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 20 articles , 1 standard article )

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  1. Hildenbrand, Dietmar: Introduction to geometric algebra computing (2019)
  2. Hildenbrand, Dietmar; Benger, Werner; Zhaoyuan, Yu: Analyzing the inner product of 2 circles with Gaalop (2018)
  3. Benger, Werner; Dobler, Wolfgang: Massive geometric algebra: visions for C++ implementations of geometric algebra to scale into the big data era (2017)
  4. Franchini, Silvia; Gentile, Antonio; Sorbello, Filippo; Vassallo, Giorgio; Vitabile, Salvatore: Embedded coprocessors for native execution of geometric algebra operations (2017)
  5. Hildenbrand, D.; Albert, J.; Charrier, P.; Steinmetz, Chr.: Geometric algebra computing for heterogeneous systems (2017)
  6. Hildenbrand, Dietmar; Franchini, Silvia; Gentile, Antonio; Vassallo, Giorgio; Vitabile, Salvatore: GAPPCO: an easy to configure geometric algebra coprocessor based on GAPP programs (2017)
  7. Papaefthymiou, Margarita; Hildenbrand, Dietmar; Papagiannakis, George: A conformal geometric algebra code generator comparison for virtual character simulation in mixed reality (2017)
  8. Sangwine, Stephen J.; Hitzer, Eckhard: Clifford multivector toolbox (for MATLAB) (2017)
  9. Tingelstad, Lars; Egeland, Olav: Automatic multivector differentiation and optimization (2017)
  10. Tørdal, Sondre Sanden; Hovland, Geir; Tyapin, Ilya: Efficient implementation of inverse kinematics on a 6-DOF industrial robot using conformal geometric algebra (2017)
  11. Ahmad Hosney Awad Eid: Optimized Automatic Code Generation for Geometric Algebra Based Algorithms with Ray Tracing Application (2016) arXiv
  12. López-González, Gehová; Altamirano-Gómez, Gerardo; Bayro-Corrochano, Eduardo: Geometric entities voting schemes in the conformal geometric algebra framework (2016)
  13. 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)
  14. Benger, Werner; Heinzl, René; Hildenbrand, Dietmar; Weinkauf, Tino; Theisel, Holger; Tschumperlé, David: Differential methods for multi-dimensional visual data analysis (2015)
  15. Charrier, Patrick; Klimek, Mariusz; Steinmetz, Christian; Hildenbrand, Dietmar: Geometric algebra enhanced precompiler for C++, OpenCL and Mathematica’s OpenCLLink (2014)
  16. Fuchs, Laurent; Théry, Laurent: Implementing geometric algebra products with binary trees (2014)
  17. Hildenbrand, Dietmar: Foundations of geometric algebra computing. (2013)
  18. Yuan, Linwang; Yu, Zhaoyuan; Luo, Wen; Yi, Lin; Lü, Guonian: Geometric algebra for multidimension-unified geographical information system (2013)
  19. Franchini, Silvia; Gentile, Antonio; Sorbello, Filippo; Vassallo, Giorgio; Vitabile, Salvatore: Fixed-size quadruples for a new, hardware-oriented representation of the 4D Clifford algebra (2011)
  20. Hildenbrand, Dietmar; Pitt, Joachim; Koch, Andreas: Gaalop -- high performance parallel computing based on conformal geometric algebra (2010)