Line-cyclide intersection and colinear point quadruples in the double conformal model. (English) Zbl 1541.15035
Silva, David W. (ed.) et al., Advanced computational applications of geometric algebra. First international conference, ICACGA 2022, Denver, CO, USA, October 2–5, 2022. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 13771, 3-14 (2024).
Summary: In this paper, we look at using the double conformal model for ray tracing. In particular, we explore the intersection of a line with a cyclide in the double conformal model, and how to extract the four points from the resulting colinear point quadruple. Further, we show how to directly construct a colinear point quadruple from four points, and we show how to find the line containing the points of a colinear point quadruple. We also briefly touch on barycentric coordinates in DCGA.
For the entire collection see [Zbl 1539.68035].
For the entire collection see [Zbl 1539.68035].
MSC:
| 15A67 | Applications of Clifford algebras to physics, etc. |
| 68U05 | Computer graphics; computational geometry (digital and algorithmic aspects) |
| 51-08 | Computational methods for problems pertaining to geometry |
Software:
GaigenReferences:
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