Questions tagged [perspective]
The perspective tag has no usage guidance.
64
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Difference between perspective and parallel projection
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 ...
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1answer
66 views
Why are vanishing point and centre of projection the same
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(...
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1answer
50 views
How do I perform a perspective transform on a straight line?
I'm trying to make a software renderer, but I want to avoid creating extra triangles with clipping. For this I want to transform lines which compose triangles, instead of individual points. However I'...
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1answer
55 views
Deriving formula for perspective correct interpolation
I am trying to derive the formula for perspective correct texture interpolation on my own while implementing my own software rasterizer (projecting an arbitrarily rotated triangle in camera space on ...
4
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2answers
129 views
Rendering Hypercentric Perspective
I came across some Non-Euclidean Games which involve Hyperbolic Spaces, Spherical Spaces, Portals, etc. And, I noticed that they give quite deep feel of what Non-Euclidean Spaces feel like. So, I was ...
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0answers
43 views
Mapping an image from one camera pose to another given a planar scene
I'm trying to map an image of a 3D object to another one from a different camera position. My assumption is that the pose change between two cameras is so small and the object is far enough from the ...
3
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1answer
63 views
Why perspective division ( div by w) when applying the inverse to a perspective transformation?
For example, when you want to compute the world space position of a fragment in the fragment shader, you can construct the fragment's NDC coordinates, then multiply by the inverse of whatever ...
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1answer
76 views
Simulate projection matrix deformation in two camera setup
For educational purposes I'm trying to simulate what a scene would look like with a perspective matrix deformation (before everything is brought to NDC) but I'm unsure how to do this.
I'd like to do ...
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1answer
91 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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0answers
25 views
Writing perspective transformation matrix for x=0?
I see the discussion at this link, but I still get confused and I think my question is rather a simple one.
If I assume the center of projection as p = (1,0,0), how can I write the 4x4 projection ...
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1answer
378 views
What is principal vanishing point in perspective projection?
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
' ...
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1answer
30 views
Does angular diameter to FoV ratio equal object's image to total image ratio?
If we have an object at certain distance D in front of a camera. The object has a horizontal diameter d, giving us an angular diameter theta (2*arctan(d/2D)) of 50 degrees (converted from radians). ...
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0answers
85 views
Project grid on 2d plane based on camera perspective
Unsure if this is the right network to post this, but maybe someone can help...
I'm working on a personal project where, with the help of AI, I want to automatically estimate the perspective of a ...
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1answer
79 views
Perspective projection near plane not in world coordinates
I have a camera I have placed zunits away from a billboarded rect. My goal is to discard all other geometry that is closer to the camera/in front of this rect.
With ...
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2answers
87 views
Shear(?) matrix projection along Z (depth) axis
I'm creating a primarily 2d game (platformer perspective) with 2d background parallax layers. The parallax effect falls out of the fact that I'm positioning a bunch of layers in 3d and using a ...
3
votes
1answer
113 views
Interpolate vertex attributes with $z$ AFTER homogeneous divide
Usually, if we want to interpolate some vertex attributes, say $A_1$, $A_2$ and $A_3$, we have to first divide them by their corresponding $z$ in view space, then we interpolate them using barycentric ...
4
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1answer
409 views
Perspective correct interpolation z-buffer
While I was deriving expressions for perspective-correct linear interpolation on triangles, I reached the conclusion that the interpolation may be kept linear only if view-space $Z$ is available. ...
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1answer
227 views
Which perspective projection matrix to use
I've seen two different perspective projection matrices being used but I want to know which one of them is the best. I think that they both output the same but I'm not sure. So if anyone can help me ...
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1answer
82 views
Is there a general rule with regard to using the inverse of the "camera" to world when using a homogeneous transform matrix?
Not sure if this is just specific to this article but it says:
We learned how to convert points from world to any local coordinate
system. If we know the local-to-world matrix, we can multiply the
...
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0answers
34 views
How to get "Equal" (saturation, brightness) Red and Green Colours in a Web-based Application?
I am looking for a red and a green hue that are equally discernable against a gray background on any PC monitor, using HTML/CSS-based application. There are many possible solutions to balance these ...
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1answer
76 views
Apply Projective Transformation 2D Rectangle
I want to write code from scratch about Projective Transformation in order to apply this transformation to 2d rectangular. I searched about this transformation, but I could not figure out completely. ...
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1answer
66 views
Keep constant number of visible circles in 3D animation
I have created a 3D animation with a perspective projection of white circles moving randomly in a fake 3D space projected on a 2D computer screen (GIF 1).
Since I need to keep the same number of ...
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3answers
754 views
perspective matrix derivation
Now there has already been an answer here in this stackexchange, but I don't understand certain aspects of it. The author has MORE DETAILED DESCRIPTION HERE(#1) but the problem is he doesn't describe ...
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0answers
233 views
how is zooming done in computer graphics
Since a projection plane and a center of projection is used for achieving perspective projection, the shape of the view frustum doesn't change changing the focal length(which is the distance from the ...
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0answers
45 views
Project a Square as rectangle in projection plane using perspective projection
Consider a square S with vertices (1,1,0), (1,-1,0), (-1,-1,0) and (-1,1,0) and a plane P defined by $z=1$. Let the perspective projection of S on P is denoted by S'.
What coordinates of the Center ...
2
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1answer
237 views
Rasterizing spheres?
I want to start developing a hybrid renderer: it first applies a rasterizer, then stores for each pixel the surface pointer, normal vector, and distance to the camera.
Then it raytraces reflections, ...
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0answers
70 views
Issue with perspective projection
I have the following problem. Perspective projection is often referred to when talking about camera models. I don’t think I understand it very well though this concept is taught when I was at junior ...
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1answer
94 views
Change of speed but no change of size after OpenGL Perspective Projection
I am new to OpenGL and I am trying to code un optic flow with dots appearing from the background and moving towards the viewer. As a consequence of a perspective projection, the dots are faster and ...
0
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1answer
145 views
WebGL Can't render anything, wrong projection?
I'm trying to understand and learn WebGL and computer graphics from the bottom up, that is why I started to work on my own little library for that. I've spent a couple of days looking for a right ...
5
votes
1answer
390 views
Do straight lines always remain straight when projected with a perspective camera?
If I have a straight line in 3D space and I use a camera matrix to do a perspective projection into a 2D plane/screen will the resulting line always be straight too? If I project the start point and ...
2
votes
1answer
121 views
Computing perspective directly
Assume the screen is axis aligned with origin at 0 and there is absolutely no view transformation.
in other words we will simply try to project the model onto the screen plane following perspective. ...
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0answers
144 views
How to calculate solid angle subtended by a pixel?
How is the solid angle subtended by a pixel calculated?
both in perspective and fish eye lens.
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0answers
217 views
Using GPU instead of CPU in Scala
I wrote a program that displays points expressed in 3D in a 2D canvas, using perspective projection. The aim is to display a cube. Each face of the cube is drawn by linearly interpolating the points ...
4
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1answer
1k views
Inverse value in a Perspective Matrix
I am a new leaner of computer graphics. I'm trying to understand a code I found online and I got stuck in the following formula:
...
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1answer
2k views
Why does this gl_FragDepth calculation work?
I am raytracing in GLSL. My gl_FragDepth calculation wasn't right, so I did some hunting and found this solution (P is the world-...
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1answer
70 views
Determining slopes of lines in perspective projection
Suppose I have parallel lines running along the ground (into the horizon). If I have a camera and I know its tilt angle, is there a way to calculate the slopes of the lines as projected to the 2D ...
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2answers
2k views
Changing the projection reference point in Open GL
By default, the eye an the projection reference point PRP are in (0,0,0). I can change the eye position with gluLookAt(), but how can I change the PRP (i.e., the convergence position for a set of ...
3
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1answer
329 views
Determining Vanishing Points of edges of Triangle using given Point
Due to perspective foreshortening, the projections of parallel lines (1D geometric objects) meet in their vanishing point (a 0D geometric object). Higher dimensional geometric objects also has higher ...
2
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1answer
361 views
How to calculate camera distance so that after projective transformation a quad is filling the whole screen
First of all, I'm using OpenGL and GLM.
Now, I have a square perpendicular to the z-axis and centered around it. Let's say that it has Z-value (offset along the Z-axis) X. Now, I want to set up a ...
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0answers
42 views
3D reconstruction using 2D matched points
I have 2 images, called left and right images. I have some matched points $[c_l,r_l]$ and $[c_r,r_r]$ in both of them (these points are in pixel coordinates).
For a 3D point in the real world, they ...
2
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1answer
844 views
Why is the line from the camera to vanishing point parallel to the other parallel lines?
When trying to find the vanishing point of an image, why is it that the vector from the center of the camera to the vanishing point is parallel to the parallel lines of the image?
What's the ...
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2answers
98 views
Supporting multiple camera types in a deferred renderer without specializing the shaders or in the shaders
Perspective Camera
A (row-major) perspective transformation matrix has the following format:
$$\begin{align} \mathrm{T}
&= \begin{bmatrix}
\mathrm{T}_{00} &0 &0 &0 \\
0 &\...
3
votes
1answer
324 views
Creating a vanishing point perspective shader
I have done my due hour of research before asking this question, it's a simple question, but I have found no hint at an answer online.
I want the ability to extend an object infinitely in one ...
3
votes
3answers
677 views
Point of view and rotation
Two questions which cross over maths/3D imaging/computer science. I'm trying to describe a point of view of an item in a 3d space and subsequently its rotation in a paper I'm writing. Versions I've ...
5
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1answer
791 views
Is placing z value of vertex in w enough to achieve perspective projection in OpenGL?
I have been learning about projection matrix in OpenGL and I am finding it really hard to understand. All I know is that there are other configurations in the projection matrix besides placing z in w ...
5
votes
3answers
651 views
Why is the back of a perspective frustrum larger than the front?
I'm following this tutorial on the perspective projection.
Question: If the point of a perspective projection is to create the perspective effect (where objects faraway appear to be smaller):
then ...
7
votes
2answers
2k views
How am I able to perform perspective projection without a near plane?
I'm learning about 3D computer graphics, but I'm having a hard time understanding why the near plane of a viewing frustum can not be placed at z position $0$ (right at the camera).
I can understand ...
4
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1answer
2k views
Render with camera perspective off-center
So ordinarily we have this
But I'm after this!
Is it possible to do this? Ideally by changing the projection matrix?
The reasoning is kinda interesting - I am developing for mobile VR, and I have ...
2
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1answer
38 views
Getting from the default view volume to an image on the screen
I don't completely understand the last part of the MVP matrix (projection).
In orthographic projection we simply scale the view volume into the default view volume (+-1 on all axis).
In perspective ...
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0answers
195 views
Calculate Camera parameters and HandEyeCalibration
I'm trying to calculate camera paramters and a hand eye calibration (Transformation from camera to eye (display) coordinates) for rendering on a see-through HMD.
I have already calculated a ...
