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

Click For Summary
The discussion centers on the concept of a "3D line" in the context of trajectory triangulation and projective geometry. The term "3D line" raises questions about how a line, inherently one-dimensional, can be described as three-dimensional. The mention of Plücker coordinates introduces complexity, as they involve four coordinates while discussing a trajectory in three-dimensional space. The conclusion drawn is that the term "3D line" likely refers to the trajectory existing in three-dimensional space rather than the line itself being three-dimensional. This highlights the nuances in terminology within computer science and geometry.
MathematicalPhysicist
Science Advisor
Gold Member
Messages
4,662
Reaction score
372
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?
 
Mathematics news on Phys.org
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.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

Studying Skipping Chapters in Stewart’s Calculus? (Pearson's Edexcel IAL Background)
  • · Replies 2 ·
Replies
2
Views
601
Seemingly Simple Kinematics Problem II: the Vector Strikes Back
  • · Replies 2 ·
Replies
2
Views
4K
Surface roughness in 2D sinusoidal corrugation
  • · Replies 1 ·
Replies
1
Views
4K
Visit With Paul Davies on Block Time
  • · Replies 53 ·
2
Replies
53
Views
15K
Preparing for math REUs next summer
  • · Replies 5 ·
Replies
5
Views
6K
Are Women and New Researchers Shaping the Future of Quantum Gravity Studies?
  • · Replies 24 ·
Replies
24
Views
8K
BRS: Random Comments on Some Recent PF Threads
  • · Replies 94 ·
4
Replies
94
Views
12K
Are Finkelstein/Kruskal Black Hole Solutions Compatible with Einstein's GR?
  • · Replies 124 ·
5
Replies
124
Views
17K
Mathematica This Week's Finds in Mathematical Physics (Week 255)
  • · Replies 1 ·
Replies
1
Views
3K
BRS: Those Damnable Paradoxes I. Overview
  • · Replies 19 ·
Replies
19
Views
2K