# Questions tagged [projections]

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

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### Object appears in unintended parts of the screen when using manual WorldToScreenPoint

Hy guys I'm new to 3d graphics and i lack some Linear algebra knowledge. I tried to recreate Unity's worldToScreenPoint method with kotlin on android. I copied some code from their forum and wrote ...
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### 3D engine projection distortions

I'm trying to write my own 3D engine using Python and Pygame. I have successfully implemented rotation and projection matrices to display 3D models. However I am so far unable to implement translation ...
1 vote
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### Is it possible to render to a octahedron texture directly?

I am considering using octahedron textures for environment mapping, opposed to sphere or cube mapping due to their low memory footprint and the quality they result in. Is there a possibility to render ...
89 views

### Normalized Device Coordinates: Why normalize the Z value?

I understand that the normalized device coordinates are the result of the perspective divide of clip space coordinates and allow for an easy mapping of the xy coordinates to a physical screen. What I ...
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### What are applications of 3D geometry to 2D geometry projection and occlusion handling?

As a layperson in the field of computer graphics, I rarely see practical applications of algorithms that take 3D geometry as the input (along with some camera and lighting parameters) and output the ...
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### My projection matrix for OpenGL fails on non-symmetric boundaries

Assuming my viewing volume has x coordinates varies from l to r, and y varies from top to bottom, and finally z-axis varies n to f, I derived the following projection matrix: ...
233 views

### How do I evenly subdivide the projection of a circle in 3D?

I want to draw a circle in 3D from line segments. There are plenty of examples how to do this with an even number of subdivisions in 3D space, but I want the minimum number of subdivisions to produce ...
57 views

### find radial distortion coefficients for equidistant angle distribution

I've implemented the Kannala Brandt algorithm for radial distortion. The user can insert several distortion coefficients (k1 ... kn) to define the lens. The algorithm works very fine! But this should ...
1 vote
192 views

### Clever projection of point onto triangle?

I know of at leas tone way to project a point onto a triangle. Project onto the plane, check barycentric coordinates, if outisde triangle, project onto the 3 segments, check distance, retain closest ...
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### Why is my cube triangle glitching?

This is driving me absolutely insane, I am battered and defeated I'm following a tutorial on projection matrices and everything seems good......... except this ONE polygon. I have checked all 3 ...
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### 3D projection Axis inversion problem (Java/Processing)

Unfortunately, I always had problems with math and was never good at it. I'm currently trying to combine math with my knowledge and my passion for programming. Brief introduction: In math, we have ...
71 views

I have a projection calculation which maps points from 3D space to pixel (image) space, and I want to use it as instead of the standard MVP projections in a vertex shader. In the image below the lower ...
1 vote
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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 ...
1 vote
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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 ...
352 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 ...
364 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 ...
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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.
1 vote
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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 ...
374 views

### 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 ...
665 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 ...
312 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 ...
78 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:...
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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 ...
98 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 ...
273 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
2k 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
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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 $Y_{new}... 3 votes 1 answer 637 views ### Difference between 2D and 3D pipeline 2D transformation and viewing: The camera projects the 2D world co-ordinate$(x_w, y_w)$on its projection plane which co-ordinates$(x_v, y_v)$. 3D transformation and viewing: The camera projects the ... 2 votes 2 answers 220 views ### Parallel projection is special case of perspective projection I synchronized with @David k's first and second answer regarding perspective and parallel projection. From the first question I understand that the image on the screen is typically described in ... 3 votes 1 answer 706 views ### Difference between transformation and projection? [closed] We know that world coordinates$(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)$... 1 vote 1 answer 77 views ### Why shearing coefficients multiplying by y? [closed] We know that shear is transformation that distorts the shape of the object. Shear relative to X-axis that is$y=0$line can be written as:$x'=x+sh_x.y, y'=y$My question is why$sh_x$is multiplying ... 1 vote 2 answers 229 views ### Difference between perspective and parallel projection [closed] We know that in orthographic Projection Projectors (projection vectors) are perpendicular to the projection plane. And in Perspective Projection Object positions are transformed to the view plane ... 1 vote 1 answer 1k views ### Why are vanishing point and centre of projection the same [closed] We know that in perspective projection object positions are transformed to the view plane along lines that converge to the projection reference (center) point like this: But many websites say that COP(... 2 votes 1 answer 207 views ###$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 ... 1 vote
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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 ...
288 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
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### 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
162 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 ...
126 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
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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 ...
66 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 ...
1 vote
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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). ...
152 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 ...
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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 ... 1 vote