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Intersection Points (intersection + point)

Distribution by Scientific Domains

Engineering	33%

Selected Abstracts

Minimal realizations of spatial stiffnesses with parallel or serial mechanisms having concurrent axes

JOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 3 2001
Shuguang Huang
This article presents a new method for the synthesis of an arbitrary spatial elastic behavior with an elastic mechanism. The mechanisms considered are parallel and serial mechanisms with concurrent axes. We show that any full-rank spatial stiffness matrix can be realized using a parallel mechanism with all spring axes intersecting at a unique point. It is shown that this intersection point must be the center of stiffness. We also show that any full-rank spatial compliance matrix can be realized using a serial mechanism with all joint axes intersecting at a unique point. This point is shown to be the center of compliance. Synthesis procedures for mechanisms with these properties are provided. The realizations are shown to be minimal in the sense that both the number of screw components and the total number of components are minimum. © 2001 John Wiley & Sons, Inc. [source]

Approximate implicitization and recursive surface intersection algorithms

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2007
Tor Dokken
Most published work on intersection algorithms for Computer Aided Design (CAD) systems addresses transversal intersections [1], situations where the surface normals of the surfaces intersected are well separated along all intersection curves. For transversal intersections the divide and conquer strategy of recursive subdivision, Sinha's theorem [2] and the convex hull property of NonUniform Rational B-Spline surfaces (NURBS) efficiently identify all intersection branches. However, in singular or near singular intersections, situations where the surfaces are parallel or near parallel in an intersection region, along an intersection curve or in an intersection point, even deep levels of subdivision will frequently not sort out the intersection topology. The paper will focus on the novel approach of Approximate Implicitization to address these challenges. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Progressive Hulls for Intersection Applications

COMPUTER GRAPHICS FORUM, Issue 2 2003
Nikos Platis
Abstract Progressive meshes are an established tool for triangle mesh simplification. By suitably adapting the simplification process, progressive hulls can be generated which enclose the original mesh in gradually simpler, nested meshes. We couple progressive hulls with a selective refinement framework and use them in applications involving intersection queries on the mesh. We demonstrate that selectively refinable progressive hulls considerably speed up intersection queries by efficiently locating intersection points on the mesh. Concerning the progressive hull construction, we propose a new formula for assigning edge collapse priorities that significantly accelerates the simplification process, and enhance the existing algorithm with several conditions aimed at producing higher quality hulls. Using progressive hulls has the added advantage that they can be used instead of the enclosed object when a lower resolution of display can be tolerated, thus speeding up the rendering process. ACM CSS: I.3.3 Computer Graphics,Picture/Image Generation, I.3.5 Computer Graphics,Computational Geometry and Object Modeling, I.3.7 Computer Graphics,Three-Dimensional Graphics and Realism [source]

Traveltime computation by wavefront-orientated ray tracing

GEOPHYSICAL PROSPECTING, Issue 1 2005
Radu Coman
ABSTRACT For multivalued traveltime computation on dense grids, we propose a wavefront-orientated ray-tracing (WRT) technique. At the source, we start with a few rays which are propagated stepwise through a smooth two-dimensional (2D) velocity model. The ray field is examined at wavefronts and a new ray might be inserted between two adjacent rays if one of the following criteria is satisfied: (1) the distance between the two rays is larger than a predefined threshold; (2) the difference in wavefront curvature between the rays is larger than a predefined threshold; (3) the adjacent rays intersect. The last two criteria may lead to oversampling by rays in caustic regions. To avoid this oversampling, we do not insert a ray if the distance between adjacent rays is smaller than a predefined threshold. We insert the new ray by tracing it from the source. This approach leads to an improved accuracy compared with the insertion of a new ray by interpolation, which is the method usually applied in wavefront construction. The traveltimes computed along the rays are used for the estimation of traveltimes on a rectangular grid. This estimation is carried out within a region bounded by adjacent wavefronts and rays. As for the insertion criterion, we consider the wavefront curvature and extrapolate the traveltimes, up to the second order, from the intersection points between rays and wavefronts to a gridpoint. The extrapolated values are weighted with respect to the distances to wavefronts and rays. Because dynamic ray tracing is not applied, we approximate the wavefront curvature at a given point using the slowness vector at this point and an adjacent point on the same wavefront. The efficiency of the WRT technique is strongly dependent on the input parameters which control the wavefront and ray densities. On the basis of traveltimes computed in a smoothed Marmousi model, we analyse these dependences and suggest some rules for a correct choice of input parameters. With suitable input parameters, the WRT technique allows an accurate traveltime computation using a small number of rays and wavefronts. [source]

Structured matrix methods for CAGD: an application to computing the resultant of polynomials in the Bernstein basis

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 8 2005
Dario A. Bini
Abstract We devise a fast fraction-free algorithm for the computation of the triangular factorization of Bernstein,Bezoutian matrices with entries over an integral domain. Our approach uses the Bareiss fraction-free variant of Gaussian elimination, suitably modified to take into account the structural properties of Bernstein,Bezoutian matrices. The algorithm can be used to solve problems in algebraic geometry that arise in computer aided geometric design and computer graphics. In particular, an example of the application of this algorithm to the numerical computation of the intersection points of two planar rational Bézier curves is presented. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Elastic Potential Grids: Accurate and Efficient Representation of Intermolecular Interactions for Fully Flexible Docking

CHEMMEDCHEM, Issue 8 2009
Sina Kazemi
Potential fields represented by irregular, deformable 3D grids provide an accurate and efficient lookup table function for evaluating intermolecular interactions in docking algorithms that consider target flexibility. Target movements can be translated into appropriate displacements of grid intersection points in a binding site region if the irregular deformable 3D grid is modeled as a homogeneous linear elastic body. [source]