KamiWaAi -- interactive 3D sketching with Java based on $Cl(4,1)$ conformal model of Euclidean space This paper introduces the new interactive Java sketching software KamiWaAi, recently developed at the University of Fukui. Its graphical user interface enables the user without any knowledge of both mathematics or computer science, to do full three dimensional “drawings” on the screen. The resulting constructions can be reshaped interactively by dragging its points over the screen. The programming approach is new. KamiWaAi implements geometric objects like points, lines, circles, spheres, etc. directly as software objects (Java classes) of the same name. These software objects are geometric entities mathematically defined and manipulated in a conformal geometric algebra, combining the five dimensions of origin, three space and infinity. Simple geometric products in this algebra represent geometric unions, intersections, arbitrary rotations and translations, projections, distance, etc. To ease the coordinate free and matrix free implementation of this fundamental geometric product, a new algebraic three level approach is presented. Finally details about the Java classes of the new GeometricAlgebra software package and their associated methods are given. KamiWaAi is available for free internet download.

References in zbMATH (referenced in 13 articles , 1 standard article )

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  1. Eid, Ahmad Hosny: An extended implementation framework for geometric algebra operations on systems of coordinate frames of arbitrary signature (2018)
  2. Yuan, Linwang; Yu, Zhaoyuan; Luo, Wen; Zhang, Jiyi; Hu, Yong: Clifford algebra method for network expression, computation, and algorithm construction (2014)
  3. Hitzer, Eckhard; Ichikawa, Daisuke: Representation of crystallographic subperiodic groups in Clifford’s geometric algebra. (2013)
  4. Yuan, Linwang; Yu, Zhaoyuan; Luo, Wen; Yi, Lin; Lü, Guonian: Geometric algebra for multidimension-unified geographical information system (2013)
  5. Hitzer, E.: Crystal planes and reciprocal space in Clifford geometric algebra (2011)
  6. Cruz, Benjamin; Barron, Ricardo; Sossa, Humberto: Geometric associative memories and their applications to pattern classification (2010)
  7. Hitzer, Eckhard; Perwass, Christian: Interactive 3D space group visualization with CLUCalc and the Clifford geometric algebra description of space groups. (2010)
  8. Hitzer, Eckhard; Tachibana, Kanta; Buchholz, Sven; Yu, Isseki: Carrier method for the general evaluation and control of pose, molecular conformation, tracking, and the like (2009)
  9. Hildenbrand, Dietmar; Zamora, Julio; Bayro-Corrochano, Eduardo: Inverse kinematics computation in computer graphics and robotics using conformal geometric algebra (2008)
  10. Hitzer, Eckhard M. S.: Conic sections and meet intersections in geometric algebra (2005)
  11. Abłamowicz, Rafał (ed.); Sobczyk, Garret (ed.): Lectures on Clifford (geometric) algebras and applications (2004)
  12. Hitzer, Eckhard M. S.: Euclidean geometric objects in the Clifford geometric algebra of \origin, 3-space, infinity (2004)
  13. Hitzer, Eckhard M. S.: KamiWaAi -- interactive 3D sketching with Java based on (Cl(4,1)) conformal model of Euclidean space (2003)