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Flowers stereographic projection

Projection is already ubiquitous in life. Projection is used in life. For example, in class, teachers will use projection to show the content of this lesson, and leaders at work will also use it as an auxiliary tool to show the next goal. Projection is widely used in life. It is a great auxiliary tool. Why? Because of its special properties, it can be adjusted by people, and the image can be enlarged and reduced by changing the distance. For example, the picture we watched in the cinema is a long-distance projection. These are all very well realized. Through the way of projection, the pattern on the cardboard can be projected by letting light pass through some cardboard with special patterns. These are all projected from one plane to another, and stereographic projection is a projection that projects a spherical surface to a plane. For example, the map is the stereographic projection of the earth. There will be a large gap between the actual projected image and the sphere itself. This kind of mapping will not maintain the same distance or area. So if we want to project some regular, special patterns, we need to change the spherical shape.
Because it will change the characteristics of graphics, in most cases, flat projection is used, and what I can think of is some colorful lights on the dance floor. Their appearance is some hollow spheres, and some colorful lights are placed inside and then projected. Various shapes. This is a great example, so I decided to try to make a projected pattern of evenly arranged flowers.

The pattern of the flower is very simple. We learned it when we was young. For example, you can get a small flower by overlapping four circles.
Uh... of course, the middle should be removed too, so put another square in the middle, then make some fine adjustments to the position, you can get a small flower.
Just one is not enough. We need more flowers so that we can project a larger area and observe the changes in the shape of the flowers on the sphere.
In this way, the evenly arranged small flowers are done. Above them is the light path. The light projected from the light source is set to a point, passes through the sphere from here, and then is projected onto the plane. This is the effect we want. So will the hollows of the sphere be arranged in an orderly manner?
It seems that the distance has changed. Although they are no longer equally spaced, their positions are also regular to follow. The closer to the top, the smaller the pattern and the smaller the distance between flowers.
This is the final version after some minor adjustments and moving the position of the flowers. The only difficulty is that my notebook is too stuck. I don’t know why it is stuck. Although I want to add another pattern, it’s stuck. It barely moved, so I had to give up the idea of adding leaves (one rectangle for the flower stem and two triangles for the leaves to make a real flower), but overall, it was good.

Its size is about: x = 59.2613, y = 59.2613, z = 58.8606

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