Validating Flight Networks for Drones – part 2

In part-1 I described how we validate flight-networks at Flytrex to make sure that no two nodes of a flight network are too close. Now let’s turn our attention to validating that no two edges are too close.

First, how does one define “edges being too close”? What is the distance between edges?

Here’s a good definition – the distance between edges e1 and e2 is

D(e1, e2) = min D(p1, p2) for p1 ∈ e1 and p2 ∈ e2

That means, the minimal distances of all distances between pairs of points taken from e1 and e2 respectively.

Given that definition – if two edges cross, then of course the distance between them is zero. This is useful – two edges crossing is a more extreme case of two edges being too close to one another.

So how can we implement this? Unfortunately our “closest pair” algorithm for vertices from previous post is not good enough here. I was unsure what to do – and so the easiest solution like all lazy programmers – is going to stackoverflow. Note, just looking for an existing question and answer pair is not good enough – I didn’t find a solution. As I wrote previously – it’s better to not be shy and actually ask for help.

What did I learn? I saw a suggestion to use Rtree. What is that?
Rtree is a wrapper around libspatialindex, which is a library that provides you with, well, a spatial index. A spatial index is a data structure that indexes objects according to their position in space. Read here for some theoretical details.

Visualization of an R*-tree for 3D points using ELKI (the cubes are directory pages).
Taken from the R-tree page on wikipedia

So our approach to solving our problem is relatively straightforward. For each edge in our graph, we will add it to our spatial index. Then, for each edge we will look up the closest edges to it, and make sure that distance between our edge and the closest edges is still more than our MINIMAL_DISTANCE.

How many edges should we retrieve? Well, that depends. Obviously, if two edges share a vertex then the distance between them is zero, however, we do not want to alert on edges that share a vertex. So we need to get the N closest edges such that N > number of neighbour edges of our edge. For some simple graphs that is simple, but for the general case that might include all of the edges (e.g. a sun-shaped graph with a single vertex all edges share.)

Here is some sample code:

def _prepare(self):
    for idx, edge in enumerate(self.edges):
        self.tree.add(idx, self._get_bounds(idx))
def validate(self):
    for idx, edge in enumerate(self.edges):
        neighbor_edges = (
            self.node_to_edges[edge.from_vertex_id] |
            self.node_to_edges[edge.to_vertex_id]) - {idx}
        # The +10 there is because we want the few edges that are not
        # our neighbors. (The distance to our neighbors will always
        # be 0 and we should ignore them)
        nearest = self.tree.nearest(
            self._get_bounds(idx), len(neighbor_edges) + 10)
        for nearest_idx in nearest:
            if nearest_idx in neighbor_edges or nearest_idx <= idx:
            dist = self._get_distance(idx, nearest_idx)
            if dist < MIN_EDGE_DISTANCE_M:
                p1 = self.id_to_node[edge.from_vertex_id]
                p2 = self.id_to_node[edge.to_vertex_id]
                edge2 = self.edges[nearest_idx]
                q1 = self.id_to_node[edge2.from_vertex_id]
                q2 = self.id_to_node[edge2.to_vertex_id]
                raise ValidationError(
                    f"The edges {} -> {}" 
                    f"and {} -> {}" 
                    f"are too close to one another. "
                    f"Distance is {dist:.1f}m but should be" 

The result of this code worked well. It manages to find issues in flight networks, and does it in reasonable speed.

For myself, I’m happy to have added another tool to my arsenal – Rtree.

Game Development

QA by Child

I recently published a home project I was working on, an app to teach children to read Hebrew. I wrote it originally to help my son learn to read Hebrew.

A screenshot of “Learn to Read Hebrew Easily”

In an early version my son was very excited to play it. He quickly understood the principle – see a word, then tap one of four emojis this word describes. Every time you tap a right answer, you get a few more points, which in that early version were displayed prominently at the top of the screen.

It took him less than five minutes to find a “cheat” – if you tap the right answer very quickly many times – you get points for every time you tap it, as long as the “correct answer” animation is running and the word is not changed.

It reminds that a few years back I was working on Desti and when I gave that same kid an early version of our iPad app – he broke it in less than 30 seconds just by moving his hand on the screen and touching everything at once.

Generally, if you have a GUI, one of the ways to find issues is to let a kid hack at it. One reason is that GUIs have the curious property that changes take non-zero time, and usually buttons are not disabled once they are initially tapped. As a result – you sometimes get the effect multiple times – which can result in extra score, multiple transitions, repeated actions on now incorrect state, and so on. In the extreme case this can lead to resource exhaustion very quickly and your app crashing. I’ve seen that happen to my app!

What else do you get by giving your app to a child? You can see very quickly if your UI and UX are clear and easy to understand. If you need to explain what needs to be done – it’s not good enough. That’s true in general – and doubly so for a kid. If your kid gets it on their own – you did something right.

More deeply than UX- you can learn if your gamification works. Is your app/game engaging enough? Does it invite gameplay? Does the meta-game encourage repeated plays? It took me a lot of thought to get my reading app to work well – and it’s far from done.

Did you test your app with your kid? What was your experience with that?


How to hire a freelancer – 25 useful tips

Over the years I’ve had many opportunities to work with freelancers. Recently a friend had a bad experience looking for freelancers, and I tried to help her find new ones. That prompted me to write a bit about my method. While not completely foolproof, it will increase your chances of finding better freelancers.

Defining the job offer

Before we start, there are a few questions you need to ask yourself.

1) Is this for a job I know how to do myself, but just need someone else to do it, or is it for a job I don’t know how to do myself?

Sometimes, I need someone to do some programming for me. Sometimes it’s some programming that I know how to do but just need manpower, and sometimes it’s in an area that I’m really unfamiliar with, say, machine-learning image analysis. Sometimes it’s for something completely different – e.g. narration, or graphic design – where I really can’t do it myself.

2) For a job that I don’t know how to do myself, do I know how to evaluate the quality of the work?

Let’s say I’m looking for a narrator – I can certainly judge the quality of the work. My judgement might not be the best – I will probably miss some finer points, but I will still be able to see if someone did a good job and it sounds good to me. On the other hand, let’s say I’m looking for someone to port my system to Azure for me, and at best I’m familiar with AWS. They might be making major mistakes in design and I wouldn’t know, because I’m not familiar with Azure.

3) Do I know how to evaluate the quality of the freelancer?

Prior to hiring the freelancer and looking at the result of their work, how well can I predict how good of a job they will do? Of course, looking at past work is the most obvious thing, but sometimes that’s also hard. Many people can boast of impressive demo projects but still will not be able to do what I want them to. Sometimes, their past work is protected by NDAs, e.g. security advisors. In these cases I will usually need to rely on recommendations.

4) Do I have fixed requirements, or is this a project with changing requirements?

Sometimes the requirements are very clear – I need some narration done, a background drawn, some specific functionality implemented. Sometimes, I want a large feature developed, with the details not yet specified, and I need the first mockup version implemented to be able to be specific. Sometimes, I need a result “make my DB go faster” or “make my website secure” – and the particular actions to take are as yet unknown.

5) Is this a long term or a short term, one time engagement?

Sometimes you just need some small task done. Sometimes you are looking for someone to work with for the long term. If I’m looking for a short term and fixed price project, then the requirements must be well known beforehand, and I must be able to judge the quality of the result.
Long term projects can be opportunities for freelancers, so they provide you a way to get a better price or more leeway in changes requested.

6) What is my budget for this project?

That’s one of the most critical questions. You might have a total project budget – or just a monthly budget for work done. Having a tight budget might force you to be very strict about your plans and requirements. Having some experimentation budget might allow you to hire multiple freelancers and pick the best one.

Specific techniques

Once you are clear with yourself about the answers to all of these questions, many decisions will become much easier to make. Here are some techniques to handle various situations.

My requirements are around results and I don’t know what steps need to be done. Examples: “Make my code faster”, “Make my website secure”, “Propose a design to my website pretty”

  1. Make sure you know how to measure or evaluate the results. Specify clear criteria for success.
  2. Do you need just proposals for changes, or actual implementation? Actual implementation is better, unless you can clearly evaluate the proposed changes.
  3. When looking for freelancers, ask them what steps they will take to do their work, and what they expect the proposed changes are going to be. Then compare the results of multiple experts, this will allow you to evaluate who makes sense and who does not.
  4. Building on the previous step – if you had one freelancer suggest that he will do X and the other not suggest it – ask the first “Why did you propose X?” and the second “Why didn’t you propose X?”. For example, when optimizing a database, one freelancer can suggest she will “Set up a read replicate”. Ask the other one why he didn’t suggest it.

I have a lot of budget and I want to get the best freelancers

  1. It depends on what you mean by “a lot of budget” – but one easy way to get good freelancers is to hire multiple freelancers to do the job of just one, and pick the best result.
  2. A cheaper alternative, is to hire multiple freelancers to do a test task, and keep only the best. You won’t even need a lot of budget for that, and if the project is critical for you, there’s a very good chance it’s worth it.
  3. If you’re working with developers, and you are hiring multiple freelancers, consider having them code-review each other. This will increase overall quality and give you another opportunity to evaluate their work.

I am looking for a freelancer for a long-term engagement

  1. The first task must be an evaluation task, and this should be communicated to the freelancer.
  2. Similar to the previous situation – you can use the evaluation task to pick the best freelancer out of a group. You can have all freelancers do the same task, or give each one a different task, as you still get to keep the results even if you don’t continue working with them.

General advice

  1. Always communicate clearly what are your requirements, and what is the evaluation criteria you will be using. This applies to all communications; to the first message, and to your reply when the job is done.
  2. Don’t be afraid to disagree with the freelancer. Don’t be afraid to say that you want changes. Just be clear and upfront about your expectations, and keep to the terms you agreed.
  3. If you’re not an expert in the area – get a friend to give you some advice, especially if a lot of money is at stake.
  4. Don’t be afraid to add requirements and questions when you are selecting a freelancer. Worst case – they will decide not to work with you.
  5. When choosing which freelancer to work with, don’t forget to evaluate the freelancer on their communication ability. If someone doesn’t answer your job interview questions, or doesn’t understand them – how will they complete your requirements? How will they understand the urgent bug you’re trying to explain?
  6. When hiring developers – you MUST either know how to manage a development project, or have a team manager, or at least have a friend advising you.
  7. If you’re hiring for a small non-programming work, consider using
  8. If you’re hiring for a more complex project or engagement, consider using upwork.
  9. If you’re using upwork, my preference is to filter on >90% job success, and prefer freelancers with significant experience on the platform – which means a lot of money earned or many job-hours done.
  10. For an additional useful listen (in Hebrew), try which I listened to recently – a lot of useful advice there.

I hope this is useful for you, please share with me in the comments your own techniques for hiring freelancers!


Validating Flight Networks for Drones – part 1

A Flytrex drone lowering a package.

At Flytrex, in order to ensure drones fly only where allowed, and do not collide with each other, they are allowed to fly only in preplanned paths. However, if our goal is to deliver food to backyards, we can’t have a predefined path from our delivery center to each back yard, that would be wasteful. Instead, we created a flight network, which is a graph similar to a railway map, only instead of trains we have drones flying on it. This way, when a drone is required to a fly to a certain delivery point, a path is calculated on the flight network graph.

(Interesting note: while we could theoretically support a 3D flight network with routes above each other, we decided for simplicity’s sake to only allow planar flight networks for now.)

In order to support multiple drones flying at the same time, we also support semaphores and locking, but I’ll cover that subject at another time.

It is critical to verify that a flight network is correct and will not cause problems. We need to make sure that no two edges in the graph cross, otherwise the two drones flying through them might collide. Additionally, no two waypoints (nodes in the graph) may be too close to each other – for the same reason.

How do we do that?

First problem – for every two nodes n1 and n2, we need to make sure that distance(n1, n2) >= MIN_DISTANCE.

Second problem – for every two edges e1 and e2 that don’t share a node, we need to make sure that distance(e1, e2) >= MIN_DISTANCE. Of course, if they intersect then the distance is 0.

The simplest way to solve this is using brute force – go over every possible pair of nodes, and every possible pair of edges. This way however, is too slow – it’s the classic quadratic complexity. Can we do better?

For nodes, it is relatively easy: find the closest pair of nodes, n1 and n2. If distance(n1, n2) < MIN_DISTANCE return error, otherwise, the flight network is ok. How quickly can we implement closest-pair() for nodes? Apparently in O(nlogn), see this Wikipedia article and implementation guide.

We still have a problem though – both implementations assume Euclidean distance – and we need this implemented using e.g. Geodesic distance.

Here, this can be solved using one of two approaches:

  1. Project our nodes n1, n2 over an Euclidean surface such P(n1)=p1 and P(n2)=p2, and Geodesic-distance(n1, n2) ~= Euclidean-distance(p1, p2).
  2. Implement our closest-pair algorithm in a way that will work well enough over the earth’s surface.

(Note: happily enough, we can assume a maximum radius of a few kilometers for our flight network, otherwise this would have been much more complicated)

I tried first to go with option (1). However, how do you implement this projection correctly? I thought – let’s do a naive projection myself, using Wikipedia as a guide. Unfortunately again, this did not pan out. I took a sample of a few points, and calculated the Euclidean and Geodesic distances between them and compared. I got errors of 0%-15%.

15% error is way way too high.

Well, I don’t know, let’s get some help. Unfortunately, I wasn’t able to get this solution working using pyproj, and after some time spent I gave up on that direction. I decided to go back and try to reimplement closest-pair in a way that would work for Geodesic distances.

That worked!

To achieve that, I needed to replace all distance calculations with geodesic distance, and be able to go from a distance to latitude delta. Well, using the same calculation from before that is not too complicated. Also, we can have this support points with altitude without much effort/

Let’s write the function definition for closest-pair in a generic typed way:

def find_closest_pair(
        points: List[P],
        x_getter: Callable[[P], float],
        y_getter: Callable[[P], float],
        distance: Callable[[P, P], float],
        distance_to_x_delta: Callable[[float, P], float]) -> Tuple[P, P, float]:

    """Find the two points p1, p2 in points with the shortest distance between them
        points: a list of points from which we would like to find the closest pair
        x_getter: a function that returns the x coordinate of a point
        y_getter: a function that returns the y coordinate of a point
        distance: a function that returns the distance between two points
        distance_to_x_delta: a function that given a point and a distance, 
            returns the difference in the x coordinate to get a 
            new point that is the given distance away

            The pair of closest points and the distance between them

In Part 2 I will write about validating the distance between all edges.