Questions tagged [projections]

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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 ...
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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 \...
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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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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 ...
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1 answer
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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.
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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 ...
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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 ...
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1 answer
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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 ...
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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 ...
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1 answer
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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:...
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-1 votes
1 answer
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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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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 ...
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1 answer
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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 ...
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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 $(...
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2 answers
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$(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 ...
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1 vote
1 answer
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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 ...
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1 answer
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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 ...
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5 answers
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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 ...
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1 vote
0 answers
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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}...
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3 votes
1 answer
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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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1 vote
1 answer
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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 ...
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3 votes
1 answer
191 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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1 vote
1 answer
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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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1 vote
2 answers
159 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 ...
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1 vote
1 answer
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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(...
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2 votes
1 answer
159 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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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 ...
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1 vote
0 answers
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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 ...
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0 votes
1 answer
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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 ...
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1 vote
1 answer
158 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 ...
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1 vote
2 answers
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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 ...
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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 ...
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1 vote
1 answer
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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 ...
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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 ...
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1 vote
1 answer
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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). ...
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4 votes
0 answers
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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 ...
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2 votes
0 answers
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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 ...
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1 vote
0 answers
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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 ...
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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 ...
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1 vote
1 answer
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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 ...
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2 votes
1 answer
161 views

How is orthographic projection used in computer graphics technically classified as a projection?

I'm wondering why the orthographic projection we use in computer graphics is called a projection, if all it does is just scale and translate a mesh? According to wiki orthographic projection is ...
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4 votes
1 answer
669 views

Perspective correct interpolation z-buffer

While I was deriving expressions for perspective-correct linear interpolation on triangles, I reached the conclusion that the interpolation may be kept linear only if view-space $Z$ is available. ...
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1 vote
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Why does my self-written rendering engine make further away objects look larger?

I am writing a very simple rendering engine. I have already made a few tests, but somehow the images it creates look wrong. Objects that are further away from the camera look larger than objects ...
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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. ...
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Consistent Video Depth Estimation from Monocular Lens to approximate LiDAR?

If the iPhone had LiDAR sensors, it would be possible to generate a 3D point cloud that you could theoretically use to furnish a 3D AR reconstruction of your surroundings. E.g. you could create an AR ...
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Does rotating object inside unit cube [-1,1] by homogenous matrix move it outside unit cube

I am just trying to rotate my pointcloud object which is inside the unit cube ([-1,1] in all x,y,z axis). What I did is use the basic rotation matrix from wiki and extend it to homogenuous 4x4 matrix (...
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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 ...
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3 answers
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perspective matrix derivation

Now there has already been an answer here in this stackexchange, but I don't understand certain aspects of it. The author has MORE DETAILED DESCRIPTION HERE(#1) but the problem is he doesn't describe ...
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how is zooming done in computer graphics

Since a projection plane and a center of projection is used for achieving perspective projection, the shape of the view frustum doesn't change changing the focal length(which is the distance from the ...
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2 votes
1 answer
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Y axis inversion in 3D rasterization

What is the correct way to invert the y axis during the 3D projection? I see a lot a people doing: ...
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