Designing a 3d sphere in the 2nd circle on the screen

Question

What are some rasterization algorithms that can simply project a 3D sphere into a pixel grid? I want to avoid beam casting. Essentially, given the 3d coordinate and radius, is there a quick way to create a 2d circle / ellipse on a pixel grid?

For example: a circle at a point (2,2,2) with a radius of 4 is projected into five pixels: p1 (2,0) p2 (0,1) p3 (1,1) p4 (2,1) p5 (1,2)

I have come across methods such as splitting pixels into particle systems, but I have not found a clear answer on how to do this.

thanks

Answer 1

What projection do you have?

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Answer 2

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Answer 3

, ( - ) - 4x4. , 3D- 4x4.

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Answer 4

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Answer 5

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Answer 6

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, (X = 0, Y = 0), (X = 0, Y = 0, Z = 0). (sX, sY, sZ) sR, - D ( ), (cX = sX * D/sZ, cY = sY * D/sZ) cR = sR * D/sZ. D/sZ.

This circle is a good approximation of the projection of the ball if the focal length (D) is large or the coordinates sX and sY of the sphere are close to zero.