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A New VoronoiBased Surface Reconstruction Algorithm
, 2002
"... We describe our experience with a new algorithm for the reconstruction of surfaces from unorganized sample points in R³. The algorithm is the first for this problem with provable guarantees. Given a “good sample” from a smooth surface, the output is guaranteed to be topologically correct and converg ..."
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Cited by 422 (9 self)
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We describe our experience with a new algorithm for the reconstruction of surfaces from unorganized sample points in R³. The algorithm is the first for this problem with provable guarantees. Given a “good sample” from a smooth surface, the output is guaranteed to be topologically correct and convergent to the original surface as the sampling density increases. The definition of a good sample is itself interesting: the required sampling density varies locally, rigorously capturing the intuitive notion that featureless areas can be reconstructed from fewer samples. The output mesh interpolates, rather than approximates, the input points. Our algorithm is based on the threedimensional Voronoi diagram. Given a good program for this fundamental subroutine, the algorithm is quite easy to implement.
Surface Reconstruction by Voronoi Filtering
 Discrete and Computational Geometry
, 1998
"... We give a simple combinatorial algorithm that computes a piecewiselinear approximation of a smooth surface from a finite set of sample points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled ..."
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Cited by 418 (15 self)
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We give a simple combinatorial algorithm that computes a piecewiselinear approximation of a smooth surface from a finite set of sample points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled surfaces, where density depends on "local feature size", the output is topologically valid and convergent (both pointwise and in surface normals) to the original surface. We describe an implementation of the algorithm and show example outputs. 1 Introduction The problem of reconstructing a surface from scattered sample points arises in many applications such as computer graphics, medical imaging, and cartography. In this paper we consider the specific reconstruction problem in which the input is a set of sample points S drawn from a smooth twodimensional manifold F embedded in three dimensions, and the desired output is a triangular mesh with vertex set equal to S that faithfully represen...
Practical volumetric sculpting
 the Visual Computer
, 2000
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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Cited by 37 (5 self)
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Enhancing spatial deformation for virtual sculpting
"... Pages ii–iv and vi have been removed from this Technical Report to save space; they contained only a formal declaration relating to the PhD submission or were blank. Technical reports published by the University of Cambridge Computer Laboratory are freely available via the Internet: ..."
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Cited by 6 (2 self)
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Pages ii–iv and vi have been removed from this Technical Report to save space; they contained only a formal declaration relating to the PhD submission or were blank. Technical reports published by the University of Cambridge Computer Laboratory are freely available via the Internet:
Sculpting by numbers
 ACM Trans. Graph
, 2012
"... of guidance onto a work in progress (b) that indicate how it must be deformed to match the target model. As the user follows this guidance, the physical object’s shape approaches that of the target (c). With our system, unskilled users are able to produce accurate physical replicas of complex 3D mod ..."
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Cited by 8 (0 self)
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of guidance onto a work in progress (b) that indicate how it must be deformed to match the target model. As the user follows this guidance, the physical object’s shape approaches that of the target (c). With our system, unskilled users are able to produce accurate physical replicas of complex 3D
Dynamic NURBS with Geometric Constraints for Interactive Sculpting
, 1994
"... This article develops a dynamic generalization of the nonuniform rational Bspline (NURBS) model. NURBS have become a de facto standard in commercial modeling systems because of their power to represent freeform shapes as well as common analytic shapes. To date, however, they have been viewed as pu ..."
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Cited by 105 (26 self)
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into the popular NURBS geometric substrate. Using DNURBS, a modeler can interactively sculpt curves and surfaces and design complex shapes to required specifications not only in the traditional indirect fashion, by adjusting control points and weights, but also through direct physical manipulation, by applying
Sculpting multidimensional nested structures
, 2013
"... Solid shape is typically segmented into surface regions to define the appearance and function of parts of the shape; these regions in turn use curve networks to represent boundaries and creases, and feature points to mark corners and other shape landmarks. Conceptual modeling requires these multidi ..."
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dimensional nested structures to persist throughout the modeling process, an aspect not supported, up to now, in freeform sculpting systems. We present the first shape sculpting framework that preserves and controls the evolution of such nested shape features. We propose a range of geometric and topological
Efficient collision detection using bounding volume hierarchies of kdops
 IEEE Transactions on Visualization and Computer Graphics
, 1998
"... Abstract—Collision detection is of paramount importance for many applications in computer graphics and visualization. Typically, the input to a collision detection algorithm is a large number of geometric objects comprising an environment, together with a set of objects moving within the environment ..."
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Cited by 289 (4 self)
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Abstract—Collision detection is of paramount importance for many applications in computer graphics and visualization. Typically, the input to a collision detection algorithm is a large number of geometric objects comprising an environment, together with a set of objects moving within the environment. In addition to determining accurately the contacts that occur between pairs of objects, one needs also to do so at realtime rates. Applications such as haptic forcefeedback can require over 1,000 collision queries per second. In this paper, we develop and analyze a method, based on boundingvolume hierarchies, for efficient collision detection for objects moving within highly complex environments. Our choice of bounding volume is to use a “discrete orientation polytope” (“kdop”), a convex polytope whose facets are determined by halfspaces whose outward normals come from a small fixed set of k orientations. We compare a variety of methods for constructing hierarchies (“BVtrees”) of bounding kdops. Further, we propose algorithms for maintaining an effective BVtree of kdops for moving objects, as they rotate, and for performing fast collision detection using BVtrees of the moving objects and of the environment. Our algorithms have been implemented and tested. We provide experimental evidence showing that our approach yields substantially faster collision detection than previous methods. Index Terms—Collision detection, intersection searching, bounding volume hierarchies, discrete orientation polytopes, bounding boxes, virtual reality, virtual environments. 1
Manipulation of Volumetric Solids with applications to sculpting
, 2002
"... ii The topic of this thesis is volume graphics, and in particular techniques which are applicable to volume sculpting. A volume sculpting system is an interactive computer program for shape modelling where the shape is represented volumetrically in a 3D lattice of so–called voxels. It is argued that ..."
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Cited by 2 (0 self)
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ii The topic of this thesis is volume graphics, and in particular techniques which are applicable to volume sculpting. A volume sculpting system is an interactive computer program for shape modelling where the shape is represented volumetrically in a 3D lattice of so–called voxels. It is argued
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