Questions tagged [projections]

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10
votes
2answers
484 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 (...
2
votes
0answers
202 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 ...
4
votes
2answers
102 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 ...
9
votes
1answer
11k 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 ...
1
vote
1answer
359 views

A question about derivation in oblique view frustum

Problem Description: Reference: Oblique View Frustum Depth Projection and Clipping "Mathematics for 3D Game Programming and Computer Graphics" 3rd edition, chapter 5.6. M is the original projection ...
14
votes
1answer
402 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, ...
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 ...
3
votes
1answer
544 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: ...
4
votes
2answers
186 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 ...
8
votes
1answer
443 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 ...
5
votes
1answer
108 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 ...
22
votes
5answers
9k 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 ...
8
votes
2answers
221 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 ...