Questions tagged [perspective]
The perspective tag has no usage guidance.
83
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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 ...
25
votes
1
answer
956
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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 ...
13
votes
1
answer
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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 ...
9
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2
answers
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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 ...
9
votes
1
answer
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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 ...
8
votes
1
answer
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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
1
answer
213
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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 ...
7
votes
0
answers
726
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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 ...
6
votes
1
answer
877
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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 ...
5
votes
3
answers
741
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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 ...
5
votes
2
answers
261
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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 ...
5
votes
1
answer
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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-...
5
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1
answer
994
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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
1
answer
802
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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 ...
4
votes
1
answer
2k
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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 ...
4
votes
1
answer
2k
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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. ...
4
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1
answer
821
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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 ...
4
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1
answer
2k
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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:
...
4
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1
answer
803
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How to derive Field of View (FOV) angles from a 2D projection
I'm looking for some guidance.
I'm not sure if this is possible, and I'm not sure where to start.
I need to measure the FOV angles of a first-person, 3D game using only gameplay screenshots.
I'm bound ...
4
votes
0
answers
166
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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 ...
4
votes
0
answers
67
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 ...
3
votes
2
answers
132
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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
2
answers
864
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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 ...
3
votes
1
answer
208
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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 ...
3
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1
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446
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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
3
answers
759
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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 ...
3
votes
1
answer
6k
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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 ...
3
votes
1
answer
79
views
Camera model for rendering the viewport as a window frame?
I want to render as if someone is looking at a landscape through a window, adjusting for the viewer's head position. The landscape is easy enough (just a distant plane), but I'm not sure how to ...
3
votes
1
answer
395
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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
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0
answers
94
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What vergence angle is commonly used for "infinitely far away" objects in stereoscopic displays?
I think that VR / AR experts will know the answer to this.
At what vergence angle are "infinitely far away" objects such as star field textures drawn in head-mounted VR / AR displays ?
I ...
3
votes
0
answers
215
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 ...
3
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0
answers
84
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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
...
2
votes
1
answer
130
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. ...
2
votes
1
answer
269
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 ...
2
votes
1
answer
453
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, ...
2
votes
1
answer
1k
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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 ...
2
votes
1
answer
47
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 ...
2
votes
2
answers
2k
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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 ...
2
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1
answer
518
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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 ...
2
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0
answers
85
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Can anyone tell me why my projection perspective matrix isn't working?
I'm a beginner in WebGL and graphics programming in general. I'm trying to render procedurally generated terrain. My first stab at this seemed to work and I get the following result.
I want to add ...
2
votes
0
answers
188
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physics/math of lighting gradient of a 3D object
Consider a monochrome ball. The colours of the pixels is a function of the point height, the light intensity, the light angle, and the surface material (reflection).
What is the simplest formula ...
2
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0
answers
78
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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0
answers
204
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
0
answers
263
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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 ...
2
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0
answers
259
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
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0
answers
66
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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 ...
1
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5
answers
2k
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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 ...
1
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2
answers
260
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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 ...
1
vote
1
answer
1k
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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(...
1
vote
1
answer
2k
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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
' ...