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271
Dual Contouring of Hermite Data
, 2002
"... This paper describes a new method for contouring a signed grid whose edges are tagged by Hermite data (exact intersection points and normals). This method avoids the need to explicitly identify and process "features" as required in previous Hermite contouring methods. We extend this contou ..."
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Cited by 257 (15 self)
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This paper describes a new method for contouring a signed grid whose edges are tagged by Hermite data (exact intersection points and normals). This method avoids the need to explicitly identify and process "features" as required in previous Hermite contouring methods. We extend this contouring method to the case of multisigned functions and demonstrate how to model textured contours using multisigned functions. Using a new, numerically stable representation for quadratic error functions, we develop an octreebased method for simplifying these contours and their textured regions. We next extend our contouring method to these simplified octrees. This new method imposes no constraints on the octree (such as being a restricted octree) and requires no "crack patching". We conclude with a simple test for preserving the topology of both the contour and its textured regions during simplification.
Simulating Water and Smoke with an Octree Data Structure
, 2004
"... We present a method for simulating water and smoke on an unrestricted octree data structure exploiting mesh refinement techniques to capture the small scale visual detail. We propose a new technique for discretizing the Poisson equation on this octree grid. The resulting linear system is symmetric ..."
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Cited by 207 (18 self)
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We present a method for simulating water and smoke on an unrestricted octree data structure exploiting mesh refinement techniques to capture the small scale visual detail. We propose a new technique for discretizing the Poisson equation on this octree grid. The resulting linear system is symmetric positive definite enabling the use of fast solution methods such as preconditioned conjugate gradients, whereas the standard approximation to the Poisson equation on an octree grid results in a nonsymmetric linear system which is more computationally challenging to invert. The semiLagrangian characteristic tracing technique is used to advect the velocity, smoke density, and even the level set making implementation on an octree straightforward. In the case of smoke, we have multiple refinement criteria including object boundaries, optical depth, and vorticity concentration. In the case of water, we refine near the interface as determined by the zero isocontour of the level set function.
Filling Holes In Complex Surfaces Using Volumetric Diffusion
, 2001
"... We address the problem of building watertight 3D models from surfaces that contain holesfor example, sets of range scans that observe most but not all of a surface. We specifically address situations in which the holes are too geometrically and topologically complex to fill using triangulation al ..."
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Cited by 173 (2 self)
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We address the problem of building watertight 3D models from surfaces that contain holesfor example, sets of range scans that observe most but not all of a surface. We specifically address situations in which the holes are too geometrically and topologically complex to fill using triangulation algorithms. Our solution begins by constructing a signed distance function, the zero set of which defines the surface. Initially, this function is defined only in the vicinity of observed surfaces. We then apply a diffusion process to extend this function through the volume until its zero set bridges whatever holes may be present. If additional information is available, such as knownempty regions of space inferred from the lines of sight to a 3D scanner, it can be incorporated into the diffusion process. Our algorithm is simple to implement, is guaranteed to produce manifold noninterpenetrating surfaces, and is efficient to run on large datasets because computation is limited to areas near holes. By showing results for complex range scans, we demonstrate that our algorithm produces holefree surfaces that are plausible, visually acceptable, and usually close to the intended geometry.
Automatic Rigging and Animation of 3D Characters
 ACM Transactions on Graphics (SIGGRAPH proceedings
"... Copyright Notice ..."
Feature Sensitive Surface Extraction from Volume Data
"... The representation of geometric objects based on volumetric data structures has advantages in many geometry processing applications that require, e.g., fast surface interrogation or boolean operations such as intersection and union. However, surface based algorithms like shape optimization (fairing) ..."
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Cited by 151 (10 self)
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The representation of geometric objects based on volumetric data structures has advantages in many geometry processing applications that require, e.g., fast surface interrogation or boolean operations such as intersection and union. However, surface based algorithms like shape optimization (fairing) or freeform modeling often need a topological manifold representation where neighborhood information within the surface is explicitly available. Consequently, it is necessary to find effective conversion algorithms to generate explicit surface descriptions for the geometry which is implicitly defined by a volumetric data set. Since volume data is usually sampled on a regular grid with a given step width, we often observe severe alias artifacts at sharp features on the extracted surfaces. In this paper we present a new technique for surface extraction that performs feature sensitive sampling and thus reduces these alias effects while keeping the simple algorithmic structure of the standard Marching Cubes algorithm. We demonstrate the effectiveness of the new technique with a number of application examples ranging from CSG modeling and simulation to surface reconstruction and remeshing of polygonal models. 1
Collision Detection for Deformable Objects
"... Interactive environments for dynamically deforming objects play an important role in surgery simulation and entertainment technology. These environments require fast deformable models and very efficient collision handling techniques. While collision detection for rigid bodies is wellinvestigated, c ..."
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Cited by 117 (18 self)
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Interactive environments for dynamically deforming objects play an important role in surgery simulation and entertainment technology. These environments require fast deformable models and very efficient collision handling techniques. While collision detection for rigid bodies is wellinvestigated, collision detection for deformable objects introduces additional challenging problems. This paper focuses on these aspects and summarizes recent research in the area of deformable collision detection. Various approaches based on bounding volume hierarchies, distance fields, and spatial partitioning are discussed. Further, imagespace techniques and stochastic methods are considered. Applications in cloth modeling and surgical simulation are presented.
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 113 (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.
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 102 (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 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?