methods above can be joined to build more complex objects via Boolean operators (constructive solid geometry, CSG). Constructing an object one has to assure that the object is in agreement with the topological requirements of the modeling system. Notoriously difficult problems are caused by the fact that most modeling systems can compute surface intersections only with a limited precision. This yields numerical results that may finally cause major errors e.g. topologically contradictory conclusions. The rather new method of "Medial Modeling" is also presented. Here an object is described by its medial axis and an associated radius function. The medial axis itself is a collection of lower dimensional objects, i.e. for a 3D-solid a set of points, curves and surface patches. This medial modeling concept developed at the Welfenlab yields a very intuitive user interface useful for solid modeling, and also gives a natural meshing of the solid for FEM computations. Additional attributes can be attached to an object, i.e. attributes of physical origin or logical attributes. Physical attributes include photometric, haptical and other material properties, such as elasticity or roughness. Physical attributes are often specified by textures, i.e. functions that relate surface points to certain quantities of ...

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Heterogeneous material modeling with distance fields

Cited by 138 publications

References 22 publications

Flow-based fabrication: An integrated computational workflow for design and digital additive manufacturing of multifunctional heterogeneously structured objects

Flow-based fabrication: An integrated computational workflow for design and digital additive manufacturing of multifunctional heterogeneously structured objects

Web-based Constructive Shape Modeling Using Real Distance Functions

Geometric Modeling of Complex Shapes and Engineering Artifacts

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