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3D distance fields: A survey of techniques and applications
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
, 2006
"... A distance field is a representation where, at each point within the field, we know the distance from that point to the closest point on any object within the domain. In addition to distance, other properties may be derived from the distance field, such as the direction to the surface, and when the ..."
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Cited by 74 (3 self)
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A distance field is a representation where, at each point within the field, we know the distance from that point to the closest point on any object within the domain. In addition to distance, other properties may be derived from the distance field, such as the direction to the surface, and when the distance field is signed, we may also determine if the point is internal or external to objects within the domain. The distance field has been found to be a useful construction within the areas of computer vision, physics, and computer graphics. This paper serves as an exposition of methods for the production of distance fields, and a review of alternative representations and applications of distance fields. In the course of this paper, we present various methods from all three of the above areas, and we answer pertinent questions such as How accurate are these methods compared to each other? How simple are they to implement?, and What is the complexity and runtime of such methods?
Multiresolution distance volumes for progressive surface compression
 International Symposium on 3D Data Processing Visualization and Transmission
, 2002
"... We present a surface compression method that stores surfaces as waveletcompressed signeddistance volumes. Our approach enables the representation of surfaces with complex topology and arbitrary numbers of components within a single multiresolution data structure. This data structure elegantly hand ..."
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We present a surface compression method that stores surfaces as waveletcompressed signeddistance volumes. Our approach enables the representation of surfaces with complex topology and arbitrary numbers of components within a single multiresolution data structure. This data structure elegantly handles topological modification at high compression rates. Our method does not require the costly and sometimes infeasible base mesh construction step required by subdivision surface approaches. We present several improvements over previous attempts at compressing signeddistance functions, including an distance transform, a zero set initialization method for triangle meshes, and a specialized thresholding algorithm. We demonstrate the potential of sampled distance volumes for surface compression and progressive reconstruction for complex high genus surfaces. 1.
Signed Distance Computation using the Angle Weighted Pseudonormal
"... The normals of closed, smooth surfaces have long been used to determine whether a point is inside or outside such a surface. It is tempting also to use this method for polyhedra represented as triangle meshes. Unfortunately, this is not possible since at the vertices and edges of a triangle mesh, th ..."
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Cited by 7 (1 self)
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The normals of closed, smooth surfaces have long been used to determine whether a point is inside or outside such a surface. It is tempting also to use this method for polyhedra represented as triangle meshes. Unfortunately, this is not possible since at the vertices and edges of a triangle mesh, the surface is not C 1 continuous, hence, the normal is undefined at these loci. In this paper, we undertake to show that the angle weighted pseudonormal (originally proposed by Thürmer and Wüthrich and independently by Sequin) has the important property that it allows us to discriminate between points that are inside and points that are outside a mesh, regardless of whether a mesh vertex, edge or face is the closest feature. This insideoutside information is usually represented as the sign in the signed distance to the mesh. In effect, our result shows that this sign can be computed as an integral part of the distance computation. Moreover, it provides an additional argument in favour of the angle weighted pseudonormals being the natural extension of the face normals. Apart from the theoretical results, we also propose a simple and efficient algorithm for computing the signed distance to a closed C⁰ mesh. Experiments indicate that the sign computation overhead when running this algorithm is almost negligible.
Optimized bounding polyhedra for GPUbased distance transform
 Proceedings of Dagstuhl Seminar 023231 on Scientific Visualization
, 2005
"... Many problems in areas such as computer graphics, scientific visualization, computational geometry, or image processing require the computation of a distance field. The distance field indicates at each point in space the shortest distance to a given object. Depending on the problem setting, the obje ..."
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Cited by 4 (0 self)
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Many problems in areas such as computer graphics, scientific visualization, computational geometry, or image processing require the computation of a distance field. The distance field indicates at each point in space the shortest distance to a given object. Depending on the problem setting, the object is described either by a voxel attribute within a volume data set or by a surface representation such as a triangle mesh. The two cases require separate approaches, and only the case of the triangle mesh is studied in this paper. Often, the distance field is needed as a regular grid of samples. The samples can be computed either in image space or object space, referring to the outer loop of the algorithm, which iterates over all samples or all triangles of the mesh, respectively. Object space methods can be competitive, especially for higher resolutions. An ideal object space method would compute a generalized Voronoi diagram (GVD) of the mesh and then scan convert its cells. At each sample location, the distance to the Voronoi site associated with the cell would yield the field value. A practical method however, avoids the expensive GVD computation and instead works with bounding polyhedra for the Voronoi cells. In this paper, we propose a new type of bounding polyhedra. This reduces the number of polyhedra and simplifies their geometry. The choice of these bounding polyhedra pays off especially if scan conversion is run on graphics hardware. 1
OctreeBased Virtual Dental Training System With a Haptic Device,” Comput.Aided Des.
 Appl.,
, 2006
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D.: Interactive freeform levelset surfaceediting operators
, 2009
"... We present a set of interactive, freeform editing operators for direct manipulation of levelset models that supports the creation and removal of surface detail. The mathematics, data structures and algorithms needed to implement numerous levelset modeling capabilities have been developed. The fir ..."
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We present a set of interactive, freeform editing operators for direct manipulation of levelset models that supports the creation and removal of surface detail. The mathematics, data structures and algorithms needed to implement numerous levelset modeling capabilities have been developed. The first component of these capabilities identifies the RegionofInfluence (ROI) on the surface to be modified, and the specification of user handles, i.e. a point or a curve within the ROI, that are used to control the freeform surface edits. The editing operators include pulling the levelset surface by a handle with the surface changes occurring symmetrically around the handle or within the ROI, surface offsetting and carving, deformations towards a profile curve and localized smoothing. The editing operators are implemented with specialized speed functions, which are incorporated into the level set partial differential equation (PDE). The PDE is then evolved to produce the desired model modification. The specific form of each speed function is described in detail. The operators have been combined with an OpenGL interface and the VISPACK levelset library to create a preliminary interactive levelset modeling system. VISPACK’s narrowband data structures have been extended to localize all computations and updates to optimize running time and provide interactive performance. Additional sketchbased levelset editing operators have been implemented within the system, and are described elsewhere [1]. A variety of levelset models are presented to demonstrate the effectiveness of the editing operators. Key words: implicit modeling, levelset modeling, volume modeling, freeform surface editing 1.
Adaptively Represented Complete Distance Fields
"... Distance fields are an important volume representation. A high quality distance field facilitates accurate surface characterization and gradient estimation. However, due to Nyquist’s Law, no existing volumetric methods based on the linear sampling theory can fully capture surface details, such as co ..."
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Distance fields are an important volume representation. A high quality distance field facilitates accurate surface characterization and gradient estimation. However, due to Nyquist’s Law, no existing volumetric methods based on the linear sampling theory can fully capture surface details, such as corners and edges, in 3D space. We propose a novel complete distance field representation (CDFR) that does not rely on Nyquist’s sampling theory. To accomplish this, we construct a volume where each voxel has a complete description of all portions of surface that affect the local distance field. We also show here that CDFR can be adaptively represented, without comprising accuracy. The adaptively represented complete distance field is shorted for ARCDF. For any desired distance, we can extract a surface contour in true Euclidean distance, at any level of accuracy, from the same CDFR representation. Such pointbased isodistance contours have faithful perpoint gradients and can be interactively visualized using splatting, providing perpoint shaded image quality. We also demonstrate applying CDFR to a cutting edge design for manufacturing application involving highcomplexity parts at unprecedented accuracy using only commonly available computational resources. 1.
Feature preserving distance fields
 In VV ’04: Proceedings of the 2004 IEEE Symposium on Volume Visualization and Graphics (VV’04
, 2004
"... We present two distance field representations which can preserve sharp features in original geometric models: the offset distance field (ODF) and the unified distance field (UDF). The ODF is sampled on a special curvilinear grid named an offset grid. The sample points of the ODF are not on a regular ..."
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We present two distance field representations which can preserve sharp features in original geometric models: the offset distance field (ODF) and the unified distance field (UDF). The ODF is sampled on a special curvilinear grid named an offset grid. The sample points of the ODF are not on a regular grid and they can float in the cells of a regular base grid. The ODF can naturally adapt to curvature variations in the original mesh and can preserve sharp features. We describe an energy minimization approach to convert geometric models to ODFs. The UDF integrates multiple distance field representations into one data structure. By adaptively using different representations for different parts of a shape, the UDF can provide high fidelity surface representation with compact storage and fast rendering speed.
Computing Local Signed Distance Fields for Large Polygonal Models
"... The signed distance field for a polygonal model is a useful representation that facilitates efficient computation in many visualization and geometric processing tasks. Often it is more effective to build a local distance field only within a narrow band around the surface that holds local geometric i ..."
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The signed distance field for a polygonal model is a useful representation that facilitates efficient computation in many visualization and geometric processing tasks. Often it is more effective to build a local distance field only within a narrow band around the surface that holds local geometric information for the model. In this paper, we present a novel technique to construct a volumetric local signed distance field of a polygonal model. To compute the local field efficiently, exactly those cells that cross the polygonal surface are found first through a new voxelization method, building a list of intersecting triangles for each boundary cell. After their neighboring cells are classified, the triangle lists are exploited to compute the local signed distance field with minimized voxeltotriangle distance computations. While several efficient methods for computing the distance field, particularly those harnessing the graphics processing unit’s (GPU’s) processing power, have recently been proposed, we focus on a CPUbased technique, intended to deal flexibly with large polygonal models and highresolution grids that are often too bulky for GPU computation.