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Level set surface editing operators
 SIGGRAPH
, 2002
"... Figure 1: Surfaces edited with level set operators. Left: A damaged Greek bust model is repaired with a new nose, chin and sharpened hair. Right: A new model is constructed from models of a griffin and dragon (small figures), producing a twoheaded, winged dragon. We present a level set framework fo ..."
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Cited by 103 (10 self)
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Figure 1: Surfaces edited with level set operators. Left: A damaged Greek bust model is repaired with a new nose, chin and sharpened hair. Right: A new model is constructed from models of a griffin and dragon (small figures), producing a twoheaded, winged dragon. We present a level set framework for implementing editing operators for surfaces. Level set models are deformable implicit surfaces where the deformation of the surface is controlled by a speed function in the level set partial differential equation. In this paper we define a collection of speed functions that produce a set of surface editing operators. The speed functions describe the velocity at each point on the evolving surface in the direction of the surface normal. All of the information needed to deform a surface is encapsulated in the speed function, providing a simple, unified computational framework. The user combines predefined building blocks to create the desired speed function. The surface editing operators are quickly computed and may be applied both regionally and globally. The level set framework offers several advantages. 1) By construction, selfintersection cannot occur, which guarantees the generation of physicallyrealizable, simple, closed surfaces. 2) Level set models easily change topological genus, and 3) are free of the edge connectivity and mesh quality problems associated with mesh models. We present five examples of surface editing operators: blending, smoothing, sharpening, openings/closings and embossing. We demonstrate their effectiveness on several scanned objects and scanconverted models.
3d scan conversion of csg models into distance volumes
 Proc. 1998 IEEE Symposium on Volume Visualization
, 1998
"... A distance volume is a volume dataset where the value stored at each voxel is the shortest distance to the surface of the object being represented by the volume. Distance volumes are a useful representation in a number of computer graphics applications. In this paper we present a technique for gener ..."
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Cited by 58 (4 self)
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A distance volume is a volume dataset where the value stored at each voxel is the shortest distance to the surface of the object being represented by the volume. Distance volumes are a useful representation in a number of computer graphics applications. In this paper we present a technique for generating a distance volume with subvoxel accuracy from one type of geometric model, a Constructive Solid Geometry (CSG) model consisting of superellipsoid primitives. The distance volume is generated in a two step process. The first step calculates the shortest distance to the CSG model at a set of points within a narrow band around the evaluated surface. Additionally, a second set of points, labeled the zero set, which lies on the CSG model’s surface are computed. A point in the zero set is associated with each point in the narrow band. Once the narrow band and zero set are calculated, a Fast Marching Method is employed to propagate the shortest distance and closest point information out to the remaining voxels in the volume. Our technique has been used to scan convert a number of CSG models, producing distance volumes which have been utilized in a variety of computer graphics applications, e.g. CSG surface evaluation, offset surface generation, and 3D model morphing. 1
Offsetting operations in solid modelling
, 1986
"... The range of operations on solids supported by current geometric modelling systems is very limited. Typically, solids represented in a modeller can be transformed by rigid motions and combined by Boolean operations. This paper introduces another family of transformations, called solid offsetting, ..."
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Cited by 51 (10 self)
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The range of operations on solids supported by current geometric modelling systems is very limited. Typically, solids represented in a modeller can be transformed by rigid motions and combined by Boolean operations. This paper introduces another family of transformations, called solid offsetting, which map solids into solids. Offset solids are expanded or contracted versions of an original object. Offsetting operations are potentially useful for tolerance analysis, clearance testing, designrule checking in VLSI, modelling of etching and coating processes, cutter path generation for numericallycontrolled machine tools, collision free path planning for robot motions, and for constantradius rounding and filleting ('blending') of solids. This paper discusses mathematical properties of solid offsetting, associated representations and algorithms, support of offsetting operations in solid modellers, and applications, Results of an experimental implementation are presented.
Constructive Volume Geometry
 Computer Graphics Forum
, 2000
"... We present an algebraic framework, called Constructive Volume Geometry (CVG), for modelling complex spatial objects using combinational operations. By utilising scalar fields as fundamental building blocks, CVG provides highlevel algebraic representations of objects that are defined mathematically ..."
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Cited by 47 (17 self)
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We present an algebraic framework, called Constructive Volume Geometry (CVG), for modelling complex spatial objects using combinational operations. By utilising scalar fields as fundamental building blocks, CVG provides highlevel algebraic representations of objects that are defined mathematically or built upon sampled or simulated datasets. It models amorphous phenomena as well as solid objects, and describes the interior as well as the exterior of objects. We also describe a hierarchical representation scheme for CVG, and a direct rendering method with a new approach for consistent sampling. The work has demonstrated the feasibility of combining a variety of graphics data types in a coherent modelling scheme.
Constructive Solid Geometry for Polyhedral Objects
, 1986
"... Constructive Solid Geometry (CSG) is a powerful way of describing solid objects for computer graphics and modeling. The surfaces of any primitive object (such as a cube, sphere or cylinder) can be approximated by polygons. Being abile to find the union, intersection or difference of these objects al ..."
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Cited by 45 (1 self)
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Constructive Solid Geometry (CSG) is a powerful way of describing solid objects for computer graphics and modeling. The surfaces of any primitive object (such as a cube, sphere or cylinder) can be approximated by polygons. Being abile to find the union, intersection or difference of these objects allows more interesting and complicated polygonal objects to be created. The algorithm presented here performs these set operations on objects constructed from convex polygons. These objects must bound a finite volume, but need not be convex. An object that results from one of these operations also contains only convex polygons, and bounds a finite volume; thus, it can be used in later combinations, allowing the generation of quite complicated objects. Our algorithm is robust and is presented in enough detail to be implemented.
Interactive Boolean Operations for Conceptual Design of 3D Solids
, 1997
"... Interactive modeling of 3D solids is an important and difficult problem in computer graphics. The Constructive Solid Geometry (CSG) modeling scheme is highly attractive for interactive design, due to its support for hierarchical modeling and Boolean operations. Unfortunately, current algorithms for ..."
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Cited by 41 (1 self)
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Interactive modeling of 3D solids is an important and difficult problem in computer graphics. The Constructive Solid Geometry (CSG) modeling scheme is highly attractive for interactive design, due to its support for hierarchical modeling and Boolean operations. Unfortunately, current algorithms for interactive display of CSG models require expensive specialpurpose hardware that is not easily available. In this paper we present a method for interactive display of CSG models using standard, widely available graphics hardware. The method enables the user to interactively modify the affine transformations associated with CSG subobjects. The application we focus upon is that of conceptual design, a stage in the design process in which rapid, interactive visualization of the model and highlevel design operations are of crucial importance, while the objects are relatively simple. The method converts the CSG graph to a novel Convex Differences Aggregate(CDA) representation. The CDA utili...
Matchmaker: Manifold BReps for nonmanifold rsets
 Proceedings of the ACM Symposium on Solid Modeling
, 1999
"... Many solid modeling construction techniques produce nonmanifold rsets (solids). With each nonmanifold model N we can associate a family of manifold solid models that are infinitely close to N in the geometric sense. For polyhedral solids, each nonmanifold edge of N with 2k incident faces will be ..."
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Cited by 40 (20 self)
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Many solid modeling construction techniques produce nonmanifold rsets (solids). With each nonmanifold model N we can associate a family of manifold solid models that are infinitely close to N in the geometric sense. For polyhedral solids, each nonmanifold edge of N with 2k incident faces will be replicated k times in any manifold model M of that family. Furthermore, some nonmanifold vertices of N must also be replicated in M, possibly several times. M can be obtained by defining, in N, a single adjacent face TA(E,F) for each pair (E,F) that combines an edge E and an incident face F. The adjacency relation satisfies TA(E,TA(E,F))=F. The choice of the map A defines which vertices of N must be replicated in M and how many times. The resulting manifold representation of a nonmanifold solid may be encoded using simpler and more compact datastructures, especially for triangulated model, and leads to simpler and more efficient algorithms, when it is used instead of a nonmanifold repre...
Efficient Polyhedral Modeling from Silhouettes
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2008
"... Modeling from silhouettes is a popular and useful topic in computer vision. Many methods exist to compute the surface of the visual hull from silhouettes, but few address the problem of ensuring good topological properties of the surface, such as manifoldness. This article provides an efficient algo ..."
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Cited by 39 (6 self)
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Modeling from silhouettes is a popular and useful topic in computer vision. Many methods exist to compute the surface of the visual hull from silhouettes, but few address the problem of ensuring good topological properties of the surface, such as manifoldness. This article provides an efficient algorithm to compute such a surface in the form of a polyhedral mesh. It relies on a small number of geometric operations to compute a visual hull polyhedron in a single pass. Such simplicity enables the algorithm to combine the advantages of being fast, producing pixelexact surfaces, and repeatably yield manifold and watertight polyhedra in general experimental conditions with real data, as verified with all datasets tested. The algorithm is fully described, its complexity analyzed and modeling results given.
Active zones in CSG for accelerating boundary evaluation, redundancy elimination, interference detection, and shading algorithms
 ACM Transactions on Graphics
, 1989
"... Solids defined by Boolean combinations of solid primitives may be represented in constructive solid geometry (CSG) as binary trees. Most CSGbased algorithms (e.g., for boundary evaluation, graphic shading, interference detection) do various forms of setmembership classification by traversing the t ..."
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Cited by 29 (9 self)
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Solids defined by Boolean combinations of solid primitives may be represented in constructive solid geometry (CSG) as binary trees. Most CSGbased algorithms (e.g., for boundary evaluation, graphic shading, interference detection) do various forms of setmembership classification by traversing the tree associated with the solid. These algorithms usually generate intermediate results that do not contribute to the final result, and hence may be regarded as redundant and a source of inefficiency. To reduce such inefficiencies, we associate with each primitive A in a tree S an active zone 2 that represents the region of space where changes to A affect the solid represented by S, and we use a representation of 2 instead of S for setmembership classification. In the paper we develop a mathematical theory of active zones, prove that they correspond to the intersection of certain nodes of the original trees, and show how they lead to efficient new algorithms for boundary evaluation, for detecting and eliminating redundant nodes in CSG trees, for interference (nullset) detection, and for graphic shading.