Is a 3D Line Really Just a 1D Object?

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    Trajectory Triangulation
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SUMMARY

The discussion centers on the concept of a "3D line" in the context of Trajectory Triangulation, specifically referencing the paper found at http://www.faculty.idc.ac.il/avidan/Traj-Trian-Pami.pdf. Participants clarify that while a line is inherently one-dimensional, its representation in a three-dimensional space pertains to its trajectory rather than the line itself. The mention of Plücker coordinates (L = P ^ Q) introduces a four-coordinate system that describes the intersection of lines in projective geometry, further complicating the understanding of dimensionality in this context.

PREREQUISITES
  • Understanding of Trajectory Triangulation concepts
  • Familiarity with projective geometry
  • Knowledge of Plücker coordinates
  • Basic principles of dimensionality in geometry
NEXT STEPS
  • Study the principles of Trajectory Triangulation in depth
  • Learn about projective geometry and its applications
  • Explore Plücker coordinates and their significance in geometry
  • Investigate the relationship between dimensionality and geometric representations
USEFUL FOR

Students and professionals in computer science, particularly those focused on geometry, computer graphics, and trajectory analysis, will benefit from this discussion.

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im reading about the subject Trajectory Triangulation from here:
http://www.faculty.idc.ac.il/avidan/Traj-Trian-Pami.pdf

i haven't finished reading (so perhaps it explained in further pages) and i encoutered to words 3D line.
now i presume D represents dimension so the next question is how can a line be a 3d if it's by definition is 1d?

perhaps it something with the terminology of the computer science any way what do you think?
 
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this T.T has connection to projective geometry. interesting...
 
in page 3 it discuss about plucker coordinates and it states L(represents the line of intersection of the other lines you should read it, it's hard to explain))=P ^ Q
and it's have 4 coordinates which is weird because they are discussing the trajectory of 3d line and not of a 4d so how can it be?

btw i think i have understood what they meant by 3d line the trajectory is in 3d not line itself.
 

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