What Do Colors and Shapes Represent in Stereographic Projections?

In summary, a stereographic projection is a map projection technique used to represent a spherical surface on a flat plane. It works by projecting the center of the sphere onto a tangent plane, resulting in a distorted representation of the spherical surface. Some advantages of using this projection include preserving both shape and area and minimal distortion near the poles. However, it has limitations such as only being able to show a limited area and significant distortion near the edges. Stereographic projections are commonly used in cartography, geology, and astronomy, particularly for mapping polar regions and creating celestial maps.
  • #1
scott_alexsk
336
0
Hello,

Can anyone tell me what the triangles, squares, and ovals mean in the projection on page 19? Does this have something to do with the directions for the third axis? On the next page several of the symbols are black. What significance does this have, also?

Thanks
-scott

"[PLAIN 19"]http://neon.mems.cmu.edu/rollett/27750/L19A_Single_Xtal_Aniso1_3Apr06.ppt#317,19,Slide 19[/URL]
 
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  • #2
They indicate symmetries of the lattice, ie a square is a 4-fold rotation, triangle a 3-fold rotation etc...
 
  • #3



Hello Scott,

The triangles, squares, and ovals in the stereographic projection are symbols used to represent specific crystallographic directions. These symbols are known as Miller indices and they are used to label crystal faces and directions in a crystal structure. The third axis in the projection represents the direction perpendicular to the plane of the projection, and the symbols indicate the orientation of the crystal in three-dimensional space.

On the next page, the black symbols represent specific crystallographic planes. In stereographic projections, different colors or shades are often used to differentiate between different crystallographic planes or directions. This can help to visually distinguish between different crystallographic features and aid in understanding the orientation of the crystal.

I hope this helps to clarify the symbols in the projection. If you have any further questions, please don't hesitate to ask.

 

1. What is a stereographic projection?

A stereographic projection is a map projection technique used to represent a spherical surface on a flat plane. It is commonly used to create maps of the Earth and other celestial bodies.

2. How does a stereographic projection work?

In a stereographic projection, the center of the sphere is projected onto a tangent plane, which becomes the map's surface. All other points on the sphere are projected onto this plane, resulting in a distorted representation of the spherical surface.

3. What are the advantages of using a stereographic projection?

One advantage of stereographic projections is that they preserve both shape and area, making them useful for mapping regions near the projection's center. They also have minimal distortion near the poles.

4. What are the limitations of stereographic projections?

Stereographic projections can only show a limited area of the spherical surface, making them unsuitable for mapping large regions. They also have significant distortion near the edges of the map.

5. How is a stereographic projection used in science?

Stereographic projections are used in a variety of scientific fields, including cartography, geology, and astronomy. They are particularly useful for mapping the Earth's polar regions and for creating star charts and celestial maps.

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