Daniela Velichová
Slovak Society for Geometry and Graphics, Bratislava
Presentation brings information on an interesting determination of well-known conoidal surfaces generated in 4D as Minkowski quaternionic point set product and ratio of a circle and line segment. In addition to some old synthetic constructions there will be presented 3D views of the surface form 4D into 3 dimensional subspaces by means of double orthogonal projection (as extension of Monge method to 4D) and 4-D perspective.
References
1. Hamilton, W.R.: Elements of Quaternions. Longmans, Green, London (1866).
2. Sanderson, G. (3Blue1Brown): Visualizing the 4D numbers – quaternions. YouTube video (2018).
url https://www.youtube.com/watch?v=d4EgbgTm0Bg
3. Stachel, H.: Plucker’s conoid revisited. G – Slovenský časopis pre geometriu a grafiku 19(38), 21-34 (2022).
4. Velichová, D.: Classification of manifolds resulting as Minkowski operation products of basic geometric point sets. J. Geom. Graph. 19(1), 13-29 (2015).
5. Zamboj, M.: Double orthogonal projection of four-dimensional objects onto two perpendicular three-dimensional spaces. Nexus Netw. J. 20(1), 267–281 (2018).
doi:10.1007/s00004-017-0368-2