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103
Shape modeling with pointsampled geometry
 ACM Transactions on Graphics
, 2003
"... Figure 1: Objects created with our system. (a) boolean operations with scanned geometry, (b) an Octopus modeled by deforming and extruding a sphere, (c) a design study for a Siggraph coffee mug created by boolean operations, freeform deformation and displacement mapping. We present a versatile and ..."
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Cited by 201 (30 self)
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Figure 1: Objects created with our system. (a) boolean operations with scanned geometry, (b) an Octopus modeled by deforming and extruding a sphere, (c) a design study for a Siggraph coffee mug created by boolean operations, freeform deformation and displacement mapping. We present a versatile and complete freeform shape modeling framework for pointsampled geometry. By combining unstructured point clouds with the implicit surface definition of the moving least squares approximation, we obtain a hybrid geometry representation that allows us to exploit the advantages of implicit and parametric surface models. Based on this representation we introduce a shape modeling system that enables the designer to perform large constrained deformations as well as boolean operations on arbitrarily shaped objects. Due to minimum consistency requirements, pointsampled surfaces can easily be restructured on the fly to support extreme geometric deformations during interactive editing. In addition, we show that strict topology control is possible and sharp features can be generated and preserved on pointsampled objects. We demonstrate the effectiveness of our system on a large set of input models, including noisy range scans, irregular point clouds, and sparsely as well as densely sampled models.
Mesh Editing with PoissonBased Gradient Field Manipulation
 ACM TRANS. GRAPH
, 2004
"... In this paper, we introduce a novel approach to mesh editing with the Poisson equation as the theoretical foundation. The most distinctive feature of this approach is that it modifies the original mesh geometry implicitly through gradient field manipulation. Our approach can produce desirable and pl ..."
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Cited by 175 (17 self)
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In this paper, we introduce a novel approach to mesh editing with the Poisson equation as the theoretical foundation. The most distinctive feature of this approach is that it modifies the original mesh geometry implicitly through gradient field manipulation. Our approach can produce desirable and pleasing results for both global and local editing operations, such as deformation, object merging, and smoothing. With the help from a few novel interactive tools, these operations can be performed conveniently with a small amount of user interaction. Our technique has three key components, a basic mesh solver based on the Poisson equation, a gradient field manipulation scheme using local transforms, and a generalized boundary condition representation based on local frames. Experimental results indicate that our framework can outperform previous related mesh editing techniques.
Nonconvex rigid bodies with stacking
 ACM Trans. Graph
"... We consider the simulation of nonconvex rigid bodies focusing on interactions such as collision, contact, friction (kinetic, static, rolling and spinning) and stacking. We advocate representing the geometry with both a triangulated surface and a signed distance function defined on a grid, and this d ..."
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Cited by 115 (12 self)
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We consider the simulation of nonconvex rigid bodies focusing on interactions such as collision, contact, friction (kinetic, static, rolling and spinning) and stacking. We advocate representing the geometry with both a triangulated surface and a signed distance function defined on a grid, and this dual representation is shown to have many advantages. We propose a novel approach to time integration merging it with the collision and contact processing algorithms in a fashion that obviates the need for ad hoc threshold velocities. We show that this approach matches the theoretical solution for blocks sliding and stopping on inclined planes with friction. We also present a new shock propagation algorithm that allows for efficient use of the propagation (as opposed to the simultaneous) method for treating contact. These new techniques are demonstrated on a variety of problems ranging from simple test cases to stacking problems with as many as 1000 nonconvex rigid bodies with friction as shown in Figure 1.
Realtime raycasting and advanced shading of discrete isosurfaces
 COMPUTER GRAPHICS FORUM
, 2005
"... This paper presents a realtime rendering pipeline for implicit surfaces defined by a regular volumetric grid of samples. We use a raycasting approach on current graphics hardware to perform a direct rendering of the isosurface. A twolevel hierarchical representation of the regular grid is emplo ..."
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Cited by 82 (11 self)
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This paper presents a realtime rendering pipeline for implicit surfaces defined by a regular volumetric grid of samples. We use a raycasting approach on current graphics hardware to perform a direct rendering of the isosurface. A twolevel hierarchical representation of the regular grid is employed to allow objectorder and imageorder empty space skipping and circumvent memory limitations of graphics hardware. Adaptive sampling and iterative refinement lead to highquality ray/surface intersections. All shading operations are deferred to image space, making their computational effort independent of the size of the input data. A continuous thirdorder reconstruction filter allows onthefly evaluation of smooth normals and extrinsic curvatures at any point on the surface without interpolating data computed at grid points. With these local shape descriptors, it is possible to perform advanced shading using highquality lighting and nonphotorealistic effects in realtime.
A Virtual Node Algorithm for Changing Mesh Topology during Simulation
 ACM Trans. Graph. (SIGGRAPH Proc
, 2004
"... We propose a virtual node algorithm that allows material to separate along arbitrary (possibly branched) piecewise linear paths through a mesh. The material within an element is fragmented by creating several replicas of the element and assigning a portion of real material to each replica. This resu ..."
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Cited by 82 (6 self)
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We propose a virtual node algorithm that allows material to separate along arbitrary (possibly branched) piecewise linear paths through a mesh. The material within an element is fragmented by creating several replicas of the element and assigning a portion of real material to each replica. This results in elements that contain both real material and empty regions. The missing material is contained in another copy (or copies) of this element. Our new virtual node algorithm automatically determines the number of replicas and the assignment of material to each. Moreover, it provides the degrees of freedom required to simulate the partially or fully fragmented material in a fashion consistent with the embedded geometry. This approach enables efficient simulation of complex geometry with a simple mesh, i.e. the geometry need not align itself with element boundaries. It also alleviates many shortcomings of traditional Lagrangian simulation techniques for meshes with changing topology. For example, slivers do not require small CFL time step restrictions since they are embedded in well shaped larger elements. To enable robust simulation of embedded geometry, we propose new algorithms for handling rigid body and self collisions. In addition, we present several mechanisms for influencing and controlling fracture with grain boundaries, prescoring, etc. We illustrate our method for both volumetric and thinshell simulations.
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?
Spatially adaptive techniques for level set methods and incompressible flow
 Comput. Fluids
"... Since the seminal work of [92] on coupling the level set method of [69] to the equations for twophase incompressible flow, there has been a great deal of interest in this area. That work demonstrated the most powerful aspects of the level set method, i.e. automatic handling of topological changes ..."
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Cited by 73 (15 self)
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Since the seminal work of [92] on coupling the level set method of [69] to the equations for twophase incompressible flow, there has been a great deal of interest in this area. That work demonstrated the most powerful aspects of the level set method, i.e. automatic handling of topological changes such as merging and pinching, as well as robust geometric information such as normals and curvature. Interestingly, this work also demonstrated the largest weakness of the level set method, i.e. mass or information loss characteristic of most Eulerian capturing techniques. In fact, [92] introduced a partial differential equation for battling this weakness, without which their work would not have been possible. In this paper, we discuss both historical and most recent works focused on improving the computational accuracy of the level set method focusing in part on applications related to incompressible flow due to both its popularity and stringent accuracy requirements. Thus, we discuss higher order accurate numerical methods such as HamiltonJacobi WENO [46], methods for maintaining a signed distance function, hybrid methods such as the particle level set method [27] and the coupled level set volume of fluid method [91], and adaptive gridding techniques such as the octree approach to free surface flows proposed in [56].
Hierarchical RLE level set: A compact and versatile deformable surface representation
, 2006
"... This article introduces the Hierarchical RunLength Encoded (HRLE) Level Set data structure. This novel data structure combines the best features of the DTGrid (of Nielsen and Museth [2004]) and the RLE Sparse Level Set (of Houston et al. [2004]) to provide both optimal efficiency and extreme vers ..."
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Cited by 49 (9 self)
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This article introduces the Hierarchical RunLength Encoded (HRLE) Level Set data structure. This novel data structure combines the best features of the DTGrid (of Nielsen and Museth [2004]) and the RLE Sparse Level Set (of Houston et al. [2004]) to provide both optimal efficiency and extreme versatility. In brief, the HRLE level set employs an RLE in a dimensionally recursive fashion. The RLE scheme allows the compact storage of sequential nonnarrowband regions while the dimensionally recursive encoding along each axis efficiently compacts nonnarrowband planes and volumes. Consequently, this new structure can store and process level sets with effective voxel resolutions exceeding 500030003000 (45 billion voxels) on commodity PCs with only 1 GB of memory. This article, besides introducing the HRLE level set data structure and its efficient core algorithms, also describes numerous applications that have benefited from our use of this structure: our unified implicit object representation, efficient and robust mesh to level set conversion, rapid ray tracing, level set metamorphosis, collision detection, and fully sparse fluid simulation (including RLE vector and matrix representations.) Our comparisons of the popular octree level set and Peng level set structures to the HRLE level set indicate that the latter is superior in both narrowband sequential access speed and overall memory usage
Controllable smoke animation with guiding objects
 ACM Transactions on Graphics
, 2005
"... This article addresses the problem of controlling the density and dynamics of smoke (a gas phenomenon) so that the synthetic appearance of the smoke (gas) resembles a still or moving object. Both the smoke region and the target object are represented as implicit functions. As a part of the target im ..."
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Cited by 46 (3 self)
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This article addresses the problem of controlling the density and dynamics of smoke (a gas phenomenon) so that the synthetic appearance of the smoke (gas) resembles a still or moving object. Both the smoke region and the target object are represented as implicit functions. As a part of the target implicit function, a shape transformation is generated between an initial smoke region and the target object. In order to match the smoke surface with the target surface, we impose carefully designed velocity constraints on the smoke boundary during a dynamic fluid simulation. The velocity constraints are derived from an iterative functional minimization procedure for shape matching. The dynamics of the smoke is formulated using a novel compressible fluid model which can effectively absorb the discontinuities in the velocity field caused by imposed velocity constraints while reproducing realistic smoke appearances. As a result, a smoke region can evolve into a regular object and follow the motion of the object, while maintaining its smoke appearance.