We present a data structure and an algorithm for efficient and exact interference detection amongst complex models undergoing rigid motion. The algorithm is applicable to all general polygonal models. It pre-computes a hierarchical representation of models using tight-fitting oriented bounding box trees (OBBTrees). At runtime, the algorithm traverses two such trees and tests for overlaps between oriented bounding boxes based on a separating axis theorem, which takes less than 200 operations in practice. It has been implemented and we compare its performance with other hierarchical data structures. In particular, it can robustly and accurately detect all the contacts between large complex geometries composed of hundreds of thousands of polygons at interactive rates. CR

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OBBTree: a hierarchical structure for rapid interference detection

A text that makes the mathematical underpinnings of robot motion accessible and relates low-level details of implementation to high-level algorithmic concepts. Robot motion planning has become a major focus of robotics. Research findings can be applied not only to robotics but to planning routes on circuit boards, directing digital actors in computer graphics, robot-assisted surgery and medicine, and in novel areas such as drug design and protein folding. This text reflects the great advances that have taken place in the last ten years, including sensor-based planning, probabalistic planning, localization and mapping, and motion planning for dynamic and nonholonomic systems. Its presentation makes the mathematical underpinnings of robot motion accessible to students of computer science and engineering, rleating low-level implementation details to high-level algorithmic concepts.

Principles of Robot Motion: Theory, Algorithms, and Implementations

Determination of side-chain conformations is an important step in protein structure prediction and protein design. Many such methods have been presented, although only a small number are in widespread use. SCWRL is one such method, and the SCWRL3 program (2003) has remained popular because of its speed, accuracy, and ease-of-use for the purpose of homology modeling. However, higher accuracy at comparable speed is desirable. This has been achieved in a new program SCWRL4 through: (1) a new backbone-dependent rotamer library based on kernel density estimates; (2) averaging over samples of conformations about the positions in the rotamer library; (3) a fast anisotropic hydrogen bonding function; (4) a short-range, soft van der Waals atom–atom interaction potential; (5) fast collision detection using k-discrete oriented polytopes; (6) a tree decomposition algorithm to solve the combinatorial problem; and (7) optimization of all parameters by determining the interaction graph within the crystal environment using symmetry operators of the crystallographic space group. Accuracies as a function of electron density of the side chains demonstrate that side chains with higher electron density are easier to predict than those with low-electron density and presumed conformational disorder. For a testing set of 379 proteins, 86% of χ1 angles and 75% of χ1+2 angles are predicted correctly within 40° of the X-ray positions. Among side chains with higher electron density (25–100th percentile), these numbers rise to 89 and 80%. The new program maintains its simple command-line interface, designed for homology modeling, and is now available as a dynamic-linked library for incorporation into other software programs. Proteins 2009. © 2009 Wiley-Liss, Inc.

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Improved prediction of protein side-chain conformations with SCWRL4.

Collision detection is of paramount importance for many applications in computer graphics and visualization. Typically, the input to a collision detection algorithm is a large number of geometric objects comprising an environment, together with a set of objects moving within the environment. In addition to determining accurately the contacts that occur between pairs of objects, one needs also to do so at real-time rates. Applications such as haptic force feedback can require over 1000 collision queries per second. We develop and analyze a method, based on bounding-volume hierarchies, for efficient collision detection for objects moving within highly complex environments. Our choice of bounding volume is to use a discrete orientation polytope (k-DOP), a convex polytope whose facets are determined by halfspaces whose outward normals come from a small fixed set of k orientations. We compare a variety of methods for constructing hierarchies (BV-trees) of bounding k-DOPs. Further, we propose algorithms for maintaining an effective BV-tree of k-DOPs for moving objects, as they rotate, and for performing fast collision detection using BV-trees of the moving objects and of the environment. Our algorithms have been implemented and tested. We provide experimental evidence showing that our approach yields substantially faster collision detection than previous methods.

/pdf/efficient-collision-detection-using-bounding-volume-3we401iylh.pdf

Efficient collision detection using bounding volume hierarchies of k-DOPs

We present a scheme for exact collision detection between complex models undergoing rigid motion and deformation. The scheme relies on a hierarchical model representation using axis-aligned bounding boxes (AABBs). Recent work has shown that AABB trees are slower than oriented bounding box (OBB) trees for performing overlap tests. In this paper, we describe a way to speed up overlap tests between AABBs, such that for collision detection of rigid models, the difference in performance between the two representations is greatly reduced. Furthermore, we show how to update an AABB tree quickly as a model is deformed. We thus find AABB trees to be the method of choice for collision detection of complex models undergoing deformation. In fact, because they are not much slower to test, are faster to build, and use less storage than OBB trees, AABB trees might be a reasonable choice for rigid models as well.

Efficient collision detection of complex deformable models using AABB trees

Heuristics for the Generation of Random Polygons

Evaluation of Collision Detection Methods for Virtual Reality Fly-Throughs

We introduce a new algorithm for generating a spiral tool path for high-speed machining of pockets without islands. The pocket may be an arbitrary simply-connected 2D shape bounded by straight-line segments and circular arcs. The tool path is generated by interpolating growing disks placed on the medial axis of the pocket. It starts inside the pocket and spirals out to the pocket boundary. The tool path is guaranteed to be free of self-intersections and allows machining of the pocket without tool retractions. The start point of the spiral may be chosen freely by the user anywhere within the pocket. Most importantly, the spiral tool path complies with a user-specified maximum cutting width. The output of our algorithm is a G^1-continuous spiral path. However, in a post-processing step, a properly adapted variant of the recent ''PowerApx'' package [Heimlich M, Held M. Biarc approximation, simplification and smoothing of polygonal curves by means of Voronoi-based tolerance bands. International Journal of Computational Geometry & Applications 2008;18(3):221-50] can be used to boost the tool path to C^2-continuity. Our new algorithm was implemented and tested successfully on real-world data. We conclude our paper by an analysis of sample tool paths produced by our implementation.

A smooth spiral tool path for high speed machining of 2D pockets

We describe ERIT, a collection of C routines for efficiently and reliably handling intersection queries between pairs of primitive objects in three dimensions. ERIT supports intersection queries between the following pairs of primitives: triangle/line-segment, triangle/triangle, sphere/line-segment, sphere/triangle, cylinder/line-segment, cylinder/triangle, cylinder/sphere, cone/line-segment, cone/ triangle, toroid/line-segment, toroid/triangle, and sphere/sphere. All intersection routines are based on standard "epsilon-based" floating-point arithmetic. Practical tests have proved that ERIT's routines are efficient and reliable, and we provide performance statistics for three widely-used hardware platforms.

Martin Held

Papers

Efficient collision detection using bounding volume hierarchies of k-DOPs

Heuristics for the Generation of Random Polygons

Evaluation of Collision Detection Methods for Virtual Reality Fly-Throughs

A smooth spiral tool path for high speed machining of 2D pockets

ERIT: a collection of efficient and reliable intersection tests