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Expansion to 3D Computations
Published in Dietmar Hildenbrand, Introduction to Geometric Algebra Computing, 2020
In 3D, Conformal Geometric Algebra (CGA) provides a great variety of basic geometric entities to compute with, namely points, spheres, planes, circles, lines, and point pairs. Table 15.2 shows the extension of the 2D geometric objects of the previous chapters to 3D objects. These entities have two algebraic representations: the IPNS (inner product null space) and the OPNS (outer product null space).4 They are duals of each other (a superscript asterisk denotes the dualization operator). In Table 15.2, x and n are in bold type to indicate that they represent 3D entities obtained by linear combinations of the 3D basis vectors e1, e2, and e3: x=x1e1+x2e2+x3e3.
Requirements of a data storage infrastructure for effective land administration systems: case study of Victoria, Australia
Published in Journal of Spatial Science, 2022
Davood Shojaei, Farshad Badiee, Hamed Olfat, Abbas Rajabifard, Behnam Atazadeh
Data types in cadastral data storage is an important aspect. Various spatial data types are supported in databases. The primitive geometric objects in a 2D space include points, curve, face, geometry collection to model simple features. These spatial data types are supported in spatial databases. In addition to spatial data types, databases support other data types such as XMLType (Garcia-Molina et al. 2009) that can be considered for spatial data (See Section 2.3). Zhang et al. (2016) also discussed conformal geometric algebra (CGA) for defining cadastral objects in a database rather than using Euclidean space and proposed a data model. Sulistyawati et al. (2018) also looked at representing spatio-temporal cadastral objects and proposed an approach to store cadastral objects in PostgreSQL database based on LADM.
Comparative study of the neural and neuro-fuzzy networks for direct path generation of a new fully spherical parallel manipulator
Published in Australian Journal of Mechanical Engineering, 2020
The spherical movement of a rigid body around an optional coordinate and a point allows variable orientation of a rigid body and end-effector (Gosselin and Angeles 1989). A fully spherical parallel manipulator (SPM) is a developed parallel manipulator that its moving platform has rotational movement around a spherical joint (Enferadi and Shahi 2015). A new family of SPMs was introduced by Di Gregorio (2002). He showed that the 3(RRPRR) architectures matching the geometric conditions for elementary spherical motion make the platform accomplish finite spherical motion. Alici and Shirinzadeh (2004) introduced the 3(SPS)-S SPMs. This manipulator has three kinematics chains and each one consists of spherical (S), prismatic (P) and spherical (S) joints. Spherical joint of the fixed platform is connected to the spherical joint of the moving platform with a prismatic link. Recent researches have been done solving the forward kinematics of this manipulator using methods such as conformal geometric algebra (Kim and Jeong 2016). The workspace of spherical manipulators has been the topic of some researches as well. To exemplify, Bonev presented a technique for the analytical determining the workspace boundaries of symmetrical spherical parallel mechanisms. The technique is based on an intuitive orientation representation that is very useful for the analysis of a symmetrical parallel mechanisms (Bonev and Gosselin 2006).