Questions tagged [projections]

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22
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 ...
15
votes
1answer
2k views

How can I generate procedural noise on a sphere?

I would like to generate procedural noise on the surface of a sphere (e.g. to procedurally generate planets or marble-textured balls). Of course, I could just take a standard noise algorithm and map ...
14
votes
1answer
394 views

Need a reputable source for the formula for the shape of Earth's horizon

What I'm asking for I stress that I am not asking for the formula---I know the formula, and how to derive it. Several different versions of it are reproduced near the end of the post. In fact, ...
10
votes
2answers
455 views

How to unproject quadrilateral into rectangle?

tl;dr: Math problem in projective geometry: How does one find some 4x4 camera matrix that gives a projection as illustrated below, such that points A,B,C,D are somewhere on the edges of the unit box (...
9
votes
1answer
10k 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
2answers
832 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://...
8
votes
1answer
1k views

Why are width and height divided by 2 in the perspective projection matrix?

I'm using OpenGL to learn computer graphics. I'm trying to understand projection matrices. The following are shown in the OpenGL 'Red Book': I don't understand why the width and height are divided ...
8
votes
2answers
220 views

What transformations should I apply to a model to produce this 3D effect?

I saw a video on YouTube where a person uses a transparant, knotted pyramid to display "holograms" using their smartphone. (I have not been able to reproduce this yet, so I can't tell for sure if it ...
8
votes
1answer
414 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 ...
6
votes
1answer
136 views

3D projection that increases objects' size as they become more distant

tl;dr Is there a name for a type of (non-physical) projection that causes objects to become larger the farther they are from a camera? With a fisheye projection, an object twice as far from the ...
5
votes
2answers
868 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 ...
5
votes
3answers
575 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 ...
5
votes
1answer
824 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 ...
5
votes
1answer
180 views

Solving a problem from *Foundations of Computer Graphics*:

From Gortler's Foundations of Computer Graphics (i.e., self-study): Let $\mathbf{\vec{e}}^t = \mathbf{\vec{w}}^t E$ and let $P$ be a camera matrix that is just some arbitrary $4$ by $4$ matrix with ...
5
votes
1answer
211 views

Creating Sparks using Code

I'm new to this area and have less knowledge. I want to create some graphics like sparks and lightning by writing some code, using my own physics. I don't want to use some engine, However I can use ...
5
votes
1answer
111 views

Am I calculating perspective projection correctly?

If I have a point in world space: (wx, wy, wz) and I have a centre of projection: (cx, cy, cz) and I wanted to project that point using perspective projection would my point on the screen be ...
5
votes
1answer
103 views

Materials for research on spherical projection

I am currently doing a research on projection on a sphere, specifically for NOAA's project Science on a Sphere. What I'm trying to do is to find out how exactly do you create a video material for such ...
5
votes
1answer
126 views

Where should I project a polygon corner when it is behind me?

I am creating a simple 3D engine as a learning project to get the hang on spherical trigonometry. I am using the following approach. 1. A model consists of a lot of triangular faces. 2. Each triangle ...
5
votes
1answer
141 views

Project quad onto ellipse in 3D

I have three points P0, P1, P2, which are located on an arbitrarily oriented ellipse in 3D space. I have a square texture map with a circle on it. I would like to render a textured quad (with the ...
4
votes
1answer
111 views

Projected points and screen coordinates

I'm trying to understand part of the contents of a slide, but I'm not really understanding. So, here's the interested part. I've a few questions. Are the projected points $q_1$ and $q_2$ the points ...
4
votes
2answers
733 views

My perspective projection is messed up?

So I've been messing with perspective projection matrices recently. I used numpy and GTK/Cairo to make a very small Python renderer. I'm very confused with the results I'm getting though. I took this ...
4
votes
1answer
2k views

Zoom in orthographic vs perspective projection

I have read through this article about perspective and orthographic projection matrices. I started playing with the perspective matrix and as expected if I either increase/decrease the field of view ...
4
votes
2answers
181 views

How to get the transform amount from a screen vector and a direction vector?

I am working on the move tool in a 3D modeling software. I need to know how much to move when the user drags an axis of the gizmo (for example along the x axis). I have the 2D vector describing how ...
4
votes
2answers
101 views

2D projection from some points

I am going through an undocumented function that takes in three points and a Z-value that projects three points on the plane defined by Z-value. I want to understand the mathematical theory behind it ...
4
votes
1answer
120 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 ...
3
votes
1answer
478 views

How to use GetViewProjMatrix().TransformVector(LineDirection) in UE4?

I try to project a 3D vector (a direction, not a position) in screen space, but it does not return satisfying results: ...
3
votes
1answer
120 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 ...
3
votes
2answers
92 views

Projective texturing from many images

Problem: I'm trying to dynamically texture a mesh of the real world generated by the Hololens over time using photos also captured from the Hololens, perhaps one photo per second. Each of the photos ...
3
votes
1answer
104 views

A way to save 360° panorama video

What is the best way to save video from faces of a cube? The render can produce 6 squares (90°x90°) of 1024x1024 resolution. Faces oriented along axies and only position is changed continuously. I ...
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 ...
3
votes
1answer
3k views

understanding glm::perspective vs glm::ortho

I'm new to computer graphics. I played around with OpenGL and now am trying out Vulkan. Basically what I want to do, in 2D is have an 800x800 window, and I want that to represent 800 meters by 800 ...
3
votes
1answer
2k views

Screen to World coordinates glm::unProject

I'm having some trouble trying to figure out how to go from a coordinate on the screen, to 3D world coordinates on a plane. My case is as seen on the picture further down. World origin is in the ...
3
votes
0answers
33 views

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,...
3
votes
1answer
90 views

How would I convert a picture of a slanted surface into a straight one? [duplicate]

Suppose I took a picture of a whiteboard at an angle. If I could detect where the corners of the whiteboard are, what algorithms and linear projections could I use to convert this slanted view into a "...
3
votes
0answers
145 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 ...
2
votes
1answer
151 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 ...
2
votes
1answer
113 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
1answer
133 views

Compute area (not surface area) and perimeter of a mesh

I'm currently researching how to compute geometric properties of architectural shapes based on their 3D meshes, and am stuck for some time on the area and perimeter calculations. First, the area: ...
2
votes
2answers
221 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 ...
2
votes
1answer
4k 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), $f$(...
2
votes
1answer
1k views

How to decompose projection matrix?

I want to decompose projection matrices into near, far, top, bottom, left and right values to create a bounding box for view frustum. I used the formula described in this site Decompose the OpenGL ...
2
votes
0answers
31 views

Make 3d objects from 3 projections in 3D Studio Max

In the early 3D Studio days before it got Max in its name it was possible to make a 3d object by defining its projections in xy, xz and yz plane. 3ds would then interpolate a 3d object from the ...
2
votes
0answers
181 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
2answers
173 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 ...
1
vote
2answers
53 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?
1
vote
1answer
72 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 ...
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 ...
1
vote
1answer
45 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 ...
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 ...
1
vote
0answers
34 views

Program to visualize geodesics and linear projection of an ellipsoid simultaneously

I am trying to solve a problem in computer graphics but to do it I need to be able to see a comparison of geodesic lines and straigth line projections on the ellipsoid. I have not been able to ...