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

In summary, the conversation revolves around the subject of Trajectory Triangulation and the confusion surrounding the use of the term "3D line." The person discussing the topic is reading a paper on the subject and is unsure how a line can be in 3D when it is defined as 1D. They also mention the connection to projective geometry and the use of Plucker coordinates to represent the line of intersection of other lines. Ultimately, they come to the conclusion that the term "3D line" refers to the trajectory in 3D space, not the line itself.
  • #1
MathematicalPhysicist
Gold Member
4,699
371
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
  • #2
this T.T has connection to projective geometry. interesting...
 
  • #3
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.
 

1. What is trajectory triangulation?

Trajectory triangulation is a method used in motion analysis to determine the path of an object in motion. It involves using multiple points of observation to calculate the position and movement of the object over time.

2. How does trajectory triangulation work?

In trajectory triangulation, the positions of an object are measured from multiple points of observation. These positions are then used to calculate the object's trajectory using mathematical algorithms such as triangulation or trilateration.

3. What are the applications of trajectory triangulation?

Trajectory triangulation has various applications, including analyzing the movement of vehicles, tracking the path of projectiles, and determining the flight path of aircraft. It is also used in sports analysis to track the movement of athletes and in robotics for navigation.

4. What are the benefits of using trajectory triangulation?

Trajectory triangulation allows for accurate tracking and analysis of an object's movement, even in complex environments. It also provides a non-intrusive method of measuring motion, as it does not require physical contact with the object being tracked.

5. What are the limitations of trajectory triangulation?

One limitation of trajectory triangulation is that it requires a clear line of sight between the points of observation and the object being tracked. This can be challenging in certain environments, such as crowded areas or when tracking fast-moving objects. Additionally, errors in measurement or miscalculations can result in inaccuracies in the trajectory calculation.

Similar threads

WaveGrid - Non-equilibrium Emergence Sandbox
    • Programming and Computer Science
Replies
1
Views
1K
Exploring Causal Dynamical Triangulation: A Guide
    • Beyond the Standard Models
Replies
1
Views
5K
Please help me select my undergrad subjects [maths]
    • STEM Academic Advising
Replies
10
Views
3K
B Unlearning the Block Universe: How Relativity Challenges Our Perception of Time
    • Special and General Relativity
3
Replies
90
Views
5K
Admissions Need advice for my personal statement
    • STEM Academic Advising
Replies
27
Views
2K
List of Questions I want to ask regarding physics, philosophy, mathematics, etc.
    • Other Physics Topics
Replies
1
Views
2K
Surface roughness in 2D sinusoidal corrugation
    • Mechanical Engineering
Replies
1
Views
3K
Engineering Change of major as a junior: Physics or Aerospace Engineering?
    • STEM Career Guidance
Replies
4
Views
2K
Is Poincaré's Space Dilemma the Key to Understanding Gravity?
    • Special and General Relativity
3
Replies
71
Views
15K
Engineering Switching from Electrical Engineering to Computer Science
    • STEM Career Guidance
Replies
2
Views
12K

Hot Threads

Recent Insights

Back
Top