China
Africa
Explore chapters and articles related to this topic
Solid discrete element modeling using nonmanifold topological data structures
Published in R.F. Azevedo, E.A. Vargas, L.M. Ribeiro e Sousa, M. Matos Fernandes, Applications of Computational Mechanics in Geotechnical Engineering, 2020
Luiz Fernando Martha, João Luiz Elias Campos, Paulo Cezar Pinto Carvalho, Paulo Roma Cavalcanti, Beatriz Castier
Although a complete geometric description carries all information about the geometric shapes of the spatial subdivision entities, called cells, and their positioning in space, it is better to have both geometrical and topological information in the representation of the subdivision. For example, from the geometric description of two surface patches, their intersection curve can be found when necessary. However, this determination requires some processing, which generally is time consuming. A representation for spatial subdivisions containing explicitly all intersections not only ensures that the computation of these intersections can be done just once (when the subdivision is created), but also avoids numerical error propagation.
Applying matrix diagonalisation in the classroom with GeoGebra: parametrising the intersection of a sphere and plane
Published in International Journal of Mathematical Education in Science and Technology, 2023
Bradley Graeme Welch, Juan Carlos Ponce Campuzano
Now let us solve the main problem, posed in Section 2, using diagonalisation of quadratic forms. That is, we seek the parametrisation of the intersection curve of the sphere and plane where A, B, C are not all simultaneously zero. To simplify some calculations, first we translate both objects using the vector to obtain the equations For , rearrange the equation for to obtain and define so we can rewrite (10) as Substituting (12) into the equation for yields: After expanding the square and re-grouping all similar terms, the previous expression becomes Note that Equation (13) is in fact a quadratic form: . Then it can be re-written using matrices as follows: where and .
5-Axis tool path planning based on highly parallel discrete volumetric geometry representation: Part I contact point generation
Published in Computer-Aided Design and Applications, 2018
Dmytro Konobrytskyi, Mohammad M. Hossain, Thomas M. Tucker, Joshua A. Tarbutton, Thomas R. Kurfess
The roughing tool path generation process is a bit more complicated than the finishing process because it has to process a volume, not a surface. There are three main differences. First, it uses an iterative approach to generate a tool path that removes material layer by layer until it reaches a part surface. Second, a target surface for roughing process is a workpiece material surface itself. Similarly to the finishing process, it uses surface filling algorithm for generating a set of curves on a material surface that are used as tool center trajectory curves. And finally, roughing algorithm selects initial curves differently. The current implementation uses the intersection between a workpiece and a model offset volume for selecting an initial curve. After the intersection is calculated, the longest intersection curve is selected (Fig. 13), and the surface filling algorithm is used. This process repeats until all intersection curves are processed. All roughing path planning steps are demonstrated in Algorithm 6.
Real-time needle guidance for venipuncture based on optical coherence tomography
Published in Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, 2021
Rida T. Farouki, Jack R. Swett, Rachel Ward Rohlen, David B. Smith
This may be seen as follows. The intersection of two quadric surfaces and is, in general, an irreducible quartic space curve2 (Snyder and Sisam 1914). There are infinitely–many pairs of quadric surfaces that possess the same intersection curve as and . Any two members of the pencil of quadrics defined by