# Questions tagged [affine-transformations]

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### What are Affine Transformations?

What are Affine Tranformations? Do they apply just to points or to other shapes as well? What does it mean that they can be "composed"?
• 1,363
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### How to invert an affine matrix with small values?

I'm using an affine transformation matrix to transform 2D coordinates from screen (magnitude 10e3) to small parts of fractal sets (magnitude as little as 10e-15). I also need to map the other way ...
• 251
2k views

### How is that possible that matrices can be thought as coordinate systems?

I've been reading around that matrices (for example, rotation matrices, but not only) can be thought somehow as coordinate systems. My question is: how is that possible? I've seen for example that ...
976 views

### 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 ...
413 views

### Why does an affine transform work only on three of the corners?

I am trying to use a linear transformation to straighten out the camera angle on this image: In other words, I want to transform the image into a head-on view of the whiteboard. I applied an affine ...
311 views

### Affine Transformation

We have a matrix $$\begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{bmatrix}$$ This matrix represents a ...
1k views

### OpenGL : How to rotate an object around viewing space x-axis

I have an object(cow). This cow was translated and rotated(with arbitrary axis) in the modeling space for several times. And I can't know how much cow is translated or rotated. Only I can obtain is ...
• 61
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### What is exactly the third component in homogeneous coordinate system?

I was reading the wiki article about homogeneous coordinates , I learned that it has it's advantages when it comes to performing affine transformation, since you can represent it only matrices. But I ...
298 views

### What are forms of affine transformations?

Please help me tackle the below question: Explain THREE forms of affine transformations using relevant examples for each case. The answers I want to see are scaling, rotation and reflection.
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### $P^2$ 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 ...
467 views

### Building a lookat camera matrix

I was reading this article and found something that caught my attention. They say they are using column-major for their matrices so, in the code they have under the section Look At Camera they ...
• 969
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### Deciphering Affine/Projective Transformation Code

I've spent about 2 days trying to understand this piece of code (from here) that applies an affine/projective transformation to an image. I will link bits of the code that I'm struggling to understand ...
6k views

### OpenGL : How to translate an object with it's own axis

I'm working with OpenGL to try to rotate / translate my 3d object : a cow. The requirement is simple : If I toggle key 'r'. The cow spinning around and random axis. If I drag the cow with mouse, it ...
• 61
3k views

### how to map rectangular coordinate system onto JavaFX GraphicsContext canvas

I am trying to figure out how to apply the proper sequence of translate and scale commands (or a single .transform command) so that the default pixel grid (0,0,1920,1080) for instance is setup so that ...
• 1
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### Transform a centered isosceles trapezoid in a rectangle in 2-D

I must convert a isosceles trapezoid to a rectangle in 2-D with a shearing transformation (or with 2 shearing transformations). The isosceles trapezoid is centered in the origin of axes. It is right ...
• 321
1 vote
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### How to convert from Object space into World space (exercise from 3D Math Primer book)

This is not homework. I'm self studying Computer Graphics, using the book "3D Math Primer for Graphics and Game Development" (2nd edition). So there is the exercise 6 in chapter 3 which I can't figure ...
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1 vote
474 views

### What kind of transformation when the aspect is changed for a rotated shape?

I have a geometric shape (assuming that is a rectangle). I want to rotate it about it geometric center by an angle of 45° and plot the result using matplotlib with an equal aspect ratio, I get ...
• 111
1 vote
1k views

### How to make a translation relative to the line ax + by + c = 0, affine transformations

(sorry for my english) The task: A triangle is specified. To realize its motion on the basis of mirror reflection with respect to an arbitrary line ax + by + c = 0, the coefficients of which are ...
1 vote
83 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
371 views

### Applying 3d transformation to cuboid

I have the 8 vertices of a cuboid (red points)(XYZvox) with known distance in millimetres (vox to mm) between each vertex which I transform in 3d space using the 4d transformation matrix (M). I am ...
• 111
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### Alignment of the plane coordinate system with the square is similarity transformation

I'm reading the book "Multiple View Geometry in Computer Vision" of Hartley and Zisserman. There was something I was unable to understand correctly. Here's the example where K denotes ...
32 views

### 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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