intersection

I'm trying to find the point of intersection between a sphere and a line but honestly, I don't have any idea of how to do so. Could anyone help me on this one ? Express the line as an function of t : { x(t) = x0*(1-t) + t*x1 { y(t) = y0*(1-t) + t*y1 { z(t) = z0*(1-t) + t*z1 When t = 0 , it will be at one end-point (x0,y0,z0) . When t = 1 , it will be at the other end-point (x1,y1,z1) . Write a formula for the distance to the center of the sphere (squared) in t (where (xc,yc,zc) is the center of the sphere): f(t) = (x(t) - xc)^2 + (y(t) - yc)^2 + (z(t) - zc)^2 Solve for t when f(t) equals R^2 (

I have a dataset of ca. 9K lists of variable length (1 to 100K elements). I need to calculate the length of the intersection of all possible 2-list combinations in this dataset. Note that elements in each list are unique so they can be stored as sets in python. What is the most efficient way to perform this in python? Edit I forgot to specify that I need to have the ability to match the intersection values to the corresponding pair of lists. Thanks everybody for the prompt response and apologies for the confusion! If your sets are stored in s, for example: s = [set([1, 2]), set([1, 3]), set([1

Starting from a shapefile containing a fairly large number (about 20000) of potentially partially-overlapping polygons, I'd need to extract all the sub-polygons originated by intersecting their different "boundaries". In practice, starting from some mock-up data: library(tibble) library(dplyr) library(sf) ncircles <- 9 rmax <- 120 x_limits <- c(-70,70) y_limits <- c(-30,30) set.seed(100) xy <- data.frame( id = paste0("id_", 1:ncircles), x = runif(ncircles, min(x_limits), max(x_limits)), y = runif(ncircles, min(y_limits), max(y_limits))) %>% as_tibble() polys <- st_as_sf(xy, coords = c(2,3)) %>

I have a large number of user IDs (integers), potentially millions. These users all belong to various groups (sets of integers), such that there are on the order of 10 million groups. To simplify my example and get to the essence of it, let's assume that all groups contain 20 user IDs. I want to find all pairs of integer sets that have an intersection of 15 or greater. Should I compare every pair of sets? (If I keep a data structure that maps userIDs to set membership, this would not be necessary.) What is the quickest way to do this? That is, what should my underlying data structure be for

I am writing a program that allows a user to paint rectangles onto a JLabel , and show the intersection and union of these rectangles. I have setup the GUI for the class but am struggling to find a way to integrate the intersection and union methods from the rectangle class. I know these methods work when used separately from the GUI. When I try to run the program I keep getting an IndexOutOfBoundsException and the drawn rectangles are cleared from the gui. The intersections of each rectangle should show up in a different color on the JLabel . I tried to debug the program and for some reason

This question already has an answer here: Python -Intersection of multiple lists? 4 answers def query_RR(postings, qtext): words = tokenize(qtext) allpostings = [postings[w] for w in words] for a in allpostings: print a.keys() And this was the result of the query [0, 2, 3, 4, 6] [1, 4, 5] [0, 2, 4] [4, 5] The query is taking a user inputted term ('qtext'), tokenizing and generating a postings list for each token. The posting list is a list of nested dictionaries (e.g. [{0 : 0.68426, 1: 0.26423}, {2: 0.6842332, 0: 0.9823}]. I am attempting to find the intersection for these nested dictionaries

I'm having an issue showing that one rectangle has collided with another. So my question is, how can I get the intersect method to check for collision? Or are there any other ways to handle collision in this situation? I'm creating a turn-based combat game (similar to Final Fantasy or Legend of Dragoon) where the player's character is on the right side of the screen and the enemy is on the left side. The player and enemy each take turns attacking. So when the player attacks, the sprite animation moves across the screen from right to left until it stops in front of the enemy, attacks, and