# Projection of 3D Plane from a certain perspective on the 2D Plane

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• jisbon
In summary, the conversation discusses the challenges of creating a graph that accurately represents a trajectory motion in the 3D plane from the perspective of a person located in a different position and at a different elevation angle. The solution may involve using the concept of frustrum in 3D computer graphics to calculate the path of the image of the motion on a camera sensor. However, the exact mathematical process is still unclear.
jisbon
TL;DR Summary
Given a 3D Plane, assuming I have a trajectory motion in the XYZ plane and have some coordinates of the projection at every 1 second, how do I project this motion on a person that is standing at another point in the 3D plane in a 2D format?
Hello all!
As seen in the summary, I'm not sure if anyone can understand, but I will try to make this as clear as possible.
Working in the 3D Plane:
Given that there is a trajectory motion in the 3D Plane, and I have the coordinates of the motion at every 1s interval.
This means at t=1s, the coordinates could be at (… ,..., …) etc. and it will form a invert-u shape like a normal trajectory motion as shown below.

Now, assuming I have a person looking at this motion. This person can be standing anywhere in the 3D Plane. Hence, to his perspective, this trajectory motion will definitely look different from different locations. This can be seen below:

(The same projectile motion, but at a different location)

Furthermore, the looks of the motion will also change once we take into account of the height difference. This means that the person could be at the bottom staring at the motion, resulting in a different shape as shown.

(Again, the same motion, but looking under it this time aka an elevation angle is incurred)

Given that I have the location of the person, the location of the projectile motion at some intervals, how am I able to 'sketch'/'create' the graph that is projected onto the person given that the user has the locations (as previously stated), the elevation angle etc.?

I have thought of calculating the distance at each interval of the projectile motion to the person, but am stuck there afterwards, not knowing how do I create/sketch the perspective of the motion to the person. Any help will be greatly appreciated.

Thank you!

Are you asking for the path of the image of a ball on a camera sensor located at some point? If so, look up the frustrum as used in 3d computer graphics. If not, I didn't understand your question.

Ibix said:
Are you asking for the path of the image of a ball on a camera sensor located at some point? If so, look up the frustrum as used in 3d computer graphics. If not, I didn't understand your question.
That would be something like it. Looking up on 3D Projection, hopefully I can understand the exact math behind it.

## 1. What is the purpose of projecting a 3D plane onto a 2D plane from a certain perspective?

The purpose of this projection is to accurately represent the 3D object on a 2D surface, allowing for better visualization and analysis of the object's shape, size, and orientation.

## 2. How is the projection of a 3D plane onto a 2D plane calculated?

The projection is calculated using mathematical formulas and techniques such as perspective projection or orthographic projection, which take into account the position and orientation of the 3D object and the viewing angle of the 2D plane.

## 3. What are the main differences between perspective and orthographic projection?

Perspective projection creates a more realistic representation of the 3D object by taking into account the distance from the viewer, while orthographic projection creates a parallel projection that does not consider distance.

## 4. How does the viewing angle affect the projection of a 3D plane onto a 2D plane?

The viewing angle determines the perspective or orientation of the 3D object on the 2D plane. A different viewing angle can result in a different projection, changing the appearance of the object.

## 5. Are there any limitations to projecting a 3D plane onto a 2D plane?

Yes, there are limitations such as distortion and loss of depth perception due to the conversion from 3D to 2D. Additionally, projecting complex or irregularly shaped objects can be challenging and may require advanced techniques.

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