Computer Graphics Stack Exchange
Computer Graphics Stack Exchange

Questions tagged [projections]

Questions about the conversions of a 3D model to a 2D model.

126 questions
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5 answers

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 actively doing my own graphics programming and brought…
hippietrail
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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 it onto the sphere, but this has all the issues of…
Martin Ender
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15
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1 answer

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, someone else has not only derived it as well, but also…
linguisticturn
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1 answer

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 difference between orthographic and perspective…
phong
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9
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2 answers

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…
Jessy
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9
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1 answer

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 by 2?
mikeglaz
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9
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2 answers

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 conceptually that the near plane is essentially the…
Vilhelm Gray
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9
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2 answers

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 (e.g. OpenGL normalized device coordinates), and…
ninjagecko
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9
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1 answer

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 the display. in the example they should be roughly…
succcubbus
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9
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2 answers

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 works). I was wondering, given a model, which…
S.L. Barth
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7
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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 i have a zoom out/in effect. Similarly, if I move…
BRabbit27
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6
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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 camera is less than half the size on screen. (I think;…
Phrogz
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6
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1 answer

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 a device, because it's not as simple as making a…
Michal Kučera
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5
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1 answer

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 end point and join the dots is that equivalent to…
Owen
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5
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3 answers

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 why does it generate a frustrum in which the back…
George
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