Quickhull 3D Explained - algorithm

I'm trying to understand how quickhull works in 3D. I already understand how the algorithm works in 2D but I just don't get how the algorithm can be implemented in 3D space. Are there any tutorials or papers that can help me?

Related

Genetic algorithm for Linear Intersections problem or Overlay of Subdivisions problem

I was suggested to create a GA algorithm to solve the problem of linear intersections identification in 2d space. I have been thinking to modify the sweep line algorithm or a similar one (like Bentley Ottman) and create a GA algorithm.
I have been studying the literature and i also came accross "Overlay of Subdivisions" problem which is quite similar, but for multiple layers of data. Not a lot information on that problem and i am struggling to understand the algorithm.
I am now thinking that in the first case a GA optimization is impossible but maybe it is possible for the overlay of subdivisions problem.
Anyone with more experience thinks that this will work or am i looking for the impossible?

How does the rotational plane sweep algorithm work?

I have the task to implement the creation of a visibility graph based on a set of simple polygons which are given by the task. The polygons have positive whole number coordinates and can be non-convex. I wanted to implement the rotational plane sweep algorithm which was mentioned in the lecture but not very well explained.
The only other source I could find about this algorithm was this page, that did not make it fully clear either: https://tanergungor.blogspot.com/2015/04/robot-navigation-rotational-sweep.html
I would appreciate it if someone could explain the rotational plane sweep algorithm to an extent which I can understand.
Here is a screenshot of an example obstacle arrangement with my attempt at a solution which is not yet working and more or less based on trial and error rather than understanding and implementing the actual algorithm. The algorithm is just using a single vertex which is not located on a polygon in this example.

Convex Mixed-Integer for Non-Rigid Point Cloud Alignment

I am trying to approach non-rigid alignment using Convex Mixed-Integer Algorithm, but I am new to computer vision. Does anyone know some sample code that is similar - so that I can use that as a reference?
The algorithm is based on this research paper:
MINA: Convex Mixed-Integer Programming for Non-Rigid Shape Alignment
Thank you for showing interest in our work.
We model the constrained optimization problem in MATLAB with the help of YALMIP library and solve it using MOSEK.

Akl-Toussaint throw-away heuristic for convex hull in 3D

I am wondering whether there are any algorithms that use the Akl-Toussaint throw-away heuristic to compute the convex hull in 3D (not just as a simple pre-processing, but as the algorithmic principle or building block). And if so, what would their expected time complexity be?
Also, I am interested in experimental comparisons of such algorithms with the more traditional algorithms in 3D (e.g., Clarkson-Shor).
I would appreciate it very much if you could point me to papers or web pages that shed some light on my questions. (Or answer them directly :-) )

Best nesting algorithm

I have spent time looking for information on the best algorithm to create a nesting of irregular polygons in 2D using manual and automatic positioning. I need to use such an algorithm in the context of CAD/CAM software. Here are the real possibilities I've found so far:
Separating Axis Theorem: is a fairly quick and simple algorithm to implement, but the drawback I find with it is that it only works with convex polygons. To work with concave polygons, a convex decomposition would need to be done first. This implies an increase in the run-time and the implementation of a new algorithm that decomposes the concave polygon into convex polygons.
Nesting by a power function: calculating the partial derivatives in the X and Y axes, you could get the escape direction you should take a polygon so that there is a collision between the two polygons. This function of energy and I tested and the three major problems that I have encountered are: first obtaining local minima , second nesting when the collision occurs over a piece and finally the execution time is very high.
Using no-fit polygon: use the no-fit polygon to the nesting can be somewhat interesting. I have read several papers on the subject although there are very few online documentation on it. Not sure if it can really be a useful choice. I still have several doubts on the details of this approach.
Any idea which of these algorithms to choose? Or if you know any other options that can be used? I'm a little confused :-) .
Thank you very much.

Resources