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Delaunay Triangulation 

SCIco
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Creating quality meshes is a task common in computer graphics and numerical analysis like finite element methods. Among many others, one technique of much importance is the Delaunay triangulation.
In this video, we try to introduce you to the Delaunay triangulation and its computation by the Bowyer-Watson algorithm. This video focuses more on the computational part. So, let's enjoy the video!

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31 июл 2024

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Комментарии : 47   
@HoaDucPham
@HoaDucPham 3 года назад
I understand it this way: for a given number of points, you draw a triangle whose circumference should cover all the points 1. You take your first point randomly, connect it to each vertex of the first triangle. 2. If a triangle contains a point within its circumference, then you delete that triangle by deleting an edge which connects the chosen point to the vertex of the first triangle. Otherwise, you keep the edge- and the point becomes the new vertex of a new polygon that we will do the same thing with the second point. 3. Keep doing that till you have the ultimate outer polygon that has vertices match the outer points and the tri-elements with vertices match the inner points. (*) easily see that we should take the initial points from the outer ones then work our way in.
@sanjanakomateswar8191
@sanjanakomateswar8191 2 года назад
Amazing video.Gave me a excellent understanding and visually explained.Thank you sooo much, it was difficult to gain this understanding as not much people have written or made of video about it so clearly.
@tanzeelhassan2934
@tanzeelhassan2934 3 года назад
Just wow, the video is awesome!
@dalskiBo
@dalskiBo 3 года назад
Lovely video, thanks SCIco.
@sajedehkebriti3548
@sajedehkebriti3548 3 года назад
Awesome! Just come with other movies! It was really intuitive
@dalskiBo
@dalskiBo 3 года назад
Brilliant video, thanks for sharing; concise intro & unusually dark music.
@Undead34
@Undead34 2 года назад
Thank you, i love this video
@mwprogrammer
@mwprogrammer 2 года назад
Thanks for low key saving my exam.
@bln3615
@bln3615 3 года назад
Thank you, if you could do one also on building weighted diagrams that would be great.
@ian.ambrose
@ian.ambrose Год назад
Beautiful video.
@SecondThread
@SecondThread 4 года назад
How do we know that any edges in the 'Super Triangle" aren't relevant? It is possible for there to be some edges on the super triangle that connect to points not on the convex hull of the set of interest, isn't it?
@leonardoherfianto897
@leonardoherfianto897 4 года назад
Contruct the Super Triangle 1. find the centeroid from all points 2. create an axis heading to 3 angle (90, 210, 300) degree 3. find all max projection axis for all points that align to our 3 axis (use dot product) and scale it to 1,5 or bigger; 4. the step 3 will result 3 max projection point. 5. find intersection point of all 3 max projection point. 6. the intersection point is your super triangle.
@nataliazhang4309
@nataliazhang4309 2 года назад
Thanks! Nice video!
@muhammadbilalshahid8010
@muhammadbilalshahid8010 2 года назад
Awesome, Thanks.
@AlhambraDream
@AlhambraDream 3 года назад
this is awesome
@amolsamota9104
@amolsamota9104 3 года назад
Great work
@louise1021
@louise1021 Год назад
Amazing!!!
@seunghunlee2598
@seunghunlee2598 4 года назад
Hi! your video help to me, but I can't understand what is the standard for find new circumcircle (02:00)
@ricardopieper11
@ricardopieper11 4 года назад
If you mean "how to find the circumcircle", wikipedia has the answer en.wikipedia.org/wiki/Circumscribed_circle (Circumcenter coordinates, cartesian coordinates)
@ricardopieper11
@ricardopieper11 4 года назад
You can use it like I do here: editor.p5js.org/ricardopieper/sketches/M2lEVxA64 look at the circumscribedCircle function. This code actually has all the pieces you need to implement the algorithm in the video, together with relevant wikipedia sources.
@jamesj2869
@jamesj2869 3 года назад
Ricardo Pieper have you seen Fade2D code (in case) it is in C++. I want to ask some question if in case someone used it
@NeZversSounds
@NeZversSounds Год назад
From this presentation, which looks awesome, I gather that for this to work, the points need to be more or less evenly spaced, not truly random. I don't see how it could work with points that are forming clusters, it looks like they will be in circles of cluster's outside vertices.
@robotlegs
@robotlegs 7 месяцев назад
It actually works better when they're random because you're less likely to encounter infinite-radius circles (i.e. 3 colinear points). As long as your super-triangle encloses all your points, the algorithm will find all of them.
@stynod7422
@stynod7422 2 года назад
How do you know where to put the vertices of the super triangle??
@delicate6930
@delicate6930 2 года назад
i just put the vericies at a number i knew was outside my domain
@supergreatoli2
@supergreatoli2 2 года назад
I made a square containing all my points and then drew the equilateral triangle which circumscribes the square
@msssivadas10
@msssivadas10 4 года назад
Voronoi diagrams can be computed using the same methods of finding Delaunay triangulation.
@manuarteteco6153
@manuarteteco6153 3 года назад
seriously? That is helpful, even tough I can't really see how right now
@VADroidTS555
@VADroidTS555 3 года назад
@@manuarteteco6153 They share duality.
@temesegenabuhay9408
@temesegenabuhay9408 3 года назад
is there any rule to draw the circumcircle for the triangle... Mr
@Alkis05
@Alkis05 3 года назад
The only rule is for the circle to contain at least one vertex.
@Rajgrv100
@Rajgrv100 2 года назад
Bro can you do a video about Frontal advancement method? I'm a mallu too :-) , nice video.
@husseinjafarinia224
@husseinjafarinia224 2 года назад
I think Joker's gonna attack in the end
@user-zk1hp1wp3s
@user-zk1hp1wp3s 3 года назад
Scary sounds
@roman_roman_roman
@roman_roman_roman 3 года назад
Why music is so scary?...
@jamesj2869
@jamesj2869 3 года назад
code: geom.at (Fade2D code)
@subject2749
@subject2749 Год назад
great video odd music choice though
@paradigmnnf
@paradigmnnf Год назад
And what is the idea of this background music?
@sk-7523
@sk-7523 3 года назад
Great video, but why so scary music?
@AmanGupta-wb2xh
@AmanGupta-wb2xh 3 года назад
code ?
@jamesj2869
@jamesj2869 3 года назад
The name is Fade2D
@lovegarbage
@lovegarbage 2 года назад
The music added nothing apart from distraction. Why did you feel you had to do that?
@TauranusRex
@TauranusRex 2 года назад
The music is way too dramatic :D
@achibaba
@achibaba 3 года назад
very bad explanation, waste of time. sorry
@TheBeansChopper
@TheBeansChopper 2 года назад
Stop the music, maybe talk instead ... also why stretch the video with unnecessary text
@gandoreme
@gandoreme 3 года назад
very poor selection of music.
@fkeyvan
@fkeyvan 3 года назад
Annoying music
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