Questions tagged [projections]
Questions about the conversions of a 3D model to a 2D model.
135
questions
2
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1
answer
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3D homogenous coordinates versus 4D homogenous coordinates
We know that any 2D point $(x, y) $which represents as 3D homogeneous coordinates is of the form $(x, y, 1)$ which is the points of projective plane $P^2.$
If I use the same concepts for 3D points $(...
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3
votes
2
answers
277
views
$(x, y, 1)$ is 2D homogenous coordinates or 3D homogenous coordinates?
We know that $(x, y, 1)$ are the homogenous coordinates of a 2D point $(x, y)$. $(x, y, 1)$ has 2 degrees of freedom. That's why we should call it 2D homogenous coordinates. But many websites say it's ...
- 211
2
votes
1
answer
109
views
Finding a texture pixel (X,Y) on a Sphere
I'm using three.js combined with face recognition, I want to rotate a sphere that displays my input video according to the detected eye location,
the face recognition gives me a X,Y on the texture ...
- 23
0
votes
1
answer
340
views
Perspective transformation is perspective projection? [duplicate]
I know that (
Reference )in transformation source and destination has same coordinates dimensions. But in projection destination coordinate system has fewer dimensions than the source coordinate ...
user17337
1
vote
5
answers
2k
views
Existence of vanishing point
Consider the following example of perspective projection: I have one railway track with two parallel lines meeting at the point $X$ at infinity which is the theoretical approach. This X is called the ...
user17337
1
vote
0
answers
68
views
3D shearing w. r. t $x$-axis [closed]
Shearing in $X$ axis is achieved by using the following shearing equations-
$X_{new} = X_{old},
Y_{new} = Y_{old} + Sh_y × X_{old},
Z_{new} = Z_{old} + Sh_z × X_{old}.$
My question is during $Y_{new}...
user17337
3
votes
1
answer
848
views
Difference between 2D and 3D pipeline
2D transformation and viewing:
The camera projects the 2D world co-ordinate $(x_w, y_w)$ on its projection plane which co-ordinates $(x_v, y_v)$.
3D transformation and viewing:
The camera projects the ...
user17337
2
votes
2
answers
323
views
Parallel projection is special case of perspective projection
I synchronized with @David k's first and second answer regarding perspective and parallel projection. From the first question I understand that the image on the screen is typically described in ...
user17337
3
votes
1
answer
955
views
Difference between transformation and projection? [closed]
We know that world coordinates $(x_w, y_w)$ transform to viewport coordinates $(x_v, y_v)$ which are the physical device coordinates. And during projection, any point $(x, y, z)$ projects to $(x, y)$ ...
user17337
1
vote
1
answer
85
views
Why shearing coefficients multiplying by y? [closed]
We know that shear is transformation that distorts the shape of the object. Shear relative to X-axis that is $y=0$ line can be written as:
$x'=x+sh_x.y, y'=y$
My question is why $sh_x$ is multiplying ...
user17337
1
vote
2
answers
306
views
Difference between perspective and parallel projection [closed]
We know that in orthographic Projection Projectors (projection vectors) are perpendicular to the projection plane.
And in Perspective Projection Object positions are transformed to the view plane ...
user17337
1
vote
1
answer
1k
views
Why are vanishing point and centre of projection the same [closed]
We know that in perspective projection object positions are transformed to the view plane along lines that converge to the projection reference (center) point like this:
But many websites say that COP(...
user17390
2
votes
1
answer
220
views
$P^2$ vs projection plane
I want to explain what I understood of definition of the two things.
Projection plane:
The general processing steps for modeling and converting a world coordinate description of a scene to
device ...
user17337
1
vote
0
answers
74
views
What should be considered the origin of a ray used for object picking with perspective projection
I need to create a ray to pick objects in 3d environment using cursor.
I'm not going to go into detailed math for this question. There's tons of information on that. In short terms, for orthogonal ...
- 516
0
votes
1
answer
338
views
How does 3D graphic software adjust for distortion inherent in perspective projection?
As this question and its answers point out, projecting a sphere on a flat picture plane, with perspective projection, may result in a ellipse, not a circle, and my understanding is that the only way a ...
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