<p>Your question is a bit difficult to grasp. I guess your point is: if I only know the <em>vector</em> (regardless of the starting and the ending point), can I project this <em>direction vector</em> from 3D to 2D? Namely, from <span class="math-container">$(\Delta X, \Delta Y, \Delta Z)$</span> to <span class="math-container">$(\Delta u, \Delta v)$</span>. The answer is no, you must have the starting point for perspective projection. The following simple example can help you understand this:</p>
<p><a href="https://i.sstatic.net/JpqHpzy2.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/JpqHpzy2.png" alt="projection" /></a></p>
<p>The three cases above share the same <span class="math-container">$(\Delta X, \Delta Y, \Delta Z)$</span> but they have very different projected 2D vectors.</p>

CC BY-SA 4.0
2024-11-06T16:29:04.563Z
2024-11-06T16:29:04.563Z
Enigmatisms
<p>Suppose I have vectors in a 3D space (their starting points, dx, dy, and dz), and I would like to project them onto a camera, which I already have as a 3x4 projection matrix.</p>
<p>I can of course project the start points and end points in two passes. However, I am interested in only (dx, dy), not the starting point of a projected 2D vectors. Is there a way to compute their directly from (dx,dy,dz) of the 3D vector, perhaps using homogeneous coordinates in a different way? Thanks.</p>

<3d><geometry><projections><camera-matrix><vectors>
Projecting Vectors (3D to 2D) Using Homogeneous Coordinates, With Known Camera Calibration
erik
# Projecting Vectors (3D to 2D) Using Homogeneous Coordinates, With Known Camera Calibration

(Asked by: username_0 on 2024-11-02)

Suppose I have vectors in a 3D space (their starting points, dx, dy, and dz), and I would like to project them onto a camera, which I already have as a 3x4 projection matrix.

I can of course project the start points and end points in two passes. However, I am interested in only (dx, dy), not the starting point of a projected 2D vectors. Is there a way to compute their directly from (dx,dy,dz) of the 3D vector, perhaps using homogeneous coordinates in a different way? Thanks.

**Tags:** 3d, geometry, projections, camera-matrix, vectors


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## 1 answers

### Answer by username_1 on 2024-11-06. Score: 1

Your question is a bit difficult to grasp. I guess your point is: if I only know the *vector* (regardless of the starting and the ending point), can I project this *direction vector* from 3D to 2D? Namely, from $(\Delta X, \Delta Y, \Delta Z)$ to $(\Delta u, \Delta v)$. The answer is no, you must have the starting point for perspective projection. The following simple example can help you understand this:

[![projection](https://i.sstatic.net/JpqHpzy2.png)](https://i.sstatic.net/JpqHpzy2.png)

The three cases above share the same $(\Delta X, \Delta Y, \Delta Z)$ but they have very different projected 2D vectors.


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