Introduction
What is stereographic projection? You are probably already familiar with this topic without realizing it. We know the earth is round which is why we have globes to show the earth. However, we are also able to see the earth on a piece of paper if we want. This would be considered a stereographic projection. Stereographic projection projects a sphere onto a plane. We move from a 3-dimensional object to seeing it on the 2nd dimension. We can see our initial item, the earth, is 3-dimensional and gets projected and gets turned into a map which is 2-dimensional.
Stereographic Projection
We will look at an example but before that lets get to know more about stereographic projection. The entire sphere is projected onto the plane except the one point on the top. If we are projecting the earth this point would be the north pole. The north pole would be known as the projection point. In the picture we can see the blue lines that are being projected from the top most point. We are also able to see the closer we get to these points on the sphere the farther away the lines seem to get projected on the plane. We will be able to see this in the example. Another thing that stereographic projection can cause is distortion. When we look at the map, we can see there is some distortion especially when you look at Greenland. Greenland appears larger on maps than it really is in actuality.
Let's look at an example now. For this example, I have chosen to project flowers. The projected flowers would appear the same in size. In the picture to the right, we can see how the flowers would look when projected. The flowers are all evenly spaced out and the same size.
While the picture above is how it would look when projected. In the picture to the left we can see how the size of the flower varies on the sphere. As we are closer to our projection point the flowers appear smaller and as we get farther away, they become larger. We can also see the closer we are to the projection point the closer together our flowers seem to each other on the sphere. Which is interesting because the flowers that are projected are equal distance from each other.
We've created a sphere with flowers cut out allowing us to get projections of the flowers when a light is shined through the circle on top. In this example we were able to see how much difference there is in the two dimensions when we use stereographic projection.
Why This Example
I tried creating clouds but by doing so I was not able to produce a good file. There was only a difference of one circle between the cloud and the flower I have now. So, I settled with the flowers. It was still interesting how the shape turned out. Maybe after it prints the projections may look like clouds after all. Besides not having many other options the flowers still allows us to see the different objects we can make besides the regular shapes. We were still able to see how distortion works with stereographic projection which was the hardest for me to visualize. When printed my model will be 2 X 2 X 2 inches.
What is stereographic projection? You are probably already familiar with this topic without realizing it. We know the earth is round which is why we have globes to show the earth. However, we are also able to see the earth on a piece of paper if we want. This would be considered a stereographic projection. Stereographic projection projects a sphere onto a plane. We move from a 3-dimensional object to seeing it on the 2nd dimension. We can see our initial item, the earth, is 3-dimensional and gets projected and gets turned into a map which is 2-dimensional.
Stereographic Projection
We will look at an example but before that lets get to know more about stereographic projection. The entire sphere is projected onto the plane except the one point on the top. If we are projecting the earth this point would be the north pole. The north pole would be known as the projection point. In the picture we can see the blue lines that are being projected from the top most point. We are also able to see the closer we get to these points on the sphere the farther away the lines seem to get projected on the plane. We will be able to see this in the example. Another thing that stereographic projection can cause is distortion. When we look at the map, we can see there is some distortion especially when you look at Greenland. Greenland appears larger on maps than it really is in actuality.
Let's look at an example now. For this example, I have chosen to project flowers. The projected flowers would appear the same in size. In the picture to the right, we can see how the flowers would look when projected. The flowers are all evenly spaced out and the same size.
While the picture above is how it would look when projected. In the picture to the left we can see how the size of the flower varies on the sphere. As we are closer to our projection point the flowers appear smaller and as we get farther away, they become larger. We can also see the closer we are to the projection point the closer together our flowers seem to each other on the sphere. Which is interesting because the flowers that are projected are equal distance from each other.
We've created a sphere with flowers cut out allowing us to get projections of the flowers when a light is shined through the circle on top. In this example we were able to see how much difference there is in the two dimensions when we use stereographic projection.
Why This Example
I tried creating clouds but by doing so I was not able to produce a good file. There was only a difference of one circle between the cloud and the flower I have now. So, I settled with the flowers. It was still interesting how the shape turned out. Maybe after it prints the projections may look like clouds after all. Besides not having many other options the flowers still allows us to see the different objects we can make besides the regular shapes. We were still able to see how distortion works with stereographic projection which was the hardest for me to visualize. When printed my model will be 2 X 2 X 2 inches.
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