# Questions tagged [matrix]

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### Computer Graphics Previous Year Question asked in UGC NET 2021

What is the transformation matrix M that transforms a square in the x-y plane defined by (1, 1)T (-1, 1)T (-1, -1)T (1, -1)T to a parallelogram whose corresponding vertices are (2, 1)T (0,1)T (-2, -1)...
1 vote
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### Move the camera in orthographic 3D

I'm trying to figure out how to move a camera in orthographic 3D. The scene is orthographic in the sense that an object looks the same regardless of position. The only thing that may affect the size ...
1 vote
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### Matrix form of an open uniform cubic b-spline

I'm trying to find the matrix form for the equation of a cubic b-spline. More specifically, the "middle" part, S_i(t), is pretty straightforward and available everywhere: ...
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1 vote
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### How to display real time 3-D orthogonal vector rotations?

I'm an embedded developer here with very little experience in computer graphics. I'm currently working on a GUI that can display a calculated inertial solution at run time. I have hardware that can ...
1 vote
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### convert right handed matrix into left handed forward/up/right vectors

I have an openGL style matrix (column major, right handed ) that needs to be converted into two vectors (forward and up) I've managed to find, in a weird way, a solution that matches the the ...
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### Why are the transformations of an object calculated on CPU?

If I understood correctly this is the process of rendering an object: Array of 4d vector defining points 3d points(with the fourth component 1) representing object's vertices in object/local space: <...
65 views

### Trouble transforming vectors from view space to screen space using a perspective projection matrix

I can't for the life of me figure out how to use a perspective projection matrix. My understanding is that, once objects are in view space, the the perspective transform uses the z-coordinate to ...
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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 ...
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### Previous frame reprojection fails for camera translation

I'm trying to perform forward pixel projection based on previous frame depth. Using UV, I'm reading prevDepth for given pixel and based on that I'm recreating worldPos in camera space (where (0, 0, 0) ...
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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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### How to determine transformation matrix for an object given a graph?

I am given this image: and asked to determine the transformation matrix that took me from ΑΒΓΔΕ(let's call it ABCDE for convenience) to Α'Β'Γ'Δ'Ε' (A'B'C'D'E'). I am also given the solution, so as to ...
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### Convert one triangle to another in matrix4x4?

The context openGL instances learning. I want to transform a reference triangle to another one. So final goal is to have one triangle and the instance being a transformation of that initial triangle. ...
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 ...
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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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### How to interpolate between two MVP setups?

I am currently writing an AR experience. I have a Camera View Matrix, A Camera Perspective matrix and the Model Matrix of the content I display. The AR content should can be switched to "2D",... 166 views

### Simulate projection matrix deformation in two camera setup

For educational purposes I'm trying to simulate what a scene would look like with a perspective matrix deformation (before everything is brought to NDC) but I'm unsure how to do this. I'd like to do ...
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### Rotate a Bitmap with Shearing

I am rotating a bitmap using the three shear algorithm documented in these articles . From about 0-90°, the quality is acceptable, but beyond that it gets progressively more distorted until it's ...
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### Bezier curve : Problem deriving control points from matrix form

This is my first post on this website so i have put in a lot of research to get my point across to everyone as clearly as possible. Based on a question i posted on stack overflow i have successfully ...
1 vote
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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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### Matrix transforming with translation/rotation/scale at center of screen

I'm trying to create a camera using matrix transforms, the gist as follows: ...
2k views

### THREEjs: updating an object's matrix doesnt change it's position and rotation params

I want to set a transformation matrix to an object upon creation and then control it by position, rotation and scale, but while changing the matrix does change the object in world space, it's position ...
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### How to calculate position from depth pass of the ZED camera?

I'm using the ZED 2 camera, and although the API provides a means of getting a point cloud position from a specific pixel, for my project I need to be able to perform this calculation myself from the ...
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### Perspective projection near plane not in world coordinates

I have a camera I have placed zunits away from a billboarded rect. My goal is to discard all other geometry that is closer to the camera/in front of this rect. With ...
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### Crystal ball rotation - I don't get why the code works

For context: I'm absolutely new to graphics programming and I've always had trouble getting the math. I had the task to write code for a crystal ball interface using OpenGL. There's an object in the ... 70 views

### Compose ViewMatrix and ProjectionMatrix

As the title says, you are able to compose the ViewMatrix and the ProjectionMatrix into one instead of multiplying a vector by the individual matrices. Instead of doing this at run time for each item: ...
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### Which perspective projection matrix to use

I've seen two different perspective projection matrices being used but I want to know which one of them is the best. I think that they both output the same but I'm not sure. So if anyone can help me ...
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### Why do we call it TRS and MVP, instead of SRT and MVP or TRS and PVM?

Here's something that's been bothering me while learning graphics. We have two core concatenated matrix sets: "TRS" for transforms, and "MVP" for moving everything into the canonical view volume. TRS ...
1 vote
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### Do I need a normal matrix if I calculate lighting in an objects space?

As a quick reminder, here is what normal matrix is and why do we need it. Now the question - if I take the light position and transform it into an object space than I don't need the normal matrix at ...
1 vote
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### Help with understanding the look-at function (the view matrix)

I've been reading this article about the look-at function. I don't understand the part when they're trying to inverse the matrix N. They say that R is orthogonal because all its row and column ...
1 vote
336 views

### Camera position in vertex shader

in the vertex shader I have the vertex position vpos which is in object space and I want to get the vector going from the camera to ...
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### How to find matrix that projects 3d points into 2d plane centered in the origin?

I have a list of 3D points defined by Cartesian coordinates, i.e. [(x1,y1,z1), (x2,y2,z2), ..., (xn,yn,zn)]. I want to project them to a 2D plane which has origin in the center (0,0,0) but which is ...
2k views

### Why does opengl use 4d matrices for everything?

What I managed to figure out is that the first 3*3 is used for rotation and scale and the 1*3 at the end is used for position, but what is the bottom row used for? is it only for clipping related ...
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### My 2D translation matrix causes the box to be off screen when it shouldnt be

Now I know this isn't the way this is normally done so please bear with me. I am doing this this way so I know I have a solid conceptual understanding of everything that goes beyond example code. I ...
653 views

### Translate an arcball camera upwards or left-right

This problem is giving me a really hard time. I'm always looking at the origin and have a camera that moves around it in an arcball mode. That part works beautifully: I'm calculating the camera ...
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### Rotation of a random unit vector at a point in 3D space by an angle

I have a scenario where I need rotate a vector ( unit vector) at a point in space by an angle along Z-axis. Is it possible to help me to understand a procedure to achieve this. I'm using vb.net ...
1 vote
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### How to apply scale, translate, rotate with different origin and get new rectangle coordinates

I was reading other questions in this topic but I couldn't apply any viable solution to solve my use case. I have a crop area described with two dimensions (cropWidth, cropHeight) I can easly compute ...
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### Correctness or otherwise of the procedure for generating an orbiting camera in WebGl

I have to create a orbiting camera. I created the model of sun (a sphere) around (0,0,0) , triangulated and Phong shaded it. I would have a camera that goes around the sun thus an orbiting camera and ...
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### How do I build my tangent space matrix?

I'd like to understand how the process of building the "tangent space" matrix for normal mapping works. I'm following several tutorials, and other stackexchange questions, but I'm unfamiliar with the ...
2k views

### Inverse value in a Perspective Matrix

I am a new leaner of computer graphics. I'm trying to understand a code I found online and I got stuck in the following formula: ...
1 vote
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### Inverse matrix order of operation

If I have a rotation, $A$, and a translation, $B$, which I multiply like so $C = AB$ Does the inverse of $C$ not only inverse the magnitudes of $A$ and $B$ but also become the reverse of operations? ...
15k 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), $f$(...
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### Modulo vs Scaling vs Capping when performing filters

I'm currently taking a graphics course and we've recently covered cross-correlation with regards to using a filter matrix that is applied to a region of pixels in a sort of continual raster-type scan ...
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### why is translating in 3D space the same as shearing in 4D space?

I was reading "3D Math Primer for Computer Graphics and Game Development" and there was something the author had said that I thought was particularly interesting, he stated It is important to ...
7k views

### Screen space coordinates to Eye space conversion

I'm trying to figure out how to reverse Eye space -> projection -> clip(divide by w) -> screen space conversion. Basically, I want to get Screen space (still have z value for z-buffer) -> undivide? ...
1 vote
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### Why inverse of an allignment matrix is the same as its transpose?

$A_{v}^{-1}$ = $A_{v}^{T}$ $A_{v}$ = Allignment matrix that alligns vector v with z axis $=$\begin{bmatrix} \frac{\lambda}{|v|} & \frac{-ab}{\lambda|v|} & \frac{-ac}{\lambda|v|} &...
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### How to decompose projection matrix?

I want to decompose projection matrices into near, far, top, bottom, left and right values to create a bounding box for view frustum. I used the formula described in this site Decompose the OpenGL ...