---
# System prepended metadata

title: Supi Dupi 3d Vision -1

---

# Supi Dupi 3d Vision -1

## Lecture 1
Nada
![](https://i.imgur.com/WTbDI4A.jpg)

## Lecture 2
![](https://i.imgur.com/oqG5BIK.png)

### 1D-Transformation
Non-projective:
#### Euclidean transformation
![](https://i.imgur.com/V4XmlZj.png)
Invariant: Distances (Lengths)

#### Similarity transformation
![](https://i.imgur.com/xsDsxvA.png)
Invariant: Ratio of differences
![](https://i.imgur.com/BsCM6EI.png)

Projective:
#### Euclidean transformation
![](https://i.imgur.com/2NN5KSP.png)

#### Similarity transformation
![](https://i.imgur.com/42TvOwq.png)
Not invariant: Ratio of differences


#### General form of homogeneous (projective) transformation
![](https://i.imgur.com/cjqx4i7.png)
H can be determined using three corresponding pairs of points (in general position) (minus 1 hihihi)

Cross-ratio remains invariant

### 2D-Transformation
#### Euclidean transformation
Translation:
![](https://i.imgur.com/pOarTTv.png)

Rotation:
![](https://i.imgur.com/TFxZxr0.png)

#### Similarity transformation
Uniform (Isotropic) Scaling:
![](https://i.imgur.com/NKoDAvq.png)

#### Affin transformation
Non-uniform (Anisotropic) Scaling:
![](https://i.imgur.com/DUdca53.png)

General affine transformation (including shearing):
![](https://i.imgur.com/HzjfsWw.png)



## Questions
What are vanishing parameters in projective transformations ?

"For a point x ̃ on the plane through x ̃1, x ̃2, x ̃3 it must hold det(M) = 0 for", why ?

The span of the 2-dimensional right null-space of W is the pencil of planes with
the line as axis. ok, what ?

If u1v2 +u2v1 < 0 than L1 passes L2   counter clockwise  

![](https://i.imgur.com/dr8svsH.png)
