An Overview of Analytic Solid Modeling

Casale, Malcolm; Stanton, E. L.

doi:10.1109/mcg.1985.276402

Cited by 67 publications

(10 citation statements)

References 9 publications

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“…In meshing, a 3D grid of points is used to define a hyperpatch [9]. These points are interpolated by means of blending functions that are analogous to those used to define surface patches.…”

Section: Review Of Freeform Solid Modelling Methodsmentioning

confidence: 99%

A Uniform Representation Scheme for Freeform Geometric Modelling

Steketee

1989

Theory and Practice of Geometric Modeling

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The mesh-subdivision scheme. a uniform scheme for the representation of objects used in freeform geometric modelling. is discussed. The scheme has two parts: a mesh representing the topological structure and approximating the geometric structure. and a recursive subdivision method. using parametcrs to control the shape of the objcct. It is shown that the problem of selfintersection in known recursive subdivision methods can be solved. and it is indicated how freeform solid modelling methods can be integrated in the scheme.

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Section: Review Of Freeform Solid Modelling Methodsmentioning

confidence: 99%

A Uniform Representation Scheme for Freeform Geometric Modelling

Steketee

1989

Theory and Practice of Geometric Modeling

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“…The trivariate tensor-product B-spline solid (Casale and Stanton, 1985;Lasser, 1985) is a direct extension of the B-spline patch and has been shown to be useful in the creation and visualization of free-form geometric solids. The trivariate B-spline solid is defined by a set of (n x + l)x(n 2 +l)x(n 3 +1) control points {p, il2 , :0<i x <n x ,0<i 2 <« 2 ,0<i 3 <n 3 ), and three sets of knots {u Q ,u x ,...,u n+m }, {v 0 7v,,..., v" 2+m2 }, and {w 0 , w,,..., w^+ mj }, where n n n p(u,v,w) = XIZP^^^J V^^.…”

Section: Basic Conceptsmentioning

confidence: 99%

“…Blackmore et al (1994) extended the SDE approach from rigid sweeps to objects experiencing general smooth deformations. To accomplish this, they observed that an object that is deforming as it is swept along can be modeled by the action of a sweep of the form o(x) = x P(t) + R(t)x + A(x,t) (38) where A(x, t) represents a general nonlinear deformation. Here it is useful to note that when the sweep is rigid, R(?…”

Section: Deformable Sweepsmentioning

confidence: 99%

Swept Volumes: Fundation, Perspectives, and Applications

Abdel‐Malek

Yang

Blackmore³

et al. 2006

Int. J. Shape Model.

105

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A survey of swept volume concepts and methods is presented. It consolidates and relates seemingly different terminology and methods. The methods are divided into five major categories: method with envelope theory, method with sweep differential equation (SDE)/sweep envelope differential equation (SEDE), method with Jacobian rank deficiency, Voxel-based method, and free-form solids' sweeping methods. Commentary is provided on three fronts, concerning the advantages and pitfalls of individual methods, the different classes of methods, and the field of swept volumes as a whole. The characteristics of the most significant methods are summarized. The applicability of this seemingly simple formulation to the fields of solid modeling, robotics, manufacturing automation, and visualization is demonstrated through results reported by the authors, each in their own field.

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“…They describe techniques for performing blending, warping and boolean operations on skeletal implicit surfaces. An interesting variation of implicit modeling is presented in [28], which uses a forest of trivariate functions [29] evaluated on an octree to create a multiresolution sculpting capability.…”

Section: Related Workmentioning

confidence: 99%

Algorithms for Interactive Editing of Level Set Models

Museth

Breen

Whitaker

et al. 2005

Computer Graphics Forum

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Level set models combine a low-level volumetric representation, the mathematics of deformable implicit surfaces and powerful, robust numerical techniques to produce a novel approach to shape design. While these models offer many benefits, their large-scale representation and numerical requirements create significant challenges when developing an interactive system. This paper describes the collection of techniques and algorithms (some new, some pre-existing) needed to overcome these challenges and to create an interactive editing system for this new type of geometric model. We summarize the algorithms for producing level set input models and, more importantly, for localizing/minimizing computation during the editing process. These algorithms include distance calculations, scan conversion, closest point determination, fast marching methods, bounding box creation, fast and incremental mesh extraction, numerical integration and narrow band techniques. Together these algorithms provide the capabilities required for interactive editing of level set models.

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An Overview of Analytic Solid Modeling

Cited by 67 publications

References 9 publications

A Uniform Representation Scheme for Freeform Geometric Modelling

A Uniform Representation Scheme for Freeform Geometric Modelling

Swept Volumes: Fundation, Perspectives, and Applications

Algorithms for Interactive Editing of Level Set Models

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