# Questions tagged [transformations]

Transformations are mathematical operations that can be applied to an object to change its scale, position and orientation.

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### Can an aspect ratio be shortened to one value, best practise

I want to make a program that, for starters, list all image files in a folder and writes a warning if one dimension is (i.e.) double (2x) the other dimension, regardless of "image orientation&...
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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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### 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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### Gimbal lock confusion

I am trying to understand exactly what is happening when Gimbal lock occurs. I have read many explanations now which provide the high-level idea, in that Gimbal lock occurs when two axes are aligned ...
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### How to Achieve Radial Rendering

I'm making a POV fan and would like to display some simple graphics in real-time on it. I have a working naive solution with OpenGL, but I'm maxing out at 7 fps rending a simple cube on a raspberry pi ...
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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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### How do I perform a perspective transform on a straight line?

I'm trying to make a software renderer, but I want to avoid creating extra triangles with clipping. For this I want to transform lines which compose triangles, instead of individual points. However I'...
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### Reorder mesh triangles

Good Morning! My problem is: I need to get the vertices of a mesh and send them to a shader. Inside the shader I will reassemble the mesh from its vertices. So far so good, I send the information and ...
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### Visualize the interpolated unit quaternion on the surface of the unit sphere

My major is mechanical, please forgive me for asking questions that may seem trivial to you. First, I'm reading the following paper: Dam, Erik B., Martin Koch, and Martin Lillholm. Quaternions, ...
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### Efficient algorithm for mesh scale adjustment based on the scale of another mesh

I have a mesh (Mesh-A) with a bounding box of some arbitrary size defined by X,Y,Z scale. In runtime I import another mesh (Mesh-B),which has an overall topology similar to the Mesh-A, but it can have ...
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### How to get the surface alignment

How can I get the surface alignment of a 3D object in screen space? I found this example which, I believe, is aligning the UV coordinates to the 3D vectors (which are determined by their current ...
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### Proprietary 3D Format Reverse Engineering: What Could These Numbers And Matrices Represent?

I'm trying to reverse engineer a model format from an older Russian game (Pathologic) with limited success. It is a proprietary model format not recognized by any converters/editing tools (believe me, ...
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### Why perspective division ( div by w) when applying the inverse to a perspective transformation?

For example, when you want to compute the world space position of a fragment in the fragment shader, you can construct the fragment's NDC coordinates, then multiply by the inverse of whatever ...
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### 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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### How can i wrap the earth image around a 3D Sphere using OpenGL, GLFW, GLAD, GLM?

Please help me out with this thing and currently i am a little more than a beginner so please tell me in that context. i don't need any obsolete methods for creating this like using GLUT or GLEW.can ...
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### Could the Tetradic color pattern be expanded to allow /dev/random be "pretty" for cryptographic key purposes?

Is there a way to take a random value (or set of values), and cause them to create a "pretty" pattern (as a thumbprint), and that array of thumbprints might have a rendering mask on just for ...
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### How compute new camera parameters given a velocity vector?

My goal is to update camera parameters given a velocity vector so that the camera points in the direction of the velocity vector. How should one compute the update matrix for the camera parameters?
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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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### How to use trackball for rotating an camera matrix in eye frame

I have a QOpenGLWidget where I use camera transformation matrix(4,4), FOV and vectors Position(4), Up(4), Forward(4). I also have an ArcBall which I can use. I managed to implement zoom and pan by ...
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### Translate the camera with Pan gesture (when it is rotated )

I am new here I am not good in math SO what I need is I need to translate the 3D camera with Pan gesture on 2d Screen With below code it is working But if camera has some Euler Angle (rotated ) then I ...
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### Why is browser-resized image crispy and manually-resized image blurry?

I've come across this problem several times now and I can't really understand what causes it; my background is in Wordpress, not really in computer graphics. I hope this is the right place to ask, I ...
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### Using 2D point/polygon algorithms on polygons lying on a arbitrary plane

Is there an efficient method to apply 2D point/polygon algorithms on general planar points. For example, I need to triangulate a polygon where the input is a list of ordered points. The algorithm ...
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### What technique would I use to create fake 3d walls as seen in Realm of the Mad God

I wanted to make a little demo for a console with Realm of the Mad God esc graphics to brush up my C and SDL skills. One problem I'm running in to is creating the 3D walls. The console I'm ...
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### Transforming a ray from camera space to world space

I am writing a Raytracer and generating rays from the camera. I have a working program but slightly confused about the linear algebra concepts involved in transforming the ray from camera space to ...
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### Path tracing: How to ensure we are sampling a direction vector within the visible hemisphere of a surface?

Given a surface Normal vector of an intersection point, how can one generate a random direction vector that is guaranteed to be in the visible hemisphere? The way I ...
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### Rotate a Bitmap with Shearing

I am rotating a bitmap using the three shear algorithm documented in these articles [1][2]. From about 0-90°, the quality is acceptable, but beyond that it gets progressively more distorted until it's ...
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### rotate objects like a trackball

I know how to rotate objects around the center and there are rotation matrices for that as well, but, how do we rotate the object like a trackball, below is the example: firstly I rotate around the y ...
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### Rotating a Bitmap

I would like to rotate an bitmap image using math. I have two issues with my current implementation: the pixel-by-pixel rotation of the copied bitmap is extremely slow and it is leaving gaps between ...
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### Help me understand the derivation of this tangent space to object space matrix

I was trying to follow this http://foundationsofgameenginedev.com/FGED2-sample.pdf But had problem understanding formula 7.33. $$p_i-p_j=(u_i-u_j)\mathrm{t}+(v_i-v_j)\mathrm{b}$$ * $p_i,p_j$ being ...
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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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### 3D Bouncing Cube

I'm trying to write a little program with a bouncing cube but I can't find the right x, y, z and angle for it. I have these lines: ...
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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: ...
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### 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 "preserve texture" when transforming vertices

Maya has a feature called preserve texture. It allows you to transform vertices of an object and basically have the texture "stay in place" in object space. Say I have a plane with unwrapped ...
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### What's the name of the transformation that can remove horizontal convergence from a picture?

Say that you are taking pictures from a street like this one: As you can see, the picture is taken perpendicular to the direction of the street. The problem is that cars at the left look as if they ...
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### Interpolate vertex attributes with $z$ AFTER homogeneous divide

Usually, if we want to interpolate some vertex attributes, say $A_1$, $A_2$ and $A_3$, we have to first divide them by their corresponding $z$ in view space, then we interpolate them using barycentric ...
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### Transformations and change of basis in CG

Sometimes in CG literature a transformation is equated to a coordinate system change. This is fine as long as the transformation includes only a rotation and a translation. When scaling is involved, ...
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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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### Converting Vertex and Index buffers to a File Format

I have many sets of vertex and index buffers that I’d like to render on to the screen. Ideally each model in different locations with-in world space. I’m actually doing a statistical study on spatial ...
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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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### How to keep an object constant in screen space?

If you open the modern Blender UI and select for example scaling, and then you use the scroll wheel to "zoom" (move the camera along the radial axis). You will notice that the size of the 3D widget ...
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### Transforming fragment-to-camera to tangent space for parallax occlusion mapping

I'm trying to implement POM using this tutorial. As stated, I need to transform fragment-to-camera to tangent space and then pass it to a function. tangent space is computed using Assimp. Well I ...