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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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2answers
6k views

Why is the transposed inverse of the model view matrix used to transform the normal vectors?

When rendering 3D scenes with transformations applied to the objects, normals have to be transformed with the transposed inverse of the model view matrix. So, with a normal $n$, modelViewMatrix $M$, ...
21
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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"?
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1answer
855 views

Is it possible to turn a 3d rotation matrix (4x4) into its component parts (rotation, scale, etc.)?

To be more concrete, I'm working on an iOS app, and have a CATransform3D struct (basically a 4x4 transform array). Is it possible to deduce all the different "...
4
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2answers
223 views

Minimum requirements to uniquely represent a 3D object in space

Let's assume we have a 3D object (in 3D space). We get a single representation vertex from this whole 3D object. Given the fact that the object can be moved and rotated in the space in any direction, ...
5
votes
1answer
1k views

What is the correct order of transformations scale, rotate and translate and why?

This is a rather primitive question coming from an electronic engineer. When applying rotate (about origin), scale (in which we shall translate towards origin and then back) and translate, does it ...
5
votes
1answer
349 views

Rotation matrix for a 3D object in space

This is the follow-up question from here: Minimum requirements to uniquely represent a 3D object in space Assume I have 3 original points in a 3D object (in 3D space) as ...
5
votes
2answers
339 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
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1answer
242 views

Transformation Matrices

Consider the following problem and its answer: Given 3 points in 3D: $A=(A_x,A_y,A_z); B=(B_x,B_y,B_z) ; C=(C_x,C_y,C_z)$ Find the transformation matrix (in homogeneous coordinates) that ...
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1answer
65 views

preserving z-values during projection?

Consider this figure for projection. There are two equations that give value for the xp and yp coordinates: $x_p=x.\frac{(z_{vp}-z_{prp})}{h}+ x_{prp}.\frac{(z-z_{vp})}{h}$ and $y_p=y.\frac{(z_{vp}...