<p>Basically whenever you project a set of parallel lines in 3D space on a 2D image plane, you'll see that these lines don't remain parallel in 2D space and tend to meet at a certain point which is the so called vanishing point. Picture a long railway, both the rail lines meet at the horizon.</p>
<p>Now one confusion arises that the question doesnt give you a set of parallel lines, But it doesn't matter as long as a single line segment is provided. All you need to do is just picture the line segment extending to infinity. So for example, picture the point <span class="math-container">$B$</span> at infinity and imagine drawing a line <span class="math-container">$BE$</span>. The point at which this line intersects the image plane will be your vanishing point.</p>
<p>There is a simple pattern that applies to every case like this. Just shoot a ray in the direction of the vector <span class="math-container">$\vec{AB}$</span> from the point <span class="math-container">$E$</span>. The point at which this ray intersects the image plane will be your vanishing point which as you can see is <span class="math-container">$(0,0,0)$</span>.</p>
<p>Now imagine why this works. Picture the point <span class="math-container">$B$</span> extending up, and at each instance start drawing segments <span class="math-container">$BE$</span>. You'll see that this line segment is moving towards the <span class="math-container">$Z$</span> axis.
So if you are projecting a point <span class="math-container">$B$</span> at infinity then the projecting line or segment <span class="math-container">$BE$</span> gonna become parallel to the line <span class="math-container">$AB$</span>. However, it can't go past the <span class="math-container">$Z$</span> axis, as this will start going in the opposite direction.</p>

CC BY-SA 4.0
2020-12-20T16:24:07.567Z
2020-12-20T16:24:07.567Z
gallickgunner
<p>I am unable to visualize what is principal vanishing point w.r.t to x axis ,y axis z axis  do someone can post some simple  diagram to understand what is it? Also I have question in my text book</p>
<p>' <img src="https://i.sstatic.net/Y7F04.jpg" alt="enter image description here" /><img src="https://i.sstatic.net/5CNai.jpg" alt="enter image description here" />       Now the question is how to calculate vanishing point and what is the line A' B ?Solution is also given which is (0,0,0) as vanishing point but I am unable to understand how do they get it , figure (k)shows it as (0,0,2) ,also what is d in the solution?<img src="https://i.sstatic.net/yjCta.jpg" alt="enter image description here" /></p>

<perspective>
What is principal vanishing point in perspective projection?
anuj goyal
# What is principal vanishing point in perspective projection?

(Asked by: username_0 on 2020-12-20)

I am unable to visualize what is principal vanishing point w.r.t to x axis ,y axis z axis do someone can post some simple diagram to understand what is it? Also I have question in my text book

' ![enter image description here](https://i.sstatic.net/Y7F04.jpg)![enter image description here](https://i.sstatic.net/5CNai.jpg) Now the question is how to calculate vanishing point and what is the line A' B ?Solution is also given which is (0,0,0) as vanishing point but I am unable to understand how do they get it , figure (k)shows it as (0,0,2) ,also what is d in the solution?![enter image description here](https://i.sstatic.net/yjCta.jpg)

**Tags:** perspective


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## 1 answers

### Answer by username_1 on 2020-12-20. Score: 1

Basically whenever you project a set of parallel lines in 3D space on a 2D image plane, you'll see that these lines don't remain parallel in 2D space and tend to meet at a certain point which is the so called vanishing point. Picture a long railway, both the rail lines meet at the horizon.

Now one confusion arises that the question doesnt give you a set of parallel lines, But it doesn't matter as long as a single line segment is provided. All you need to do is just picture the line segment extending to infinity. So for example, picture the point $B$ at infinity and imagine drawing a line $BE$. The point at which this line intersects the image plane will be your vanishing point.

There is a simple pattern that applies to every case like this. Just shoot a ray in the direction of the vector $\vec{AB}$ from the point $E$. The point at which this ray intersects the image plane will be your vanishing point which as you can see is $(0,0,0)$.

Now imagine why this works. Picture the point $B$ extending up, and at each instance start drawing segments $BE$. You'll see that this line segment is moving towards the $Z$ axis.
So if you are projecting a point $B$ at infinity then the projecting line or segment $BE$ gonna become parallel to the line $AB$. However, it can't go past the $Z$ axis, as this will start going in the opposite direction.


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