Visualization of vector fields

In summary, the conversation was about the topic of seeding and visualization techniques, specifically looking for resources to learn about seeding strategies and algorithms for vector fields and different techniques for visualizing them. The person has already looked at research papers and a book called "Topology-Based Methods in Visualization," but is seeking a more introductory overview to better understand the subject. They were suggested to read the work of Professor Terence Tao, but it was noted that he mainly writes about pure mathematics and physics, not visualization techniques.
  • #1
Avatrin
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6
Summary:: Seeding and visualization techniques

Hi

I am looking for resources where I can learn the following:
  1. Seeding strategies and algorithms for vector fields (texture-based, geometry, topological)
  2. Different techniques for visualizing vector fields (streamlines, glyph-based, LIC etc)
 
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  • #2
Avatrin said:
Summary:: Seeding and visualization techniques

Hi

I am looking for resources where I can learn the following:
  1. Seeding strategies and algorithms for vector fields (texture-based, geometry, topological)
  2. Different techniques for visualizing vector fields (streamlines, glyph-based, LIC etc)
Where have you already looked?
 
  • #3
sysprog said:
Where have you already looked?
I downloaded the paper on Line Integral Convolution and also a few others, but I think a more introductory text might be helpful to grasp certain aspects since research papers assume more domain knowledge than what I currently have.

YouTube hasn't been helpful, since any search with the word "seed" in it returns videos about agriculture.

I found a book called "Topology-Based Methods in Visualization", but that seems too specific and I need more of an introductory overview with a broader overview of the field so that I can get started reading papers like the ones introduced in that book (and other non-topology-based methods).
 
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  • #4
I suggest that you read some of the work of Professor Terence Tao -- he has material for beginners and goes on to super-advanced work in such topics as smooth manifolds and more : https://www.math.ucla.edu/~tao/
 
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  • #5
sysprog said:
I suggest that you read some of the work of Professor Terence Tao -- he has material for beginners and goes on to super-advanced work in such topics as smooth manifolds and more : https://www.math.ucla.edu/~tao/
But, he doesn't really write about visualization, though... He seems to write entirely about pure mathematics and some physics.

That doesn't help me in learning specific techniques to visualize vector fields.
 

1. What is a vector field?

A vector field is a mathematical concept that describes the behavior of vectors in a given space. It is represented by a set of arrows, with each arrow representing the magnitude and direction of the vector at a specific point in the space.

2. How is a vector field visualized?

A vector field is typically visualized using arrows, with the length and direction of each arrow representing the magnitude and direction of the vector at a specific point in the space. Color can also be used to indicate the strength or magnitude of the vector at each point.

3. What are some applications of visualizing vector fields?

Visualizing vector fields has many applications in the fields of physics, engineering, and mathematics. It can be used to study the movement of fluids, such as air or water, in aerodynamics and fluid dynamics. It is also used in electromagnetic field analysis and in the study of weather patterns.

4. How is a vector field different from a scalar field?

A vector field represents the behavior of vectors in a given space, while a scalar field represents the behavior of scalar quantities, such as temperature or pressure, in a given space. In a vector field, each point in the space has a direction and magnitude, while in a scalar field, each point has only a numerical value.

5. What techniques are used to visualize complex vector fields?

There are several techniques used to visualize complex vector fields, such as streamlines, pathlines, and streaklines. Streamlines show the direction of the vector at each point, pathlines show the trajectory of a particle moving through the vector field, and streaklines show the path of particles released at different times. Other techniques include using color mapping, animation, and 3D visualization.

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