Questions tagged [projections]

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computing sheared perspective projection matrix

is it possible to calculate a "projection matrix" which is sheared as well? the usual perspective projection matrix forms a pyramid where the near clipping plane is rectangular. I have 4 ...
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is focal length equal to the distance from the optical center to the near clipping plane- openGL

The part confusing about opengl during studying the projection was that the focal length, top, left, bottom, right, wasn't declared, and it magically did it with FOV and image aspect ration. I ...
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Moving a vertex through the cursor

There is a way to move a selected point in a mesh with a cursor(assuming a camera that doesn;t change between frames). The way I remember the algorithm (but seems to be wrong) is: Unproject the ...
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1answer
27 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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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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What is the best way to calculate the projected size of a point

In a particle simulation, I am rendering particles as "spheres" using GL_POINTS instead of a mesh for efficiency. With glEnable(GL_PROGRAM_POINT_SIZE) I ...
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77 views

Model View Projection Matrix Multiplcation Order

I'm working on a simple software renderer and have a working implementation so far. I'm curious as to why it's actually working since I would expect the multiplication ordering for my world, view and ...
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20 views

Identifying 2d coordinates of texture from 3d textured sphere

this is best explained by visualization. Below webpage is a spherical textured panorama which gives the effect of being inside of the room. I want to be able to localize (eg) windows by mouse clicks ...
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Can surface normal be used for obtaining points on a plane?

Excuse my wording. I will use the picture below to explain what I mean. I want to use the surface normals for each arrow shown like below to draw lines parallel to each plane like the image shown ...
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1answer
119 views

How are textures projected onto 3d models in texture painting applications

In most modeling software you can texture paint onto 3d models using so called stencil textures. They basically project a texture from the viewport view onto the model as seen for instance in the ...
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1answer
87 views

How is orthographic projection used in computer graphics technically classified as a projection?

I'm wondering why the orthographic projection we use in computer graphics is called a projection, if all it does is just scale and translate a mesh? According to wiki orthographic projection is ...
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1answer
294 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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79 views

Why does my self-written rendering engine make further away objects look larger?

I am writing a very simple rendering engine. I have already made a few tests, but somehow the images it creates look wrong. Objects that are further away from the camera look larger than objects ...
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1answer
510 views

How to unproject cursor with orthographic projection

With perspective projection we can unproject screen space coordinates of the cursor to the near and far plane of the frustum and calculate the direction of the ray through the cursor. ...
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Consistent Video Depth Estimation from Monocular Lens to approximate LiDAR?

If the iPhone had LiDAR sensors, it would be possible to generate a 3D point cloud that you could theoretically use to furnish a 3D AR reconstruction of your surroundings. E.g. you could create an AR ...
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Does rotating object inside unit cube [-1,1] by homogenous matrix move it outside unit cube

I am just trying to rotate my pointcloud object which is inside the unit cube ([-1,1] in all x,y,z axis). What I did is use the basic rotation matrix from wiki and extend it to homogenuous 4x4 matrix (...
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1answer
62 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
648 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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182 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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1answer
74 views

Y axis inversion in 3D rasterization

What is the correct way to invert the y axis during the 3D projection? I see a lot a people doing: ...
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281 views

Intrinsic Matrix vs Perspective projection matrix

I was going through the camera matrix explained in the wikipedia article and understand how the matrix K \begin{bmatrix}f_x&s&x_0\\0&f_y&y_0\\0&0&1\end{bmatrix} is built. The ...
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1answer
86 views

Understanding the near clipping plane

I don't understand something about the near clipping plane. It's there to avoid the division by $0$ but when we compute the pixel coordinates, we just need to multiply by the clipping plane to clip ...
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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 ...
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59 views

How to Pan Zoom a spherical camera?

I asked this in regular SO but I think people are not understanding the question so i will try here: So, for anyone familiar with Google Maps, when you zoom, it does it around the cursor. That is to ...
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1answer
90 views

Why is the z direction away from the screen/viewer?

I wonder what is the reason that when z increase, the objects appear far away and when z is negative, the object is behind the camera?
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42 views

How combine multiple projections into a single pass?

We have a projector type display used in an automotive application, where a projector displays an application on the windshield. Because the projector would normally warp a flat image, we have to ...
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2answers
56 views

3d Math Primer book equation derivation - Projecting One vector onto another

I'm reading the book 3d Math Primer for Graphics and Game Development 1st edition by Fletcher Dunn and Ian Parberry. On page 61 there's this: How does it derive $ v_{||} $ there? It doesn't follow ...
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Projecting a point on a Freefrom surface

My first issue is getting a set of planes and a set of points as input, an find the projection of the those points on the nearest plane. That was pretty easy, where i just calculate the normal of the ...
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3answers
147 views

What exactly is the orthographic projection used by Matlab

I would like to imitate the orthographic projection that Matlab uses by default: Matlab View Projections and Matlab camproj It seems similar to the "Trimetric" projection described here: ...
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What quad will fill the screen, which can be inverse-projection-view transformed to map to the near frustum plane?

I've been experimenting with raytracing using GLSL. I had success rendering a cube which encloses the object. Now I want to do a full-screen raytrace, and I want to construct a quad which covers the ...
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1answer
237 views

Can pixels on the image plane be mapped to world space coordinates?

I'm trying to learn the fundamentals of 3d computer graphics by writing a toy framework in WebGL. I'm currently working on mouse based camera controls. There are plenty of good resources in the ACM ...
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271 views

Inverse texture mapping

I have a textured 3D object and looking for ways to transform back the texture. Effectively, I think this is an inverse texture mapping task. Do you know of anything close to this? Some papers or ...
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1answer
137 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 ...
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1answer
352 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 ...
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1answer
180 views

How to translate the center of an equirectangular projection?

I'm trying to perfectly align two or more equirectangular photos of the same place taken from slightly different positions. Using an example provided by openMVG I managed to get the relative position ...
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1answer
393 views

What to reproject when doing temporal filtering in stochastic screen space reflection?

I am in the middle of implementing stochastic screen space reflection based on frostbite presentation here. On page number 39, it is stated that we need to reproject the ray intersection location ...
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1answer
1k views

Need help with change of basis (world to camera frame)

I'm reading up on coordinate systems and geometric transformations but the change of basis topic still confuses me. I found this exercise but, honestly, I wouldn't know how to begin: Given a world ...
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2answers
1k views

3ds max: Z-fighting when working with Large Objects

I had a z-fighting/z-clipping issue with a scene containing some very large objects yesterday in 3ds max. It can be seen in the image below: For some reason downscaling the scene significantly (a ...
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1answer
149 views

Overlaying a grid on to a height map

What is the method used in overlaying a grid (agonostic of the grid type) on to a height map? It seems it's some sort of projection, but what are the technical details in how to implement it? An ...
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1answer
463 views

Project vertex onto plane

What I have: a plane given by its normal$\ n $ and a point on the plane$\ p $. a 3D-point$\ v $. a direction$\ d$. What I need: the projection of$\ v$ along$\ d$ onto the plane. How can I ...
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1k views

finding the projection matrix for one point perspective

I found the derivation for two point and three point perspective here on this site, even though it says review on one point perspective, it doesn't give a link to previous pages, but I'd like to ...
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1answer
2k views

perspective projection transformation matrix

In one text, the derivation for perspective projection goes like this: If $x',y',z'$ represent any point along the projection line,and $x_{prp},y_{prp},z_{prp}$ are the projection ...
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1answer
136 views

How to compute A and B in projection matrix

I'm trying to compute a projection matrix to transform from view space to NDC with a near clip plane at -1 and far plane at +1. The general form of this matrix (disregarding aspect ratio and focal ...
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1answer
120 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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3k views

Why do GPUs divide clip space Z by W, for position?

Background: I found that it is very easy to use a linear depth buffer, using only a slight modification to the canonical vertex transformation. The simplest method is found at the bottom of https://...
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Possible approach for product mockup creation including distortion created through perspective

I am not an expert in 3D nor computer graphics. Please forgive me if I use wrong wording. High level problem description: For an online shop, I would like to create mockup images of apparel (t-shirts,...
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2answers
78 views

If a 3D scene is rendered onto a hemispherical display, will there still be warping near the edges?

When a 3D scene is rendered to a 2D display, the image is distorted near the edges of the display. If a 3D scene is rendered onto a hemispherical display, will there still be warping?
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2answers
541 views

How to generate the stereographic projection of a 3D model

Given a 3D model, is there a way to stereographically project it to a 2D image? In particular, I would only need a little more than half the model (the lower half) to be mapped to the plane (mapping ...
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1answer
11k views

How to derive a perspective projection matrix from its components?

This has been haunting me for several days now. I want to find the component that makes up of this 4x4 perspective projection matrix, with $l$(left), $r$(right), $b$(bottom), $t$(top), $n$(near), $f$(...
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69 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 ...