# Midterm exam

## Information (from website)

The midterm exam will be held on March 2 at 15:45 and it will be a **1-hour exam** consisting of **6 open questions**.
That means 10 minutes per question, so try to manage your time.
There will be one question per lesson (1.1 to 3.2).
That means that it's not a problem if you're a bit behind the course.

You are free to check the course materials (videos/handouts/assignments) and any other materials you can find (eg books or the internet).
Just please don't communicate with others.
We are asking for your honesty to help us push back against invasive methods in remote education (eg online proctoring).

The exam will be a Markdown (plain text) file that will be published at 15:40 [here](https://3d.bk.tudelft.nl/courses/backup/geo1004/2022/data/midtermexam.md).
You should download it to your computer, add your answers by directly editing the file, and upload it through a Dropbox request [here](
https://www.dropbox.com/request/lEAghLBSpf23yi2kQXfV).
Exams will be accepted until 16:50, so please avoid problems by uploading it at 16:45 at the latest.
If you're worried about the time, maybe set an alarm for 16:45 on your phone?
We will also post a message on Discord at 16:45.

Markdown files look like plain text with minimal formatting, like [this](https://3d.bk.tudelft.nl/courses/backup/geo1004/2022/data/index.md).
You can edit Markdown files with any text editor, including whatever you use for Python or C++ programming.
Some possibilities: Sublime Text (my preferred option), Atom, VS Code, Notepad++.
If you *really* want to answer your questions in another software, you are allowed to upload a PDF file instead.

If you have any questions during the exam, you can send Ken (kenohori#5365) a DM on Discord.
[Email](mailto:k.ohori@tudelft.nl) is also fine.

If something goes seriously wrong (eg sudden illness or internet going down), do not worry.
Just contact Ken as soon as you can for alternative arrangements (most likely an oral exam through a video call).

## Questions

### 1.1 (Chapter 1 - dmds). Look at the 3D model on the cover of the [3D book](https://3d.bk.tudelft.nl/courses/backup/geo1004/2022/data/3dbook.pdf) and write three sentences, one for each of the following: (i) its geometry, (ii) its topology and (iii) its semantics. 

### 1.2 (Chapter 2 - brep). Is a disk (a circle that has been filled in) a 1-manifold, a 2-manifold or neither? Explain your reasoning.

### 2.1 (Chapter 8 - gmaps). In a 3D generalised map, how many darts are there in an [octahedron](https://en.wikipedia.org/wiki/Octahedron)? Explain your reasoning.

### 2.2 (Chapter 4 - voxels). Look at the voxelised model in Figure 4.1 in the 3D book. Using examples from this figure, explain how octrees could help you store this model more efficiently.


### 3.1 (Chapter 3 - dtvd3d). Imagine you have a set of 12 points in the 3D Euclidean space, all lying inside a cube, and that you have 8 other points located at the corner of that cube (total number of points is thus 20). For further processing, you want to create the Delaunay tetrahedralisation of the 20 points (not the constrained/conforming, simply of the DT). a) Describe the convex hull of the DT, how many surfaces does it have? b) How many tetrahedra will the DT contain? c) If a given vertex $v$ in the DT has 18 incident tetrahedra and 26 incident edges, describe its dual Voronoi cell: how many faces and how many vertices? Is is convex? 


### 3.2 (Chapter 9 - iso19107). We want to represent the tetrahedron below as an ISO19107 Solid, it is formed of the 4 vertices $a$, $b$, $c$, and $d$. We therefore need to store it with 4 surfaces, as shown in the figure. a) Is the Solid valid according to the ISO19107 rules? Explain your reasoning. If it is not valid, enumerate the 4 surfaces so that they represent a valid tetrahedron. b) Assume we store the same 4 input surfaces as a MultiSurface, is it a valid MultiSurface according to the ISO19107 rules? Explain your reasoning. If it is not valid, what changes need to be made?

![](https://3d.bk.tudelft.nl/courses/backup/geo1004/2022/data/tetra.png)