Questions tagged [projections]

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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 ...
2 votes
1 answer
453 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 ...
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0 answers
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Finding Camera projection matrix from known input and output

Lets say I have a rectangle with known coordinates in 3D scene, and I'm projecting it using pin point camera to the plane (screen). You can imagine it deforms on the screen per camera transformation ...
0 votes
2 answers
63 views

What projection matrix and world transformation do I need to have an isometric projection?

I'm doing my own engine in college to display a wireframe on screen with an isometric projection but I literally can't find any literature about maths behind doing it by hand just for game engines ...
0 votes
0 answers
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Object picking for a non-scaled graphic in a scaled scene

I have a visual 2d representation of a coordinate system, and a bezier graph with control points represented using a circle graphic. I need to be able to scale the coordinate system including the ...
1 vote
1 answer
124 views

Parallel projection is special case of perspective projection

I synchronized with @David k's first and second answer regarding perspective and parallel projection. From the first question I understand that the image on the screen is typically described in ...
0 votes
1 answer
77 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 ...
0 votes
1 answer
96 views

mapping of a point from a sphere into UV plane

I am reading the book An introduction to raytracing by Eric Haines and it mentions an algorithm to map a point from a sphere into a UV plane, it calls it Inverse Spherical Mapping (page 49). I googled ...
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1 answer
62 views

Understanding orthographic projection matrix clip coordinates

I'm confused about what orthographic projection matrix outputs. Based on what I know so far, orthographic projection matrix converts vertexes in eye coordinates into clip coordinates. But what exactly ...
0 votes
0 answers
29 views

What do the symbols in a fisheye projection stand for?

The wikipedia page on fisheye lenses provides multiple formulations: Stereographic Equidistant Equisolid angle Orthographic $f=\frac{r}{k \tan(\theta / k)}$ $f = \frac{r}{\theta}$ $f = \frac{r}{2 \...
1 vote
1 answer
69 views

Is it possible to make a projection matrix to not project in the center?

I have the following projection matrix: and I need to make a hole in the center of my matrix, something like that: (I don't want to project a custom W and H) Is that possible ? Thanks.
0 votes
1 answer
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Where exactly is the image plane / plane of projection

Perspective projection matrices we use map 3D coords onto some imaginary image plane in front of the cameras pinhole position by casting a ray directly from the eye position to that 3d coordinate and ...
2 votes
1 answer
115 views

How to derive Field of View (FOV) angles from a 2D projection

I'm looking for some guidance. I'm not sure if this is possible, and I'm not sure where to start. I need to measure the FOV angles of a first-person, 3D game using only gameplay screenshots. I'm bound ...
2 votes
3 answers
307 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: ...
1 vote
1 answer
63 views

What fields should a camera class have?

For a good and scalable project structure, what fields would you add to a camera class, apart from its position and orientation? Should I add the near and far planes? Or should that be global, what ...
1 vote
1 answer
190 views

3D homogenous coordinates versus 4D homogenous coordinates

We know that any 2D point $(x, y) $which represents as 3D homogeneous coordinates is of the form $(x, y, 1)$ which is the points of projective plane $P^2.$ If I use the same concepts for 3D points $(...
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1 answer
211 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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1 answer
67 views

Unity - custom shadow from sun

due to some features in materials I need to create my own directional shadow map. Everything seems to work ok, until the moment where I compare depths. First I add camera component to directional ...
0 votes
1 answer
63 views

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 ...
2 votes
1 answer
73 views

When fitting 3d cuboids into a box, how to find the order of drawing (in a 2D projection) so that the cuboids don't appear to overlap?

I am working on a 3D packing algorithm (MIT-licensed). The box and the cuboids it contains are displayed as a 2D projection. The order of drawing the cuboids (now represented as polygons) is important:...
-1 votes
1 answer
97 views

Why we calculate z buffer value from plane equation $AX+BY+CZ+D=0$?

Suppose in perspective projection $(x, y, z)$ coordinate projects to point $(x_p, y_p, z_{vp})$ in projection plane $AX+BY+CZ+D=0$ where projection plane kept at $z_{vp}$ position. And the plane $AX+...
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0 answers
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Projection of line which lies in an auxiliary inclined plane

A line PQ is 75 mm long and lies in an auxiliary inclined plane (A.I.P.) which makes an angle of 45° with the H.P. The front view of the line measures 55 mm and the end P is in the V.P. and 20 mm ...
0 votes
1 answer
79 views

OpenGL old-style diffuse shading producing unexpected effects

Question: What is going wrong with the shape of the contours of constant illumination in the below picture ? Detail: Although Lambertian shading might be ill-regarded because it exposes the hard edges ...
1 vote
1 answer
71 views

Finding a texture pixel (X,Y) on a Sphere

I'm using three.js combined with face recognition, I want to rotate a sphere that displays my input video according to the detected eye location, the face recognition gives me a X,Y on the texture ...
2 votes
2 answers
172 views

$(x, y, 1)$ is 2D homogenous coordinates or 3D homogenous coordinates?

We know that $(x, y, 1)$ are the homogenous coordinates of a 2D point $(x, y)$. $(x, y, 1)$ has 2 degrees of freedom. That's why we should call it 2D homogenous coordinates. But many websites say it's ...
0 votes
1 answer
188 views

Perspective transformation is perspective projection? [duplicate]

I know that ( Reference )in transformation source and destination has same coordinates dimensions. But in projection destination coordinate system has fewer dimensions than the source coordinate ...
1 vote
5 answers
1k views

Existence of vanishing point

Consider the following example of perspective projection: I have one railway track with two parallel lines meeting at the point $X$ at infinity which is the theoretical approach. This X is called the ...
1 vote
0 answers
55 views

3D shearing w. r. t $x$-axis [closed]

Shearing in $X$ axis is achieved by using the following shearing equations- $X_{new} = X_{old}, Y_{new} = Y_{old} + Sh_y × X_{old}, Z_{new} = Z_{old} + Sh_z × X_{old}.$ My question is during $Y_{new}...
3 votes
1 answer
337 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 ...
3 votes
1 answer
223 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 $(x, y)$ ...
1 vote
2 answers
167 views

Difference between perspective and parallel projection [closed]

We know that in orthographic Projection Projectors (projection vectors) are perpendicular to the projection plane. And in Perspective Projection Object positions are transformed to the view plane ...
1 vote
1 answer
72 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 ...
1 vote
1 answer
399 views

Why are vanishing point and centre of projection the same [closed]

We know that in perspective projection object positions are transformed to the view plane along lines that converge to the projection reference (center) point like this: But many websites say that COP(...
2 votes
1 answer
162 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 ...
0 votes
0 answers
114 views

Mapping an image from one camera pose to another given a planar scene

I'm trying to map an image of a 3D object to another one from a different camera position. My assumption is that the pose change between two cameras is so small and the object is far enough from the ...
1 vote
1 answer
250 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
0 answers
46 views

What should be considered the origin of a ray used for object picking with perspective projection

I need to create a ray to pick objects in 3d environment using cursor. I'm not going to go into detailed math for this question. There's tons of information on that. In short terms, for orthogonal ...
0 votes
1 answer
165 views

How does 3D graphic software adjust for distortion inherent in perspective projection?

As this question and its answers point out, projecting a sphere on a flat picture plane, with perspective projection, may result in a ellipse, not a circle, and my understanding is that the only way a ...
1 vote
1 answer
166 views

how to change the near clipping plane of a perspective projection matrix for OpenGL

I am trying to only change the near clipping plane of a given perspective projection matrix for OpenGL. My problem is, that the near clipping plane is way too close, and the far clipping plane is very ...
1 vote
2 answers
157 views

What is this graphical effect called?

I was watching this trailer: https://www.youtube.com/watch?v=pWh5388AEHw and at 1:22, the player used a magic trick that created a sphere that warped the projection of the scene. Does anyone know ...
0 votes
0 answers
82 views

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 ...
1 vote
1 answer
621 views

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 ...
1 vote
0 answers
138 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 ...
1 vote
1 answer
33 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). ...
4 votes
0 answers
113 views

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 ...
2 votes
0 answers
81 views

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 ...
3 votes
1 answer
642 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 ...
0 votes
0 answers
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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 ...
0 votes
2 answers
272 views

The distance from the cube sides to the parallel projection plane

I have asked this question on ru.stackoverflow.com and have no valid answers. Specification: Coordinate system Cube spins around its center on all three axes. Turn angle is not known previously. ...
1 vote
1 answer
307 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 ...