Questions tagged [perspective]
The perspective tag has no usage guidance.
4
votes
1answer
112 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
110 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. ...
1
vote
0answers
84 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.
2
votes
0answers
126 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 ...
5
votes
1answer
395 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:
...
2
votes
1answer
541 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-...
1
vote
1answer
56 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 ...
2
votes
2answers
578 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 ...
4
votes
1answer
165 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 ...
3
votes
1answer
122 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 ...
1
vote
0answers
37 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 ...
3
votes
1answer
262 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 ...
4
votes
2answers
76 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 &\...
4
votes
1answer
130 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 ...
4
votes
3answers
615 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
votes
1answer
368 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 ...
6
votes
3answers
573 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 ...
6
votes
2answers
761 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 ...
6
votes
1answer
731 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 ...
3
votes
1answer
31 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 ...
4
votes
0answers
125 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 ...
1
vote
0answers
122 views
image warping, given the rotations/translations
in OpenCV there is functions to warp any 2D image using a homography matrix (3x3), e.g. cv2.warpPerspective. These matrices are generally constructed using point ...
5
votes
0answers
52 views
Is it possible to create a forced focus with a dual layer of images in order to Avoid eye strain with Virtual and Augmented Reality?
Would eye tracking allow for the alignment of a dual layered image (a google glass like device and a screen or projection) to provide a way to force the focus of the eyes into to a real life ...
8
votes
1answer
132 views
What is this triangle sub-division scheme called?
I have thought of a triangle sub-division for the purpose of smooth triangulation (no popping) over time on the fly. I think it is very likely the scheme is already invented and has a name but I can´t ...
8
votes
1answer
2k views
Perspective Correct Texture Mapping
So I'm trying to correctly map my textures in my software renderer using the u, v coordinates but I can't seem to get it working. I got affine texture mapping working. This is what I can produce using ...
7
votes
1answer
384 views
Perspective correct interpolation of normal values
I'm currently writing a software rasterizer and I'm at the point where I can draw arbitrary triangles with vertex colors and perspective correct texture mapping. I do point and directional lighting by ...
2
votes
0answers
168 views
How to project a view frustum in an orthographic cuboid?
I know that OpenGL uses a projection matrix to project the view frustum directly into the canoical volume [-1, 1]^3. But how would I project the frustum into an orthographic cuboid, which would then ...
2
votes
0answers
56 views
Perspective Translation Of Quadrilateral
I have mapped four rectangular point(R1->R4) to four quadrilateral points(Q1->Q4) to generate a perspective view.
Now I have to translate quadrilateral in x and y direction while maintaing perspective ...
6
votes
0answers
292 views
Perspective-Correct Texture Mapping
I am working on a small rendering engine for a personal project and I am having issues with the texture mapping part of it.
It seems to work for some cases, but not for others. For example, when one ...
3
votes
1answer
2k views
Calculate vanishing point
In perspective projection, group of parallel lines have the same vanishing point. I am interesting about the reverse calculation: Getting the group of parallel lines equations that their vanishing ...
2
votes
0answers
73 views
Bilinear Transformation not working
I implemented this algorithm to fit given image to specified quadrilateral but the output is blank.
I implemented it in C# as follows
...
9
votes
1answer
9k views
What's the difference between orthographic and perspective projection?
I have been studying computer graphics, from the book Fundamentals of Computer Graphic (but the third edition), and I lastly read about projections. Though, I didn't exactly understand what's the ...
8
votes
1answer
391 views
Calculate aspect ratio from 2D shape in 3D space
Given the 4 coordinates of a 2D shape in a 3D space I want to calculate its aspect ratio.
The 3D space is created with 2 vanishing points.
The 4 coordinates - marked blue - are the 2D coordinates on ...
24
votes
1answer
732 views
Is my perspective math correct?
I've got a homework in which I have to calculate and plot some points using a pespective transformation, but I'm not sure my results are correct, since the 3d plot using Camera coordinates looks very ...
21
votes
5answers
8k views
Does a sphere projected into 2D space always result in an ellipse?
My intuition has always been that when any sphere is projected into 2D space that the result will always mathematically be an ellipse (or a circle in degenerate cases).
In the past when I was ...
