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Questions tagged [affine-transformations]

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21
votes
1answer
5k views

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"?
7
votes
1answer
231 views

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 ...
5
votes
2answers
336 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 ...
5
votes
1answer
241 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 ...
4
votes
1answer
109 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 ...
4
votes
1answer
172 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 ...
3
votes
1answer
116 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 ...
3
votes
1answer
1k 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 ...
2
votes
2answers
108 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 ...
2
votes
2answers
327 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 ...
2
votes
2answers
1k 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 ...
2
votes
0answers
131 views

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 ...
1
vote
1answer
133 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.
1
vote
0answers
51 views

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 ...
1
vote
0answers
36 views

Transform a cube in a truncated pyramid

I have to calculate the modeling transformation that transforms a cube of side=1 centered in (0,0,0) in a rectangular truncated pyramid of height=2,sides of basic rectangle equals to 3 and 2, sides of ...
1
vote
0answers
170 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 ...
1
vote
1answer
63 views

Image warping using pixel normals

I want to insert a logo into an RGB image with proper 3D transformations. I can get the estimated pixel normals of this image using the code here: https://github.com/yindaz/surface_normal. Pixel ...
0
votes
1answer
47 views

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 ...