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I found this One-point perspective formula, but I would like to know what the formulas are for two-point perspective and three-point perspective.

Here is a Desmos graph to further explain my question: https://www.desmos.com/calculator/ixbkrg092x. This post, https://computergraphics.stackexchange.com/questions/8255/finding-the-projection-matrix-for-one-point-perspective, helped me to derive a function, p(x, y, z), that I integrated into my Desmos graph. The variable d is the distance from the viewer's dominant eye to the 3D origin, (0, 0, 0). The variable q is the angle at which the back of the cube is facing. The variable y1 is the y-coordinate of the horizon on the plane of Desmos. The point (x1, y1) is the vanishing point corresponding to the z-axis. The point (x2, y1) is the vanishing point corresponding to the x-axis. Notice how when q approaches π/2 or 3π/2, the cube becomes distorted and appears longer. When it equals π/2 or 3π/2, however, the point (x1, y1) returns undefined. My goal is to incorporate two-point perspective, (and maybe even three-point perspective after I master two-point perspective) in hope of fixing the distortion problem, and making the animation of the rotating cube more realistic and more accurate to the real world.

Am I correct that including two-point perspective will fix the problem? If yes, what is the formula for two-point perspective, as well as for three-point perspective?

I have searched all over the internet and have found nothing.

Thank you in advance.

Logan Tischler
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Here are my two equations that can generate one point-, two point- and three Point Perspective view. You only need the $(x,y,z)$ coordinates of any point in the object. They also use the tilt angle of the camera (n). If (n) is set to ($0$) you will get one or two point- perspective. If (n) is set negative, such as, ($-35$, $-60$, etc.) You will get a bird's eye view. If (n) is positive you will get a worm's eye view. This GIF file shows the process. animation to show the resulting object And here are some examples of a house done by these equations using Microsoft Excel file to generate the perspective coordinates (X,Y). F Is the zoom in/ out constant. It's implied in the equations to give you the choice to magnify or shrink the resulting perspective model regardless of the object's coordinates. [![A house drawn when tilt angle n is different[How to apply the equationsHow to apply the equations? ][2]

Dhirgham Murran
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  • If you want to see how the (x,y,z) coordinates of an object are measured, you will need to consider the camera lens as the origin point of the object's coordinates (x,y,z). However, the origin point of the perspective coordinates (X,Y) Is the focal point on the projection plane. I can list another illustration to show you how the coordinates of a cube are measured if the above illustrations aren't enough. – Dhirgham Murran Feb 08 '23 at 06:28