It should be that way however it is not possible in this example to make it. Try drawing it on paper. It you find a solution, do share it.

There are perpendicular segments, they just don’t intersect the original segments

I got only one.

Depends on the algorithm

+John Smith Hi. Let me explain for the left side, and for the right side you use the same principle. Well what i did was to make new lines that connect my base with the points. So first lets do a quick naming convention. For the base line S2S7 lets name it b1. Now watch the video to the point where the pink lines appear. The pink lines represent the lines that connects the point S2 and the potencial candidates. So as you can see, we have S2S4, S2S5 and S2S3. Lets name them p1, p2 and p3. I could have connected the point S2 with S1 too, but in this example i made all my lines so that the angle between the lines p and base b1 is around 90 degrees. The criteria says the points need to be less than 180 degrees, however in this example i made it so that the angle of around 90 degrees is a valid subcriteria. However when facing unknown sets of points, we always need to consider the 2 criteria for picking the candidate. 1. the angle between 2 lines (b1 and any p) needs to be less than 180 degrees. 2. when placing a circumcircle around the points, there can not be any points in the circle which represent potencial candidates. Now then, by comparing the angles between b1 and p1, b1 and p2 and b1 and p3, we get the result that the smallest angle is made by b1 and p1. Now we draw a circumcircle around the points to check if any other potencial candidates are inside the circumcircle. Since there are none, because of fulfilling both prior given criteria, we pick point S4 as the candidate and do the triangulation. Hope the explanation is undestandable and helpful.

+Dušan Cvejić Hi, thanks for the explanation. Were you using the formula cos(theta) = dotproduct(v,u) / (magnitude(v) * magnitude(u)) or some other formula for calculating the angle? I was always getting angles less than 180 degrees which resulted in edges intersecting with other edges

+John Smith Unecessary edges, I should say, intersecting with other edges

+John Smith The same formula is usable for this example and you should get almost always that all the angles are less than 180. After obtaining information on all angles, than you need to sort them. By doing so you get a list min to max or max to min, dependable on your sort, and by picking the smallest angle you check if the circumcircle around the base and the chosen candidate contains any other potencial candidates inside. If you are trying to implement in code, i think the simple if else function could work for this.

+Dušan Cvejić Do you ignore points that are already connected to both endpoints, or do you still compare them with other potentials

Only the one in the description. Does it not work?

I didnt do a code for this. Only an explanation of how it works. You can find the paper here: www.scribd.com/document/340837645/Delaunay-Triangulacija-u-Ravni-Rekurzivni-Algoritam

It is a speed up proces. The same principle applies as for the left egde

You can find my paper of detailed explanation on how this works on this link: www.scribd.com/document/340837645/Delaunay-Triangulacija-u-Ravni-Rekurzivni-Algoritam However you are going to need to translate it first, because it is written in Sebian.

Dušan Cvejić thank you very much 👍🏼

@@kiki23s_DKC Is the source code available. Please share if you have.

@@brooks7845 I don´t have the source code, however an explanation on how it works is given is in the paper given in the video description