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Reassembling fractured objects by geometric matching
 TOG
"... We present a system for automatic reassembly of broken 3D solids. Given as input 3D digital models of the broken fragments, we analyze the geometry of the fracture surfaces to find a globally consistent reconstruction of the original object. Our reconstruction pipeline consists of a graphcuts based ..."
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Cited by 76 (9 self)
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We present a system for automatic reassembly of broken 3D solids. Given as input 3D digital models of the broken fragments, we analyze the geometry of the fracture surfaces to find a globally consistent reconstruction of the original object. Our reconstruction pipeline consists of a graphcuts based segmentation algorithm for identifying potential fracture surfaces, featurebased robust global registration for pairwise matching of fragments, and simultaneous constrained local registration of multiple fragments. We develop several new techniques in the area of geometry processing, including the novel integral invariants for computing multiscale surface characteristics, registration based on forward search techniques and surface consistency, and a nonpenetrating iterated closest point algorithm. We illustrate the performance of our algorithms on a number of realworld examples.
On the probabilistic foundations of probabilistic roadmap planning
 In Proc. Int. Symp. on Robotics Research
, 2005
"... Probabilistic roadmap (PRM) planners [5, 16] solve apparently difficult motion planning problems where the robot’s configuration space C has dimensionality six or more, and the geometry of the robot and the obstacles is described by hundreds of thousands of triangles. While an algebraic planner woul ..."
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Cited by 63 (11 self)
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Probabilistic roadmap (PRM) planners [5, 16] solve apparently difficult motion planning problems where the robot’s configuration space C has dimensionality six or more, and the geometry of the robot and the obstacles is described by hundreds of thousands of triangles. While an algebraic planner would be overwhelmed by the high cost of computing an exact representation of the free space F, defined as the collisionfree subset of C, a PRM planner builds only an extremely simplified representation of F, called a probabilistic roadmap. This roadmap is a graph, whose nodes are configurations sampled from F with a suitable probability measure and whose edges are simple collisionfree paths, e.g., straightline segments, between the sampled configurations. PRM planners work surprisingly well in practice, but why? Previous work has partially addressed this question by identifying and formalizing properties of F that guarantee good performance for a PRM planner using the uniform sampling measure (e.g.,
Cacheoblivious mesh layouts
 ACM Trans. Graph
, 2005
"... ACM acknowledges that this contribution was authored or coauthored by a contractor of affiliate of the U.S. Government. As such, the Government retains a nonexclusive, royaltyfree right to publish or reproduce this article, or to allow others to do so, for Government purposes only. ..."
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Cited by 51 (11 self)
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ACM acknowledges that this contribution was authored or coauthored by a contractor of affiliate of the U.S. Government. As such, the Government retains a nonexclusive, royaltyfree right to publish or reproduce this article, or to allow others to do so, for Government purposes only.
Fast proximity computation among deformable models using discrete Voronoi diagrams
 ACM Trans. Graph. (Proc ACM SIGGRAPH
, 2006
"... Figure 1: Multiple deformable models simulation: This sequence shows the positions of the objects at three time instances in a simulation. The environment initially consists of 10 deforming objects represented using 5.5K triangles. As the simulation proceeds, the objects break into 25 subobjects. O ..."
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Cited by 48 (9 self)
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Figure 1: Multiple deformable models simulation: This sequence shows the positions of the objects at three time instances in a simulation. The environment initially consists of 10 deforming objects represented using 5.5K triangles. As the simulation proceeds, the objects break into 25 subobjects. Our algorithm is able to perform collision and separation distance computations, including selfcollisions, among dynamically generated objects within 120 ms on a highend PC. We present novel algorithms to perform collision and distance queries among multiple deformable models in dynamic environments. These include interobject queries between different objects as well as intraobject queries. We describe a unified approach to compute these queries based on Nbody distance computation and use properties of the 2 nd order discrete Voronoi diagram to perform Nbody culling. Our algorithms involve no preprocessing and also work well on models with changing topologies. We can perform all proximity queries among complex deformable models consisting of thousands of triangles in a fraction of a second on a highend PC. Moreover, our Voronoibased culling algorithm can improve the performance of separation distance and penetration queries by an order of magnitude.
Exact and efficient construction of Minkowski sums of convex polyhedra with applications
 In Proc. 8th Workshop Alg. Eng. Exper. (Alenex’06
, 2006
"... We present an exact implementation of an efficient algorithm that computes Minkowski sums of convex polyhedra in R 3. Our implementation is complete in the sense that it does not assume general position. Namely, it can handle degenerate input, and it produces exact results. We also present applicati ..."
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Cited by 41 (10 self)
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We present an exact implementation of an efficient algorithm that computes Minkowski sums of convex polyhedra in R 3. Our implementation is complete in the sense that it does not assume general position. Namely, it can handle degenerate input, and it produces exact results. We also present applications of the Minkowskisum computation to answer collision and proximity queries about the relative placement of two convex polyhedra in R 3. The algorithms use a dual representation of convex polyhedra, and their implementation is mainly based on the Arrangement package of Cgal, the Computational Geometry Algorithm Library. We compare our Minkowskisum construction with the only three other methods that produce exact results we are aware of. One is a simple approach that computes the convex hull of the pairwise sums of vertices of two convex polyhedra. The second is based on Nef polyhedra embedded on the sphere, and the third is an outputsensitive approach based on linear programming. Our method is significantly faster. The results of experimentation with a broad family of convex polyhedra are reported. The relevant programs, source code, data sets, and documentation are available at
Finding narrow passages with probabilistic roadmaps: The small step retraction method
 in Proc. IEEE/RSJ Int. Conf. on Intelligent Robots & Systems
, 2005
"... Abstract: Probabilistic Roadmaps (PRM) have been successfully used to plan complex robot motions in configuration spaces of small and large dimensionalities. However, their efficiency decreases dramatically in spaces with narrow passages. This paper presents a new method – smallstep retraction – tha ..."
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Cited by 37 (4 self)
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Abstract: Probabilistic Roadmaps (PRM) have been successfully used to plan complex robot motions in configuration spaces of small and large dimensionalities. However, their efficiency decreases dramatically in spaces with narrow passages. This paper presents a new method – smallstep retraction – that helps PRM planners find paths through such passages. This method consists of slightly “fattening ” robot’s free space, constructing a roadmap in fattened free space, and finally repairing portions of this roadmap by retracting them out of collision into actual free space. Fattened free space is not explicitly computed. Instead, the geometric models of workspace objects (robot links and/or obstacles) are “thinned ” around their medial axis. A robot configuration lies in fattened free space if the thinned objects do not collide at this configuration. Two repair strategies are proposed. The “optimist ” strategy waits until a complete path has been found in fattened free space before repairing it. Instead, the “pessimist ” strategy repairs the roadmap as it is being built. The former is usually very fast, but may fail in some pathological cases. The latter is more reliable, but not as fast. A simple combination of the two strategies yields an integrated planner that is both fast and reliable. This planner was implemented as an extension of a preexisting singlequery PRM planner. Comparative tests show that it is significantly faster (sometimes by several orders of magnitude) than the preexisting planner. 1.
On fast construction of SAHbased bounding volume hierarchies
 In Proceedings of the 2007 IEEE/EG Symposium on Interactive Ray Tracing. IEEE
, 2007
"... Figure 1: We present a method that enables fast, perframe and fromscratch rebuilds of a bounding volume hierarchy, thus completely removing a BVHbased ray tracer’s reliance on updating or refitting. On a dual2.6GHz Clovertown system (8 cores total), our method renders the exploding dragon mode ..."
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Cited by 31 (5 self)
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Figure 1: We present a method that enables fast, perframe and fromscratch rebuilds of a bounding volume hierarchy, thus completely removing a BVHbased ray tracer’s reliance on updating or refitting. On a dual2.6GHz Clovertown system (8 cores total), our method renders the exploding dragon model (252K triangles) at around 13–21 frames per second (1024x1024 pixels) including animating the triangles, perframe rebuilds, shading, shadows, and display. The build itself takes less than 20ms, and is nearly agnostic to the distribution of the triangles; thus, the variation in frame rate (21 fps for the initial, smooth frame, and 13 fps for the timestep corresponding to the fourth image) is due only to varying traversal cost, without any deterioration in BVH quality at all (i.e., when starting with the last frame, the frame rate actually increases). With ray traversal performance reaching the point where realtime ray tracing becomes practical, ray tracing research is now shifting away from faster traversal, and towards the question what has to be done to use it in truly interactive applications such as games. Such applications are problematic because when geometry changes every frame, the ray tracer’s internal index data structures are no longer valid. Fully rebuilding all data structures every frame is the most general approach to handling changing geometry, but was long considered impractical except for gridbased grid based ray tracers, trivial scenes, or reduced quality of the index structure. In this paper, we investigate how some of the fast, approximate construction techniques that have recently been proposed for kdtrees can also be applied to bounding volume hierarchies (BVHs). We argue that these work even better for BVHs than they do for kdtrees, and demonstrate that when using those techniques, BVHs can be rebuilt up to 10 × faster than competing kdtree based techniques. 1
Path planning for deformable robots in complex environments
 In Robotics: Systems and Science
, 2005
"... Abstract — We present an algorithm for path planning for a flexible robot in complex environments. Our algorithm computes a collision free path by taking into account geometric and physical constraints, including obstacle avoidance, nonpenetration constraint, volume preservation, surface tension, a ..."
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Cited by 28 (3 self)
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Abstract — We present an algorithm for path planning for a flexible robot in complex environments. Our algorithm computes a collision free path by taking into account geometric and physical constraints, including obstacle avoidance, nonpenetration constraint, volume preservation, surface tension, and energy minimization. We describe a new algorithm for collision detection between a deformable robot and fixed obstacles using graphics processors. We also present techniques to efficiently handle complex deformable models composed of tens of thousands of polygons and obtain significant performance improvement over previous approaches. Moreover, we demonstrate a practical application of our algorithm in performing path planning of catheters in liver chemoembolization. I.
Perceived instability of virtual haptic texture
, 2004
"... This article reports the second study in a series that investigates perceived instability—unrealistic sensations associated with virtual objects—of virtual haptic texture. Our first study quantified the maximum stiffness values under which virtual haptic textures were perceived to be stable (Choi &a ..."
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Cited by 23 (10 self)
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This article reports the second study in a series that investigates perceived instability—unrealistic sensations associated with virtual objects—of virtual haptic texture. Our first study quantified the maximum stiffness values under which virtual haptic textures were perceived to be stable (Choi & Tan, 2004). The present study investigated the effect of the collisiondetection algorithm by removing the step changes in force magnitude that could have contributed to perceived instability in the first study. Our results demonstrate a significant increase in the maximum stiffness for stable haptic texture rendering. We also report a new type of perceived instability, aliveness, that is characterized by a pulsating sensation. We discuss the possible cause of aliveness and show that it is not always associated with control instability. Our results underscore the important roles played by environment modeling and human haptic perception, as well as control stability, in ensuring a perceptually stable virtual haptic environment. 1
Imagebased Collision Detection and Response between Arbitrary Volume Objects
"... We present a new imagebased method to process contacts between objects bounded by triangular surfaces. Unlike previous methods, it relies on imagebased volume minimization, which eliminates complex geometrical computations and robustly handles deep intersections. The surfaces are rasterized in thr ..."
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Cited by 21 (5 self)
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We present a new imagebased method to process contacts between objects bounded by triangular surfaces. Unlike previous methods, it relies on imagebased volume minimization, which eliminates complex geometrical computations and robustly handles deep intersections. The surfaces are rasterized in three orthogonal directions, and intersections are detected based on pixel depth and normal orientation. Perpixel contact forces are computed and accumulated at the vertices. We show how to compute pressure forces which serve to minimize the intersection volume, as well as friction forces. No geometrical precomputation is required, which makes the method efficient for both deformable and rigid objects. We demonstrate it on rigid, skinned, and particlebased physical models with detailed surfaces in contacts at interactive frame rates. 1.