---
title: Session.  3D Objects in Python
categories: session
---

# Learning Objectives

**Key learning outcome**
Improve the understanding of the mathematical descriptions of
3D Motion, by testing implementations in Python.

**Secondary outcomes**
if you have time, it is worth browsing different libraries and frameworks
to build, visualise, and animate scenes using 3D objects.

# Briefing

## Recap: a simple object

Remember, last week we worked with this data structure in Python:

```
In [1]: print(vertices)
[[-1.   0.5  0.5]
 [ 1.   0.5  0.5]
 [ 0.  -0.5  0.5]
 [-1.   0.5  0.5]
 [ 1.   0.5  0.5]
 [ 0.   0.5 -0.5]
 [-1.   0.5  0.5]
 [ 0.  -0.5  0.5]
 [ 0.   0.5 -0.5]
 [ 1.   0.5  0.5]
 [ 0.  -0.5  0.5]
 [ 0.   0.5 -0.5]]
```

The rows are points in 3D. Note that there are only four distinct points.
If we divide the matrix into sets of three rows, each triplet defines a
triangle.  These four triangles form the faces of an irregular tetrahedron.

This is a standard way to define a 3D object.  More complex objects need more
triangles.

Note that the textbook have vertices as *column* vectors, while
we here use row vectors.  This means that we need to transpose
matrices when we translate textbook formulæ to python formulæ.

Consider, for instance a rotation matrix

$$
\begin{align}
R =
\begin{bmatrix}
  \cos(\pi/6) & -\sin(\pi/6) & 0 \\
  \sin(\pi/6) & \cos(\pi/6) & 0 \\
  0 & 0 &  1
\end{bmatrix}
\end{align}
$$

```python
from numpy import *
R = array( [[ cos(pi/6), -sin(pi/6), 0], [ sin(pi/6), cos(pi/6), 0], [0,0,1]] )
```

This matrix is orthonormal, which we can check:

```python
matmul( R, transpose(R) )
```
To rotate a vector $\vec{v}$, we would calculate $\vec{u}= R\cdot \vec{v}$, where
$\vec{u}$ and $\vec{v}$ are column vectors.  If you have a shape $V$ where the columns
are points, it could be rotated as $U=R\cdot V$. In python this has to become

```python
V = transpose(vertices)
U = matmul(R, V)
newvertices = transpose(U)
```



## Homogeneous co-ordinates

## STL files and the STL library

# Exercise

## Rotations and translations

## Homogenous Coordinates 

Motion defined by homogenous matrix    

## STL files and the STL library

+ Load Model 
+ View Model
+ Change Model
+ Save Model

# Additional Materials

+ [Other relevant python libraries](Python3D)