Questions tagged [projections]

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

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28 votes
5 answers
12k 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 ...
9 votes
2 answers
4k 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://...
  • 193
3 votes
1 answer
383 views

Difference between transformation and projection? [closed]

We know that world coordinates $(x_w, y_w)$ transform to viewport coordinates $(x_v, y_v)$ which are the physical device coordinates. And during projection, any point $(x, y, z)$ projects to $(x, y)$ ...
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9 votes
2 answers
780 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 (...
3 votes
1 answer
1k 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. ...
2 votes
1 answer
14k 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), $f$(...
0 votes
1 answer
4k 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 ...
17 votes
1 answer
3k 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 ...
  • 2,700
11 votes
1 answer
24k 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 ...
  • 245
4 votes
1 answer
224 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 ...
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4 votes
1 answer
1k 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: ...
  • 377
3 votes
1 answer
492 views

Difference between 2D and 3D pipeline

2D transformation and viewing: The camera projects the 2D world co-ordinate $(x_w, y_w)$ on its projection plane which co-ordinates $(x_v, y_v)$. 3D transformation and viewing: The camera projects the ...
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2 votes
1 answer
184 views

$P^2$ vs projection plane

I want to explain what I understood of definition of the two things. Projection plane: The general processing steps for modeling and converting a world coordinate description of a scene to device ...
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1 vote
1 answer
407 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 ...
1 vote
1 answer
75 views

Why shearing coefficients multiplying by y? [closed]

We know that shear is transformation that distorts the shape of the object. Shear relative to X-axis that is $y=0$ line can be written as: $x'=x+sh_x.y, y'=y$ My question is why $sh_x$ is multiplying ...
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0 votes
1 answer
2k 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 ...