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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 54 (2 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?
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 46 (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
Permission Grids: Practical, ErrorBounded Simplification
 ACM Transactions on Graphics
, 2002
"... We introduce the permission grid, a spatial occupancy grid used to guide almost any standard polygonal surface simplification algorithm into generating an approximation with a guaranteed geometric error bound. In particular, the distance between any point on the approximation and the original surfac ..."
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Cited by 20 (1 self)
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We introduce the permission grid, a spatial occupancy grid used to guide almost any standard polygonal surface simplification algorithm into generating an approximation with a guaranteed geometric error bound. In particular, the distance between any point on the approximation and the original surface is bounded by a userspecified tolerance. Such bounds are notably absent from most current simplification methods, and are becoming increasingly important for applications such as collision detection and scientific computing. Conceptually simple, the permission grid defines a volume in which the approximation must lie, and does not permit the underlying simplification algorithm to generate approximations outside of this volume. The permission grid makes three important, practical improvements over current errorbounded simplification methods. First, it works on arbitrary triangular models, handling all manners of mesh degeneracies gracefully. Further, the error tolerance may be expanded as simplification proceeds, allowing the construction
Constructive Hypervolume Modelling
, 2001
"... This paper deals with modelling point sets with attributes. A point set in a geometric space of an arbitrary dimension is a geometric model of a real object or process under consideration. An attribute is a mathematical model of a real object or process property of an arbitrary nature (material, pho ..."
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Cited by 19 (11 self)
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This paper deals with modelling point sets with attributes. A point set in a geometric space of an arbitrary dimension is a geometric model of a real object or process under consideration. An attribute is a mathematical model of a real object or process property of an arbitrary nature (material, photometric, physical, statistical, etc.) defined for any point of the point set. We provide a survey of different modelling techniques related to point sets with attributes. This survey spans such different areas as solid modelling, heterogeneous objects modelling, scalar fields or "implicit surface" modelling, and volume graphics. Then, on the basis of this survey we formulate requirements to a general model of hypervolumes (multidimensional point sets with multiple attributes). A general hypervolume model and its components such as objects, operations, and relations are introduced and discussed. A function representation (FRep) is used as the basic model for the point set geometry and attributes represented independently using realvalued scalar functions of several variables. Each function defining the geometry or an attribute is evaluated at the given point by a procedure traversing a constructive tree structure with primitives in the leaves and operations in the nodes of the tree. This reflects the constructive nature of the symmetric approach to modelling geometry and associated attributes in multidimensional space. To demonstrate a particular application of the proposed general model, we consider in detail the problem of texturing, introduce a model of constructive hypervolume texture, and discuss its implementation. The wellknown concept of solid texturing is extended in two directions: constructive modelling of space partitions for texturing and modelling of mul...
3D Scan Conversion of CSG Models into Distance, ClosestPoint and Colour Volumes
 Proc. of Volume Graphics (2000
, 2000
"... Introduction Volume graphics is a growing field that generally involves representing three dimensional objects as a rectilinear 3D grid of scalar values, a volume dataset. Given this kind of representation numerous algorithms have been developed to process, manipulate and render volumes. Volume dat ..."
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Cited by 19 (2 self)
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Introduction Volume graphics is a growing field that generally involves representing three dimensional objects as a rectilinear 3D grid of scalar values, a volume dataset. Given this kind of representation numerous algorithms have been developed to process, manipulate and render volumes. Volume datasets may be generated in a variety of ways. Certain scanning devices, e.g. MRI and CT, generate a rectilinear grid of scalar values directly from their scanning process. The scalar values can represent the concentration of water or the density of matter at each grid point (voxel). Additionally, volume datasets can be generated from conventional geometric models, using a process called 3D scan conversion. When 3D scan converting a geometric model to a volumetric representation it is not always clear what value should be stored at each voxel of the volume, and what that value should represent. Here, we propose the use of distance volumes. A distance volume is a volume dataset where t
Complete Polygonal Scene Voxelization
, 2002
"... We present a fast and robust tool for automatically converting complete polygonal scenes into volumetric representations. A wide range of scenes are handled by storing the status (inside/outside) of the volumetric space areas in the cells of an octree. The algorithm rst looks for a point in the ..."
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Cited by 16 (1 self)
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We present a fast and robust tool for automatically converting complete polygonal scenes into volumetric representations. A wide range of scenes are handled by storing the status (inside/outside) of the volumetric space areas in the cells of an octree. The algorithm rst looks for a point in the scene for which the status can be univocally determined.
Voxels on Fire
, 2003
"... We introduce a method for the animation of fire propagation and the burning consumption of objects represented as volumetric data sets. Our method uses a volumetric fire propagation model based on an enhanced distance field. It can simulate the spreading of multiple fire fronts over a specified isos ..."
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Cited by 14 (2 self)
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We introduce a method for the animation of fire propagation and the burning consumption of objects represented as volumetric data sets. Our method uses a volumetric fire propagation model based on an enhanced distance field. It can simulate the spreading of multiple fire fronts over a specified isosurface without actually having to create that isosurface. The distance field is generated from a specific shell volume that rapidly creates narrow spatial bands around the virtual surface of any given isovalue. The complete distance field is then obtained by propagation from the initial bands. At each step multiple fire fronts can evolve simultaneously on the volumetric object. The flames of the fire are constructed from streams of particles whose movement is regulated by a velocity field generated with the hardwareaccelerated Lattice Boltzmann Model (LBM). The LBM provides a physicallybased simulation of the air flow around the burning object. The object voxels and the splats associated with the flame particles are rendered in the same pipeline so that the volume data with its external and internal structures can be displayed along with the fire.
Generating Shaded Offset Surfaces with Distance, ClosestPoint and Color Volumes
 In Proceedings of the International Workshop on Volume Graphics
, 1999
"... This paper presents a technique for colorshading offset surfaces of CSG models. The offset surfaces are generated by first scan converting the CSG model into a distance volume. A distance volume is a volume dataset where the value stored at each voxel is the shortest distance to the surface of the ..."
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Cited by 10 (1 self)
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This paper presents a technique for colorshading offset surfaces of CSG models. The offset surfaces are generated by first scan converting the CSG model into a distance volume. 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. Extracting isosurfaces from the distance volume at various offset values produces the offset surfaces. The CSG model scan conversion process also produces closestpoint and color volumes. The closestpoint volume contains at each voxel the closest point on the scan converted CSG model from that voxel location. The color volume contains at each voxel the associated color on the CSG model at the closest point. During rendering of the offset surface, the color volume values are used to shade regions of constant color, and the closest point values are used to supersample the surface colors of the CSG model in order to antialias regions of changing color. ...
HardwareBased Voxelization for 3D Spatial Analysis
 Proceedings of CGIM ’02
, 2002
"... This paper presents and evaluates a fast graphics hardwarebased voxelization method to spatial analysis, which generates objectcoded volume data utilizing the Performer scenegraph. Two colorcoding algorithms are introduced. The first one resolves one object per voxel for a large number of objects ..."
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Cited by 9 (1 self)
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This paper presents and evaluates a fast graphics hardwarebased voxelization method to spatial analysis, which generates objectcoded volume data utilizing the Performer scenegraph. Two colorcoding algorithms are introduced. The first one resolves one object per voxel for a large number of objects. The second algorithm extends the first to identify multiple objects in one voxel, by using blending and the stencil buffer. This enables us to simulate the "object to voxel" behavior of softwarebased polygon voxelization techniques. The voxelization process utilizes the application window without interfering with the visual part of the application. The results show that the voxelization time is only dependent on the z resolution  the number of slices to be rendered. The comparison of the hardwareand the softwarebased voxelization method demonstrates that, especially for small resolutions of z, the hardwarebased method is much faster.
A low Cost Antialiased Space Filled Voxelization
 Of Polygonal Objects, GraphiCon 2004
, 2004
"... In a virtual sculpting environment, we manipulate objects as a set of volume elements (voxels). In order to start the sculpture process from a polygonal object, we have to discretize this object as a set of voxels. This step is called voxelization. Several voxelization methods have already been prop ..."
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Cited by 7 (0 self)
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In a virtual sculpting environment, we manipulate objects as a set of volume elements (voxels). In order to start the sculpture process from a polygonal object, we have to discretize this object as a set of voxels. This step is called voxelization. Several voxelization methods have already been proposed, but none matches all of our criteria. In this paper, we propose a practical approach that handles these criteria, based on an optimized ray casting. The method provides a voxelization of the inner space of a polygonal object, and not only of its surface. It is designed to work with closed objects which may contain holes or tunnels. Even if our goal is not real time conversion, it is fast enough to provide voxelization of objects made of several thousands of triangles within few seconds. As voxelization is a 3D sampling process, it entails aliasing problems. Our method allows a reduction of aliasing by using a low cost oversampling in order to compute grey scale values for the voxels. Moreover our method has a very low cost in memory and allows unlimited voxelization size (but by disk size), even for low memory computers. Furthermore, the method can be used on a personal computer without specific graphics hardware.