Gaalop – high performance parallel computing based on conformal geometric algebra. We present Gaalop (Geometric algebra algorithms optimizer), our tool for high-performance computing based on conformal geometric algebra. The main goal of Gaalop is to realize implementations that are most likely faster than conventional solutions. In order to achieve this goal, our focus is on parallel target platforms like FPGA (field-programmable gate arrays) or the CUDA technology from NVIDIA. We describe the concepts, current status, and future perspectives of Gaalop dealing with optimized software implementations, hardware implementations, and mixed solutions. An inverse kinematics algorithm of a humanoid robot is described as an example.

References in zbMATH (referenced in 27 articles , 1 standard article )

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  1. Alves, R.; Hildenbrand, D.; Steinmetz, C.; Uftring, P.: Efficient development of competitive Mathematica solutions based on geometric algebra with GAALOPWeb (2020)
  2. Hildenbrand, Dietmar; Hrdina, Jaroslav; Návrat, Aleš; Vašík, Petr: Local controllability of snake robots based on CRA, theory and practice (2020)
  3. Hildenbrand, Dietmar; Steinmetz, Christian; Tichý, Radek: GAALOPWeb for Matlab: an easy to handle solution for industrial geometric algebra implementations (2020)
  4. Sousa, Eduardo Vera; Fernandes, Leandro A. F.: TbGAL: a tensor-based library for geometric algebra (2020)
  5. Hildenbrand, Dietmar: Introduction to geometric algebra computing (2019)
  6. Orouji, Niloofar; Sadr, Ali: A hardware implementation for colour edge detection using Prewitt-inspired filters based on geometric algebra (2019)
  7. Eid, Ahmad Hosny: An extended implementation framework for geometric algebra operations on systems of coordinate frames of arbitrary signature (2018)
  8. Hildenbrand, Dietmar; Benger, Werner; Zhaoyuan, Yu: Analyzing the inner product of 2 circles with Gaalop (2018)
  9. Benger, Werner; Dobler, Wolfgang: Massive geometric algebra: visions for C++ implementations of geometric algebra to scale into the big data era (2017)
  10. Franchini, Silvia; Gentile, Antonio; Sorbello, Filippo; Vassallo, Giorgio; Vitabile, Salvatore: Embedded coprocessors for native execution of geometric algebra operations (2017)
  11. Hildenbrand, D.; Albert, J.; Charrier, P.; Steinmetz, Chr.: Geometric algebra computing for heterogeneous systems (2017)
  12. Hildenbrand, Dietmar; Franchini, Silvia; Gentile, Antonio; Vassallo, Giorgio; Vitabile, Salvatore: GAPPCO: an easy to configure geometric algebra coprocessor based on GAPP programs (2017)
  13. Lopez Belon, Mauricio Cele; Hildenbrand, Dietmar: Practical geometric modeling using geometric algebra motors (2017)
  14. Papaefthymiou, Margarita; Hildenbrand, Dietmar; Papagiannakis, George: A conformal geometric algebra code generator comparison for virtual character simulation in mixed reality (2017)
  15. Sangwine, Stephen J.; Hitzer, Eckhard: Clifford multivector toolbox (for MATLAB) (2017)
  16. Tingelstad, Lars; Egeland, Olav: Automatic multivector differentiation and optimization (2017)
  17. Tørdal, Sondre Sanden; Hovland, Geir; Tyapin, Ilya: Efficient implementation of inverse kinematics on a 6-DOF industrial robot using conformal geometric algebra (2017)
  18. Ahmad Hosney Awad Eid: Optimized Automatic Code Generation for Geometric Algebra Based Algorithms with Ray Tracing Application (2016) arXiv
  19. López-González, Gehová; Altamirano-Gómez, Gerardo; Bayro-Corrochano, Eduardo: Geometric entities voting schemes in the conformal geometric algebra framework (2016)
  20. Ma, Sha; Shi, Zhiping; Shao, Zhenzhou; Guan, Yong; Li, Liming; Li, Yongdong: Higher-order logic formalization of conformal geometric algebra and its application in verifying a robotic manipulation algorithm (2016)

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