computational-geometry

I am trying to find a point (P2) in a closed area that has the minimum distance to a point (P1). The area is built of homogenous pixels, it is not shaped perfectly and it is not necessarily convex. This is basically a problem of reaching an area from the shortest path. The whole space is a stored in the form of a bitmap in the memory. What is the best method to find P2? Should I go with random search (optimization) methods? Optimization methods do not give the exact minimum but they are faster than brute forcing every pixel of the area. I need to perform thousands of these decisions in a few

in the above image I have shown two rectangles rectangle 1 whose x can vary from -900 to 13700 and Y can vary from -600 to 6458 rectangle 2 whose coordinate X can vary from 0 to 3000 and y can vary from 0 to 2000 Also: rectangle 2 has its starting point at left top position(0,0) whereas rectangle 1 has starting point( width/2, height/2). What I need to do : to convert a point of rectangle 1 to point of rectangle 2 using scaling or translation. So, what should be scaling factor for x and y coordinates in order to transform the coordinate of rectangle 1 to rectangle 2 ? Matthew Watson If:

I have a set of close of 10,000 points on the sky. They are plotted using the RA (right ascension) and DEC (declination) on the sky. When plotted, they take the shape of a circle. What I would like to do is to slice the circle into 8 equal parts and remove each part one at a time and do some calculations using the remaining parts. To do so I came up with this illustration in mind, i.e. slicing them using the arcs. I know that the equation of the arc is given by: S = r * theta where r --> radius theta --> angle (in our case 45 degrees) I would somehow like to do this like: slice1 = [] for a,b

Well, approximating a circle with a polygon and Pythagoras' story may be well known. But what about the other way around? I have some polygons, that should be in fact circles. However, due to measurement errors they are not. So, what I'm looking for is the circle that best "approximates" the given polygon. In the following figure we can see two different examples. My first Ansatz was to find the maximum distance of the points to the center as well as the minimum. The circle we are looking for is maybe somewhere in between. Is there any algorithm out there for this problem? I would use scipy to

I want to create a large set of random point cloud in 2D plane that are non-degenerate (no 3 points in a straight line in the whole set). I have a naive solution which generates a random float pair P_new(x,y) and checks with every pair of points (P1, P2) generated till now if point (P1, P2, P) lie in same line or not. This takes O(n^2) checks for each new point added to the list making the whole complexity O(n^3) which is very slow if I want to generate more than 4000 points (takes more than 40 mins). Is there a faster way to generate these set of non-degenerate points? Instead of checking the